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{{For|other features called ridges see|Ridge (disambiguation)}}
{{FeatureDetectionCompVisNavbox}}
{{Technical|date=September 2012}}
 
The attempt (via software) to locate ridges (or edges) in an image.
 
In [[mathematic]]s and [[computer vision]], the '''ridges''' (or the '''ridge set''') of a [[smooth function]] of two variables are a set of curves whose points are, in one or more ways to be made precise below, [[local maxima]] of the function in at least one dimension.  This notion captures the intuition of geographical [[ridge]]s.  For a function of <math>N</math> variables,  its ridges are a set of curves whose points are local maxima in <math>N-1</math> dimensions.  In this respect, the notion of ridge points extends the concept of a [[maxima and minima|local maximum]]. Correspondingly, the notion of '''valleys''' for a function can be defined by replacing the condition of a local maximum with the condition of a [[local minimum]].  The union of ridge sets and valley sets, together with a related set of points called the '''connector set''' form a connected set of curves that partition, intersect, or meet at the critical points of the function.  This union of sets together is called the function's '''relative critical set'''.<ref name=Damon99>{{cite journal |author=Damon, J. |title=Properties of Ridges and Cores in Two-Dimensional Images |journal=J Math Imaging Vis |volume=10 |issue=2 |doi=10.1023/A:1008379107611 |url=http://www.springerlink.com/content/l6564431145n1880/ |pages=163–174 |date=March 1999 }}</ref><ref name=Miller98>Miller, J. ''Relative Critical Sets in <math>\mathbb{R}^n</math> and Applications to Image Analysis.'' Ph.D. Dissertation.  University of North Carolina.  1998.</ref>
 
Ridge sets, valley sets, and relative critical sets represent important geometric information intrinsic to a function.  In a way, they provide a compact representation of important features of the function, but the extent to which they can be used to determine global features of the function is an open question. The primary motivation for the creation of  '''ridge detection''' and '''valley detection''' procedures has come from  [[image analysis]] and [[computer vision]] and is to capture the interior of elongated objects in the image domain. Ridge-related representations in terms of [[Watershed (algorithm)|watershed]]s have been used for [[image segmentation]]. There have also been attempts to capture the shapes of objects by graph-based representations that reflect ridges, valleys and critical points in the image domain. Such representations may, however, be highly noise sensitive if computed at a single scale only.  Because scale-space theoretic computations involve convolution with the Gaussian (smoothing) kernel, it has been hoped that use of multi-scale ridges, valleys and critical points in the context of [[scale space]] theory should allow for more a robust representation of objects (or shapes) in the image.
 
In this respect, ridges and valleys can be seen as a complement to natural [[interest point detection|interest points]] or local extremal points. With appropriately defined concepts, ridges and valleys in the [[intensity landscape]] (or in some other representation derived from the intensity landscape) may form a [[scale invariant]] [[topological skeleton|skeleton]] for organizing spatial constraints on local appearance, with a number of qualitative similarities to the way the Blum's [[medial axis|medial axis transform]] provides a [[shape skeleton]] for [[binary image]]s.  In typical applications, ridge and valley descriptors are often used for detecting roads in [[aerial image]]s and for detecting [[blood vessel]]s in [[retinal image]]s or three-dimensional [[magnetic resonance imaging|magnetic resonance images]].
 
== Differential geometric definition of ridges and valleys at a fixed scale in a two-dimensional image ==
 
Let <math>f(x, y)</math> denote a two-dimensional function, and let <math>L</math> be the [[scale space|scale-space representation]] of <math>f(x, y)</math> obtained by convolving <math>f(x, y)</math> with a Gaussian function
:<math>g(x, y, t) = \frac{1}{2 \pi t} e^{-(x^2+y^2)/2t}</math>.
Furthermore, let  <math>L_{pp}</math> and <math>L_{qq}</math> denote the [[eigenvalue]]s of the [[Hessian matrix]]
:<math>H = \begin{bmatrix}
L_{xx} & L_{xy} \\ 
L_{xy} & L_{yy}
\end{bmatrix}</math>
of the [[scale space|scale-space representation]] <math>L</math>. With a coordinate transformation (a rotation) applied to local directional derivative operators,
:<math>\partial_p = \sin \beta \partial_x - \cos \beta \partial_y, \partial_q = \cos \beta \partial_x + \sin \beta \partial_y </math>
where p and q are coordinates of the rotated coordinate system.
 
It can be shown that the mixed derivative <math>L_{pq}</math> in the transformed coordinate system is zero if we choose
:<math>\cos \beta = \sqrt{\frac{1}{2} \left( 1 + \frac{L_{xx}-L_{yy}}{\sqrt{(L_{xx}-L_{yy})^2 + 4 L_{xy}^2}} \right)}</math>,<math> \sin \beta = \sgn(Lxy) \sqrt{\frac{1}{2} \left( 1 - \frac{L_{xx}-L_{yy}}{\sqrt{(L_{xx}-L_{yy})^2 + 4 L_{xy}^2}} \right)} </math>.
Then, a formal differential geometric definition of the ridges of <math>f(x, y)</math> at a fixed scale <math>t</math> can be expressed as the set of points that satisfy
<ref>{{cite journal
| author=T. Lindeberg
| title=Scale-space
| journal=Encyclopedia of Computer Science and Engineering (Benjamin Wah, ed), John Wiley and Sons
| volume = IV
| pages = 2495–2504
| year = 2008/2009
| doi=10.1002/9780470050118.ecse609
| url = http://www.nada.kth.se/~tony/abstracts/Lin08-EncCompSci.html
}}</ref>
:<math>L_{p} = 0, L_{pp} \leq 0, |L_{pp}| \geq |L_{qq}|.</math>
Correspondingly, the valleys of <math>f(x, y)</math> at scale <math>t</math> are the set of points
:<math>L_{q} = 0, L_{qq} \geq 0, |L_{qq}| \geq |L_{pp}|.</math>
In terms of a <math>(u, v)</math> coordinate system with the <math>v</math> direction parallel to the image gradient
:<math>\partial_u = \sin \alpha \partial_x - \cos \alpha \partial_y, \partial_v = \cos \alpha \partial_x + \sin \alpha \partial_y </math>
where
:<math>\cos \alpha = \frac{L_x}{\sqrt{L_x^2 + L_y^2}},  \sin \alpha = \frac{L_y}{\sqrt{L_x^2 + L_y^2}} </math>
it can be shown that this ridge and valley definition can instead be equivalently<ref>{{cite journal |author=Lindeberg, T |title=Scale-space theory: A basic tool for analysing structures at different scales |journal=J. of Applied Statistics |volume=21 |issue=2 |pages=224–270 |year=1994 |url=http://www.nada.kth.se/~tony/abstracts/Lin94-SI-abstract.html}}</ref>  be written as
:<math> L_{uv} = 0, L_{uu}^2 - L_{vv}^2 \geq 0 </math>
where
:<math>L_v^2 L_{uu} = L_x^2 L_{yy} - 2 L_x L_y L_{xy} + L_y^2 L_{xx},</math>
:<math>L_v^2 L_{uv} = L_x L_y (L_{xx} - L_{yy})  - (L_x^2 - L_y^2) L_{xy}, </math>
:<math>L_v^2 L_{vv} = L_x^2 L_{xx} + 2 L_x L_y L_{xy} + L_y^2 L_{yy} </math>
and the sign of <math>L_{uu}</math> determines the polarity; <math>L_{uu}<0</math> for ridges and <math>L_{uu}>0</math> for  valleys.
 
== Computation of variable scale ridges from two-dimensional images ==
 
A main problem with the fixed scale ridge definition presented above is that it can be very sensitive to the choice of the scale level. Experiments show that the scale parameter of the Gaussian pre-smoothing kernel must be carefully tuned to the width of the ridge structure in the image domain, in order for the ridge detector to produce a connected curve reflecting the underlying image structures. To handle this problem in the absence of prior information, the notion of ''scale-space ridges'' has been introduced, which treats the scale parameter as an inherent property of the ridge definition and allows the scale levels to vary along a scale-space ridge. Moreover, the concept of a scale-space ridge also allows the scale parameter to be automatically tuned to the width of the ridge structures in the image domain, in fact as a consequence of a well-stated definition. In the literature, a number of different approaches have been proposed based on this idea.
 
Let <math>R(x, y, t)</math> denote a measure of ridge strength (to be specified below). Then, for a two-dimensional image, a scale-space ridge is the set of points that satisfy
:<math>L_{p} = 0, L_{pp} \leq 0, \partial_t(R) = 0,  \partial_{tt}(R) \leq 0,</math>
where <math>t</math> is the scale parameter in the [[scale space|scale-space representation]]. Similarly, a ''scale-space valley'' is the set of points that satisfy
:<math>L_{q} = 0, L_{qq} \geq 0, \partial_t(R) = 0,  \partial_{tt}(R) \leq 0.</math>
An immediate consequence of this definition is that for a two-dimensional image the concept of scale-space ridges sweeps out a set of one-dimensional curves in the three-dimensional scale-space, where the scale parameter is allowed to vary along the scale-space ridge (or the scale-space valley). The ridge descriptor in the image domain will then be a projection of this three-dimensional curve into the two-dimensional image plane,  where the attribute scale information at every ridge point can be used as a natural estimate of the width of the ridge structure in the image domain in a neighbourhood of that point.
 
In the literature, various measures of ridge strength have been proposed. When Lindeberg (1996, 1998)<ref>{{cite journal |doi=10.1023/A:1008097225773 |author=Lindeberg, T. |title=Edge detection and ridge detection with automatic scale selection |journal=International Journal of Computer Vision |volume=30 |issue=2 |pages=117–154 |year=1998 |url=http://www.nada.kth.se/cvap/abstracts/cvap191.html}} Earlier version presented at IEEE Conference on Pattern Recognition and Computer Vision, CVPR'96, San Francisco, California, pages 465–470, june 1996</ref> coined the term scale-space ridge, he considered three measures of ridge strength:
<ul>
<li>
The main principal curvature
:<math>L_{pp, \gamma-norm} = \frac{t^{\gamma}}{2} \left( L_{xx}+L_{yy} - \sqrt{(L_{xx}-L_{yy})^2 + 4 L_{xy}^2} \right)</math>
expressed in terms of ''<math>\gamma</math>-normalized derivatives'' with
:<math>\partial_{\xi} = t^{\gamma/2} \partial_x, \partial_{\eta} = t^{\gamma/2} \partial_y</math>.
<li>
The square of the <math>\gamma</math>-normalized square eigenvalue difference
:<math>N_{\gamma-norm} = \left( L_{pp, \gamma-norm}^2 - L_{qq, \gamma-norm}^2 \right)^2 = t^{4 \gamma} (L_{xx}+L_{yy})^2 \left( (L_{xx}-L_{yy})^2 + 4 L_{xy}^2 \right). </math>
<li>
The square of the <math>\gamma</math>-normalized eigenvalue difference
:<math>A_{\gamma-norm} = \left( L_{pp, \gamma-norm} - L_{qq, \gamma-norm} \right)^2 = t^{2 \gamma} \left( (L_{xx}-L_{yy})^2 + 4 L_{xy}^2 \right). </math>
</ul>
The notion of <math>\gamma</math>-normalized derivatives is essential here, since it allows the ridge and valley detector algorithms to be calibrated properly. By requiring that for a one-dimensional Gaussian ridge embedded in two (or three dimensions) the detection scale should be equal to the width of the ridge structure when measured in units of length (a requirement of a match between the size of the detection filter and the image structure it responds to), it follows that one should choose <math>\gamma = 3/4</math>. Out of these three measures of ridge strength, the first entity <math>L_{pp, \gamma-norm}</math> is a general purpose ridge strength measure with many applications such as blood vessel detection and road extraction. Nevertheless, the entity <math>A_{\gamma-norm}</math> has been used in applications such as fingerprint enhancement,<ref>{{cite journal |author=Almansa, A., Lindeberg, T. |title=Fingerprint Enhancement by Shape Adaptation of Scale-Space Operators with Automatic Scale-Selection |journal=IEEE Transactions on Image Processing |volume=9 |issue=12 |pages=2027–42 |year=2000 |url=http://www.nada.kth.se/cvap/abstracts/cvap226.html |pmid=18262941 |doi=10.1109/83.887971}}</ref> real-time hand tracking and gesture recognition<ref>[http://www.nada.kth.se/cvap/abstracts/BreLapLin-FG02.html L. Bretzner, I. Laptev and T. Lindeberg: Hand Gesture Recognition using Multi-Scale Colour Features, Hierarchical Models and Particle Filtering, Proc. IEEE Conference on Face and Gesture 2002, Washington DC, 423–428.]</ref> as well as for modelling local image statistics for detecting and tracking humans in images and video.<ref>{{cite journal |author=Sidenbladh, H., Black, M. |title=Learning the statistics of people in images and video |journal=International Journal of Computer Vision |volume=54 |issue=1–2 |pages=183–209 |year=2003 |url=http://www.csc.kth.se/~hedvig/publications/ijcv_03.pdf |format=PDF}}</ref>
 
There are also other closely related ridge definitions that make use of normalized derivatives with the implicit assumption of <math>\gamma = 1</math>.<ref>J. Furst and  J. Miller, "The Maximal Scale Ridge:  Incorporating Scale in the Ridge Definition", ''Scale Space Theory in Computer Vision: Proceedings of the First International Conference on, Scale Space '97,'' pp. 93–104.  Springer Lecture Notes in Computer Science, vol. 1682.</ref> ''Develop these approaches in further detail.'' When detecting ridges with <math>\gamma = 1</math>, however, the detection scale will be twice as large as for <math>\gamma = 3/4</math>, resulting in more shape distortions and a lower ability to capture ridges and valleys with nearby interfering image structures in the image domain.
 
== History ==
 
The notion of ridges and valleys in digital images was introduced by [[Haralick]] in 1983<ref>{{cite journal |doi=10.1016/0734-189X(83)90094-4 |author=Haralick, R. |title=Ridges and Valleys on Digital Images |journal=Computer Vision, Graphics, and Image Processing  |volume=22 |issue=10 |pages=28–38 |date=April 1983 }}</ref> and by Crowley concerning [[difference of Gaussians]] [[pyramid (image processing)|pyramid]]s in 1984.<ref>{{cite journal |doi=10.1109/TPAMI.1984.4767500 |author=Crowley, J.L., Parker, A.C. |title=A Representation for Shape Based on Peaks and Ridges in the Difference of Low Pass Transform |journal=IEEE Trans Pattern Anal Mach Intell |volume=6 |issue=2 |pages=156–170 |date=March 1984 |url=http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-Parker84.pdf |format=PDF |pmid=21869180}}</ref><ref>{{cite journal |doi=10.1109/TPAMI.1987.4767876 |author=Crowley, J.L., Sanderson, A. |title=Multiple Resolution Representation and Probabilistic Matching of 2-D Gray-Scale Shape |journal=IEEE Trans Pattern Anal Mach Intell |volume=9 |issue=1 |pages=113–121 |date=January 1987 |url=http://www-prima.inrialpes.fr/Prima/Homepages/jlc/papers/Crowley-Sanderson-PAMI87.pdf |format=PDF}}</ref> The application of ridge descriptors to medical image analysis has been extensively studied by Pizer and his co-workers<ref>{{cite journal |doi=10.1109/34.216734 |author=Gauch, J.M., Pizer, S.M. |title=Multiresolution Analysis of Ridges and Valleys in Grey-Scale Images |journal=IEEE Trans Pattern Anal Mach Intell |volume=15 |issue=6 |pages=635–646 |date=June 1993 }}</ref><ref>{{cite journal |doi=10.1007/BF01262402 |author=Eberly D., Gardner R., Morse B., Pizer S., Scharlach C. |title=Ridges for image analysis |journal=Journal of Mathematical Imaging and Vision |volume=4 |issue=4 |pages=353–373 |date=December 1994 }}</ref><ref>{{cite journal |doi=10.1006/cviu.1997.0563 |author=Pizer, Stephen  M., Eberly, David, Fritsch, Daniel S. |title=Zoom-invariant vision of figural shape: the mathematics of cores |journal=Computer Vision and Image Understanding |volume=69 |issue=1 |pages=55–71 |date=January 1998 }}</ref> resulting in their notion of M-reps.<ref>[http://citeseer.ist.psu.edu/pizer01segmentation.html S. Pizer, S. Joshi, T. Fletcher, M. Styner, G. Tracton, J. Chen (2001) "Segmentation of Single-Figure Objects by Deformable M-reps", Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer Lecture Notes In Computer Science; Vol. 2208, pp. 862–871]</ref> Ridge detection has also been furthered by Lindeberg with the introduction of <math>\gamma</math>-normalized derivatives and scale-space ridges defined from local maximization of the appropriately normalized main principal curvature of the Hessian matrix (or other measures of ridge strength) over space and over scale. These notions have later been developed with application to road extraction by Steger et al.<ref>{{cite journal |author=Steger C. |title=An unbiased detector of curvilinear structures |journal=IEEE Trans Pattern Anal Mach Intell |volume=20 |issue=2 |pages=113–125 |year=1998 |doi=10.1109/34.659930 |url=http://csdl2.computer.org/persagen/DLAbsToc.jsp?resourcePath=/dl/trans/tp/&toc=comp/trans/tp/1998/02/i2toc.xml&DOI=10.1109/34.659930}}</ref><ref>{{cite journal |doi=10.1007/s001380050121 |author=Laptev I., Mayer H., Lindeberg T., Eckstein W., Steger C., Baumgartner A. |title=Automatic extraction of roads from aerial images based on scale-space and snakes |journal=Machine Vision and Applications |volume=12 |issue=1 |pages=23 |year=2000 |url=http://www.irisa.fr/vista/Papers/2000_mva_laptev.pdf |format=PDF}}</ref> and to blood vessel segmentation by Frangi et al.<ref>{{cite journal |author=Frangi AF, Niessen WJ, Hoogeveen RM, van Walsum T, Viergever MA |title=Model-based quantitation of 3-D magnetic resonance angiographic images |journal=IEEE Trans Med Imaging |volume=18 |issue=10 |pages=946–56 |date=October 1999 |pmid=10628954 |doi=10.1109/42.811279 }}</ref> as well as to the detection of curvilinear and tubular structures by Sato et al.<ref>{{cite journal |author=Sato Y, Nakajima S, Shiraga N, Atsumi H, Yoshida S, ''et al'' |title=Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images |journal=Medical Image Analysis |volume=2 |issue=2 |pages=143–168 |year=1998 |url=http://www.image.med.osaka-u.ac.jp/member/yoshi/paper/linefilter.pdf}}</ref> and Krissian et al.<ref>{{cite journal |doi=10.1006/cviu.2000.0866 |author=Krissian K., Malandain G., Ayache N., Vaillan R., Trousset Y. |title=Model-based detection of tubular structures in 3D images |journal=Computer Vision and Image Understanding |volume=80 |issue=2 |pages=130–171 |year=2000 |url=http://portal.acm.org/citation.cfm?id=363419.363423}}</ref> A review of several of the classical ridge definitions at a fixed scale including relations between them has been given by Koenderink and van Doorn.<ref>{{cite journal |doi=10.1016/0167-8655(94)90134-1 |author=Koenderink, Jan J., van Doorn, Andrea J. |title=2+1-D differential geometry |journal=Pattern. Recognition Letters |volume=15 |pages=439–443 |date=May 1994 }}</ref> A review of vessel extraction techniques has been presented by Kirbas and Quek.<ref>{{cite journal |doi=10.1145/1031120.1031121 |author=Kirbas C, Quek F |title=A review of vessel extraction techniques and algorithms |journal=ACM Computing Surveys |volume=36 |issue=2 |pages=81–121 |year=2004 |url=ftp://cmp.felk.cvut.cz/pub/cmp/articles/matas/ps/Curvilinear/blood-vessel_review.pdf |format=PDF}}</ref>
==Definition of ridges and valleys in N dimensions==
 
In its broadest sense, the notion of ridge generalizes the idea of a local maximum of a real-valued function.  A point <math>\mathbf{x}_0</math> in the domain of a function <math>f:\mathbb{R}^n \rightarrow \mathbb{R}</math>is a local maximum of the function if there is a distance <math>\delta>0</math> with the property that if <math>\mathbf{x}</math> is within <math>\delta</math> units of <math>\mathbf{x}_0</math>, then <math>f(\mathbf{x}) < f(\mathbf{x}_0)</math>.  It is well known that critical points, of which local maxima are just one type, are isolated points in a function's domain in all but the most unusual situations (''i.e.'', the nongeneric cases).
 
Consider relaxing the condition that <math>f(\mathbf{x}) < f(\mathbf{x}_0)</math> for <math>\mathbf{x}</math> in an entire neighborhood of <math>\mathbf{x}_0</math> slightly to require only that this hold on an <math>n-1</math> dimensional subset.  Presumably this relaxation allows the set of points which satisfy the criteria, which we will call the ridge, to have a single degree of freedom, at least in the generic case.  This means that the set of ridge points will form a 1-dimensional locus, or a ridge curve.  Notice that the above can be modified to generalize the idea to local minima and result in what might call 1-dimensional valley curves.
 
This following ridge definition follows the book by Eberly<ref>{{cite book |author=Eberly, D. |title=Ridges in Image and Data Analysis |publisher=Kluwer |year=1996 |isbn=0-7923-4268-2 }}</ref> and can be seen as a generalization of some of the abovementioned ridge definitions. Let <math>U \subset \mathbb{R}^n</math> be an open set, and <math>f:U \rightarrow \mathbb{R}</math> be smooth.  Let <math>\mathbf{x}_0 \in U</math>.  Let <math>\nabla_{\mathbf{x}_0}f</math> be the gradient of <math>f</math> at <math>\mathbf{x}_0</math>, and let <math>H_{\mathbf{x}_0}(f)</math> be the <math>n \times n</math> Hessian matrix of <math>f</math>at <math>\mathbf{x}_0</math>.  Let  <math>\lambda_1 \leq \lambda_2 \leq \cdots \leq \lambda_n</math> be the <math>n</math> ordered eigenvalues of <math>H_{\mathbf{x}_0}(f)</math> and let <math>\mathbf{e}_i</math> be a unit eigenvector in the eigenspace for <math>\lambda_i</math>. (For this, one should assume that all the eigenvalues are distinct.)
 
The point <math>\mathbf{x}_0</math> is a point on the 1-dimensional ridge of <math>f</math> if the following conditions hold:
<ol>
<li><math>\lambda_{n-1}<0</math>, and
<li><math>\nabla_{\mathbf{x}_0} f \cdot \mathbf{e}_i=0</math> for <math>i=1, 2, \ldots, n-1</math>.
</ol>
This makes precise the concept that <math>f</math> restricted to ''this particular'' <math>n-1</math>-dimensional subspace has a local maxima at <math>\mathbf{x}_0</math>.
 
This definition naturally generalizes to the ''k''-dimensional ridge as follows:  the point <math>\mathbf{x}_0</math> is a point on the ''k''-dimensional ridge of <math>f</math> if the following conditions hold:
<ol>
<li><math>\lambda_{n-k}<0</math>, and
<li><math>\nabla_{\mathbf{x}_0} f \cdot \mathbf{e}_i=0</math> for <math>i=1, 2, \ldots, n-k</math>.
</ol>
 
In many ways, these definitions naturally generalize that of a local maximum of a function.  Properties of maximal convexity ridges are put on a solid mathematical footing by Damon<ref name=Damon99/> and Miller.<ref name=Miller98/>  Their properties in one-parameter families was established by Keller.<ref>Kerrel, R.  ''Generic Transitions of Relative Critical Sets in Parameterized Families with Applications to Image Analysis.''  University of North Carolina.  1999.</ref>
 
== Maximal Scale Ridge ==
 
The following definition can be traced to Fritsch<ref>Fritsch, DS, Eberly,D., Pizer, SM, and McAuliffe, MJ. "Stimulated cores and
their applications in medical imaging."  Information Processing in Medical Imaging, Y. Bizais, C Barillot, R DiPaola, eds., Kluwer Series in Computational Imaging and Vision, pp. 365–368.</ref> who was interested in extracting geometric information about figures in two dimensional greyscale images.  Fritsch filtered his image with a "medialness" filter that gave him information analogous to "distant to the boundary" data in scale-space.  Ridges of this image, once projected to the original image, were to be analogous to a shape skeleton (''e.g.'', the Blum Medial Axis) of the original image.
 
What follows is a definition for the maximal scale ridge of a function of three variables, one of which is a "scale" parameter.  One thing that we want to be true in this definition is, if <math>(\mathbf{x},\sigma)</math> is a point on this ridge, then the value of the function at the point is maximal in the scale dimension.  Let <math>f(\mathbf{x},\sigma)</math> be a smooth differentiable function on <math>U \subset \mathbb{R}^2 \times \mathbb{R}_{+}</math>.  The <math>(\mathbf{x},\sigma)</math> is a point on the maximal scale ridge if and only if
<ol>
<li> <math>\frac{\partial f}{\partial \sigma}=0</math> and <math>\frac{\partial^2 f}{\partial \sigma^2}<0</math>, and
<li><math>\nabla f \cdot \mathbf{e}_1=0</math> and <math>\mathbf{v}_1^t H(f) \mathbf{v}_1 <0</math>.
</ol>
 
== Relations between edge detection and ridge detection ==
 
The purpose of ridge detection is usually to capture the major axis of symmetry of an elongated object,{{Citation needed|date=July 2008}} whereas the purpose of [[edge detection]] is usually to capture the boundary of the object. However, some literature on edge detection erroneously{{Citation needed|date=July 2008}} includes the notion of ridges into the concept of edges, which confuses the situation.
 
In terms of definitions, there is a close connection between edge detectors and ridge detectors. With the formulation of non-maximum as given by Canny,<ref>{{cite journal |doi=10.1109/TPAMI.1986.4767851 |author=Canny J. |title=A computational approach to edge detection |journal=IEEE Trans Pattern Anal Mach Intell |volume=8 |issue=6 |pages=679–698 |year=1986 |url=http://portal.acm.org/citation.cfm?id=11275}}</ref> it holds that edges are defined as the points where the gradient magnitude assumes a local maximum in the gradient direction. Following a differential geometric way of expressing this definition,<ref>{{cite journal |doi=10.1007/BF01664794 |author=Lindeberg T. |title=Discrete Derivative Approximations with Scale-Space Properties: A Basis for Low-Level Feature Extraction |journal=J. of Mathematical Imaging and Vision |volume=3 |issue=4 |pages=349–376 |year=1993 |url=http://www.nada.kth.se/~tony/abstracts/Lin93-JMIV.html}}</ref> we can in the above-mentioned <math>(u, v)</math>-coordinate system state that the gradient magnitude of the scale-space representation, which is equal to the first-order directional derivative in the <math>v</math>-direction <math>L_v</math>, should have its first order directional derivative in the <math>v</math>-direction equal to zero
:<math>\partial_v(L_v) = 0</math>
while the second-order directional derivative in the <math>v</math>-direction of <math>L_v</math> should be negative, i.e.,
:<math>\partial_{vv}(L_v) \leq 0</math>.  
Written out as an explicit expression in terms of local partial derivatives <math>L_x</math>, <math>L_y</math> ... <math>L_{yyy}</math>, this edge definition can be expressed as the zero-crossing curves of the differential invariant
:<math>L_v^2 L_{vv} = L_x^2 \, L_{xx} + 2 \, L_x \,  L_y \, L_{xy} + L_y^2 \, L_{yy} = 0,</math>
that satisfy a sign-condition on the following differential invariant
:<math>L_v^3 L_{vvv} = L_x^3 \, L_{xxx} + 3 \, L_x^2 \, L_y \, L_{xxy} + 3 \, L_x \, L_y^2 \, L_{xyy} + L_y^3 \, L_{yyy} \leq 0</math>
(see the article on [[edge detection]] for more information). Notably, the edges obtained in this way are the ridges of the gradient magnitude.
 
== See also ==
 
*[[Scale space]]
*[[Edge detection]]
*[[Interest point detection]]
*[[Blob detection]]
*[[Computer vision]]
 
==References==
 
<references/>
 
==External links==
*[http://www.letteraturaoperaomnia.org/thesis/thesis_italy_XX_ciclo_andrea_anzalone.html Multiscale analysis for optimized vessel segmentation of fundus retina images] Ph.D Thesis
 
[[Category:Feature detection]]
[[Category:Multivariable calculus]]
[[Category:Smooth functions]]
[[Category:Singularity theory]]

Revision as of 19:20, 12 September 2013

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The attempt (via software) to locate ridges (or edges) in an image.

In mathematics and computer vision, the ridges (or the ridge set) of a smooth function of two variables are a set of curves whose points are, in one or more ways to be made precise below, local maxima of the function in at least one dimension. This notion captures the intuition of geographical ridges. For a function of N variables, its ridges are a set of curves whose points are local maxima in N1 dimensions. In this respect, the notion of ridge points extends the concept of a local maximum. Correspondingly, the notion of valleys for a function can be defined by replacing the condition of a local maximum with the condition of a local minimum. The union of ridge sets and valley sets, together with a related set of points called the connector set form a connected set of curves that partition, intersect, or meet at the critical points of the function. This union of sets together is called the function's relative critical set.[1][2]

Ridge sets, valley sets, and relative critical sets represent important geometric information intrinsic to a function. In a way, they provide a compact representation of important features of the function, but the extent to which they can be used to determine global features of the function is an open question. The primary motivation for the creation of ridge detection and valley detection procedures has come from image analysis and computer vision and is to capture the interior of elongated objects in the image domain. Ridge-related representations in terms of watersheds have been used for image segmentation. There have also been attempts to capture the shapes of objects by graph-based representations that reflect ridges, valleys and critical points in the image domain. Such representations may, however, be highly noise sensitive if computed at a single scale only. Because scale-space theoretic computations involve convolution with the Gaussian (smoothing) kernel, it has been hoped that use of multi-scale ridges, valleys and critical points in the context of scale space theory should allow for more a robust representation of objects (or shapes) in the image.

In this respect, ridges and valleys can be seen as a complement to natural interest points or local extremal points. With appropriately defined concepts, ridges and valleys in the intensity landscape (or in some other representation derived from the intensity landscape) may form a scale invariant skeleton for organizing spatial constraints on local appearance, with a number of qualitative similarities to the way the Blum's medial axis transform provides a shape skeleton for binary images. In typical applications, ridge and valley descriptors are often used for detecting roads in aerial images and for detecting blood vessels in retinal images or three-dimensional magnetic resonance images.

Differential geometric definition of ridges and valleys at a fixed scale in a two-dimensional image

Let f(x,y) denote a two-dimensional function, and let L be the scale-space representation of f(x,y) obtained by convolving f(x,y) with a Gaussian function

g(x,y,t)=12πte(x2+y2)/2t.

Furthermore, let Lpp and Lqq denote the eigenvalues of the Hessian matrix

H=[LxxLxyLxyLyy]

of the scale-space representation L. With a coordinate transformation (a rotation) applied to local directional derivative operators,

p=sinβxcosβy,q=cosβx+sinβy

where p and q are coordinates of the rotated coordinate system.

It can be shown that the mixed derivative Lpq in the transformed coordinate system is zero if we choose

cosβ=12(1+LxxLyy(LxxLyy)2+4Lxy2),sinβ=sgn(Lxy)12(1LxxLyy(LxxLyy)2+4Lxy2).

Then, a formal differential geometric definition of the ridges of f(x,y) at a fixed scale t can be expressed as the set of points that satisfy [3]

Lp=0,Lpp0,|Lpp||Lqq|.

Correspondingly, the valleys of f(x,y) at scale t are the set of points

Lq=0,Lqq0,|Lqq||Lpp|.

In terms of a (u,v) coordinate system with the v direction parallel to the image gradient

u=sinαxcosαy,v=cosαx+sinαy

where

cosα=LxLx2+Ly2,sinα=LyLx2+Ly2

it can be shown that this ridge and valley definition can instead be equivalently[4] be written as

Luv=0,Luu2Lvv20

where

Lv2Luu=Lx2Lyy2LxLyLxy+Ly2Lxx,
Lv2Luv=LxLy(LxxLyy)(Lx2Ly2)Lxy,
Lv2Lvv=Lx2Lxx+2LxLyLxy+Ly2Lyy

and the sign of Luu determines the polarity; Luu<0 for ridges and Luu>0 for valleys.

Computation of variable scale ridges from two-dimensional images

A main problem with the fixed scale ridge definition presented above is that it can be very sensitive to the choice of the scale level. Experiments show that the scale parameter of the Gaussian pre-smoothing kernel must be carefully tuned to the width of the ridge structure in the image domain, in order for the ridge detector to produce a connected curve reflecting the underlying image structures. To handle this problem in the absence of prior information, the notion of scale-space ridges has been introduced, which treats the scale parameter as an inherent property of the ridge definition and allows the scale levels to vary along a scale-space ridge. Moreover, the concept of a scale-space ridge also allows the scale parameter to be automatically tuned to the width of the ridge structures in the image domain, in fact as a consequence of a well-stated definition. In the literature, a number of different approaches have been proposed based on this idea.

Let R(x,y,t) denote a measure of ridge strength (to be specified below). Then, for a two-dimensional image, a scale-space ridge is the set of points that satisfy

Lp=0,Lpp0,t(R)=0,tt(R)0,

where t is the scale parameter in the scale-space representation. Similarly, a scale-space valley is the set of points that satisfy

Lq=0,Lqq0,t(R)=0,tt(R)0.

An immediate consequence of this definition is that for a two-dimensional image the concept of scale-space ridges sweeps out a set of one-dimensional curves in the three-dimensional scale-space, where the scale parameter is allowed to vary along the scale-space ridge (or the scale-space valley). The ridge descriptor in the image domain will then be a projection of this three-dimensional curve into the two-dimensional image plane, where the attribute scale information at every ridge point can be used as a natural estimate of the width of the ridge structure in the image domain in a neighbourhood of that point.

In the literature, various measures of ridge strength have been proposed. When Lindeberg (1996, 1998)[5] coined the term scale-space ridge, he considered three measures of ridge strength:

The notion of γ-normalized derivatives is essential here, since it allows the ridge and valley detector algorithms to be calibrated properly. By requiring that for a one-dimensional Gaussian ridge embedded in two (or three dimensions) the detection scale should be equal to the width of the ridge structure when measured in units of length (a requirement of a match between the size of the detection filter and the image structure it responds to), it follows that one should choose γ=3/4. Out of these three measures of ridge strength, the first entity Lpp,γnorm is a general purpose ridge strength measure with many applications such as blood vessel detection and road extraction. Nevertheless, the entity Aγnorm has been used in applications such as fingerprint enhancement,[6] real-time hand tracking and gesture recognition[7] as well as for modelling local image statistics for detecting and tracking humans in images and video.[8]

There are also other closely related ridge definitions that make use of normalized derivatives with the implicit assumption of γ=1.[9] Develop these approaches in further detail. When detecting ridges with γ=1, however, the detection scale will be twice as large as for γ=3/4, resulting in more shape distortions and a lower ability to capture ridges and valleys with nearby interfering image structures in the image domain.

History

The notion of ridges and valleys in digital images was introduced by Haralick in 1983[10] and by Crowley concerning difference of Gaussians pyramids in 1984.[11][12] The application of ridge descriptors to medical image analysis has been extensively studied by Pizer and his co-workers[13][14][15] resulting in their notion of M-reps.[16] Ridge detection has also been furthered by Lindeberg with the introduction of γ-normalized derivatives and scale-space ridges defined from local maximization of the appropriately normalized main principal curvature of the Hessian matrix (or other measures of ridge strength) over space and over scale. These notions have later been developed with application to road extraction by Steger et al.[17][18] and to blood vessel segmentation by Frangi et al.[19] as well as to the detection of curvilinear and tubular structures by Sato et al.[20] and Krissian et al.[21] A review of several of the classical ridge definitions at a fixed scale including relations between them has been given by Koenderink and van Doorn.[22] A review of vessel extraction techniques has been presented by Kirbas and Quek.[23]

Definition of ridges and valleys in N dimensions

In its broadest sense, the notion of ridge generalizes the idea of a local maximum of a real-valued function. A point x0 in the domain of a function f:nis a local maximum of the function if there is a distance δ>0 with the property that if x is within δ units of x0, then f(x)<f(x0). It is well known that critical points, of which local maxima are just one type, are isolated points in a function's domain in all but the most unusual situations (i.e., the nongeneric cases).

Consider relaxing the condition that f(x)<f(x0) for x in an entire neighborhood of x0 slightly to require only that this hold on an n1 dimensional subset. Presumably this relaxation allows the set of points which satisfy the criteria, which we will call the ridge, to have a single degree of freedom, at least in the generic case. This means that the set of ridge points will form a 1-dimensional locus, or a ridge curve. Notice that the above can be modified to generalize the idea to local minima and result in what might call 1-dimensional valley curves.

This following ridge definition follows the book by Eberly[24] and can be seen as a generalization of some of the abovementioned ridge definitions. Let Un be an open set, and f:U be smooth. Let x0U. Let x0f be the gradient of f at x0, and let Hx0(f) be the n×n Hessian matrix of fat x0. Let λ1λ2λn be the n ordered eigenvalues of Hx0(f) and let ei be a unit eigenvector in the eigenspace for λi. (For this, one should assume that all the eigenvalues are distinct.)

The point x0 is a point on the 1-dimensional ridge of f if the following conditions hold:

  1. λn1<0, and
  2. x0fei=0 for i=1,2,,n1.

This makes precise the concept that f restricted to this particular n1-dimensional subspace has a local maxima at x0.

This definition naturally generalizes to the k-dimensional ridge as follows: the point x0 is a point on the k-dimensional ridge of f if the following conditions hold:

  1. λnk<0, and
  2. x0fei=0 for i=1,2,,nk.

In many ways, these definitions naturally generalize that of a local maximum of a function. Properties of maximal convexity ridges are put on a solid mathematical footing by Damon[1] and Miller.[2] Their properties in one-parameter families was established by Keller.[25]

Maximal Scale Ridge

The following definition can be traced to Fritsch[26] who was interested in extracting geometric information about figures in two dimensional greyscale images. Fritsch filtered his image with a "medialness" filter that gave him information analogous to "distant to the boundary" data in scale-space. Ridges of this image, once projected to the original image, were to be analogous to a shape skeleton (e.g., the Blum Medial Axis) of the original image.

What follows is a definition for the maximal scale ridge of a function of three variables, one of which is a "scale" parameter. One thing that we want to be true in this definition is, if (x,σ) is a point on this ridge, then the value of the function at the point is maximal in the scale dimension. Let f(x,σ) be a smooth differentiable function on U2×+. The (x,σ) is a point on the maximal scale ridge if and only if

  1. fσ=0 and 2fσ2<0, and
  2. fe1=0 and v1tH(f)v1<0.

Relations between edge detection and ridge detection

The purpose of ridge detection is usually to capture the major axis of symmetry of an elongated object,Potter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. whereas the purpose of edge detection is usually to capture the boundary of the object. However, some literature on edge detection erroneouslyPotter or Ceramic Artist Truman Bedell from Rexton, has interests which include ceramics, best property developers in singapore developers in singapore and scrabble. Was especially enthused after visiting Alejandro de Humboldt National Park. includes the notion of ridges into the concept of edges, which confuses the situation.

In terms of definitions, there is a close connection between edge detectors and ridge detectors. With the formulation of non-maximum as given by Canny,[27] it holds that edges are defined as the points where the gradient magnitude assumes a local maximum in the gradient direction. Following a differential geometric way of expressing this definition,[28] we can in the above-mentioned (u,v)-coordinate system state that the gradient magnitude of the scale-space representation, which is equal to the first-order directional derivative in the v-direction Lv, should have its first order directional derivative in the v-direction equal to zero

v(Lv)=0

while the second-order directional derivative in the v-direction of Lv should be negative, i.e.,

vv(Lv)0.

Written out as an explicit expression in terms of local partial derivatives Lx, Ly ... Lyyy, this edge definition can be expressed as the zero-crossing curves of the differential invariant

Lv2Lvv=Lx2Lxx+2LxLyLxy+Ly2Lyy=0,

that satisfy a sign-condition on the following differential invariant

Lv3Lvvv=Lx3Lxxx+3Lx2LyLxxy+3LxLy2Lxyy+Ly3Lyyy0

(see the article on edge detection for more information). Notably, the edges obtained in this way are the ridges of the gradient magnitude.

See also

References

  1. 1.0 1.1 One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  2. 2.0 2.1 Miller, J. Relative Critical Sets in n and Applications to Image Analysis. Ph.D. Dissertation. University of North Carolina. 1998.
  3. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  4. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  5. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang Earlier version presented at IEEE Conference on Pattern Recognition and Computer Vision, CVPR'96, San Francisco, California, pages 465–470, june 1996
  6. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  7. L. Bretzner, I. Laptev and T. Lindeberg: Hand Gesture Recognition using Multi-Scale Colour Features, Hierarchical Models and Particle Filtering, Proc. IEEE Conference on Face and Gesture 2002, Washington DC, 423–428.
  8. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  9. J. Furst and J. Miller, "The Maximal Scale Ridge: Incorporating Scale in the Ridge Definition", Scale Space Theory in Computer Vision: Proceedings of the First International Conference on, Scale Space '97, pp. 93–104. Springer Lecture Notes in Computer Science, vol. 1682.
  10. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  11. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  12. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  13. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  14. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  15. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  16. S. Pizer, S. Joshi, T. Fletcher, M. Styner, G. Tracton, J. Chen (2001) "Segmentation of Single-Figure Objects by Deformable M-reps", Proceedings of the 4th International Conference on Medical Image Computing and Computer-Assisted Intervention, Springer Lecture Notes In Computer Science; Vol. 2208, pp. 862–871
  17. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  18. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  19. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  20. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  21. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  22. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  23. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  24. 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.

    My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
  25. Kerrel, R. Generic Transitions of Relative Critical Sets in Parameterized Families with Applications to Image Analysis. University of North Carolina. 1999.
  26. Fritsch, DS, Eberly,D., Pizer, SM, and McAuliffe, MJ. "Stimulated cores and their applications in medical imaging." Information Processing in Medical Imaging, Y. Bizais, C Barillot, R DiPaola, eds., Kluwer Series in Computational Imaging and Vision, pp. 365–368.
  27. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
  28. One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

    In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

    Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

    Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

    A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

    The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

    There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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