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In [[computer graphics]], a '''hierarchical RBF''' is an [[interpolation]] method based on [[Radial basis function]]s (RBF). Hierarchical RBF interpolation has applications in the construction of shape models in [[3d computer graphics|3D computer graphics]] (see [[Stanford Bunny]] image below), treatment of results from a [[3D scanner]], [[terrain]] reconstruction and others.
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[[Image:MyBunny.gif]]
 
This problem informally named "large scattered data point set interpolation".
 
The idea of method (for example in 3D) consists of the following:
* let the scattered points be presented a set <math>\mathbf{P}=\{\mathbf{c}_i=(\mathbf{x}_i,\mathbf{y}_i,\mathbf{z}_i)\vert^{N}_{i=0} \subset \mathbb{R}^3\}</math>
* let the exist a set of values of some function in scattered points <math>\mathbf{H}=\{\mathbf{h}_i \vert^{N}_{i=0}\subset \mathbb{R}\}</math>
* find a function <math>\mathbf{f}(\mathbf{x})</math> which will meet next condition: <math>\mathbf{f}(\mathbf{x})=1</math> for points lies on shape and <math>\mathbf{f}(\mathbf{x})\neq1</math> for points not lies on shape
* as J. C. Carr et al. showed <ref>Carr, J.C.; Beatson, R.K.; Cherrie, J.B.; Mitchell, T.J.; Fright, W.R.; McCallum B.C.; Evans, T.R. (2001),  “Reconstruction and Representation of 3D Objects with Radial Basis Functions” ACM SIGGRAPH 2001, Los Angeles, CA, P. 67–76.</ref> this function looks like <math>\mathbf{f}(\mathbf{x})=\sum_{i=1}^N \lambda_i \varphi(\mathbf{x},\mathbf{c}_i)</math> where:
<math>\varphi</math> &mdash; it is [[Radial basis function|RBF]];
<math>\lambda</math> &mdash; it is coefficients which are the solution of the [[Linear system of equations|system]] show on picture:
 
[[Image:System.gif]]
 
for determination of surface it is necessary to estimate the value of function <math>\mathbf{f}(\mathbf{x})</math> in interesting  points ''x''.
A lack of such method is considerable complication <ref>Bashkov, E.A.; Babkov, V.S. (2008) “Research of RBF-algorithm and his modifications apply
possibilities for the construction of shape computer models in medical practic”. Proc Int.
Conference "Simulation-2008", Pukhov Institute for Modelling in Energy Engineering, [http://babkov.name/article/2008-09.pdf] (in Russian)</ref> <math>\mathbf{O}(\mathbf{n}^2)</math> for calculate [[Radial basis function|RBF]], solve [[Linear system of equations|system]] and determine surface.
 
==Other similar methods==
* Reduce interpolation centres (<math>\mathbf{O}(\mathbf{n}^2)</math> for calculate [[Radial basis function|RBF]] and solve [[Linear system of equations|system]], <math>\mathbf{O}(\mathbf{m}\mathbf{n})</math> for determine surface)
* Compactly supported [[Radial basis function|RBF]] (<math>\mathbf{O}(\mathbf{n}\log{\mathbf{n}})</math> for calculate [[Radial basis function|RBF]], <math>\mathbf{O}(\mathbf{n}^{1.2..1.5})</math> for solve [[Linear system of equations|system]], <math>\mathbf{O}(\mathbf{m}\log{\mathbf{n}})</math> for determine surface)
* [[Fast multipole method|FMM]]  (<math>\mathbf{O}(\mathbf{n}^2)</math> for calculate [[Radial basis function|RBF]], <math>\mathbf{O}(\mathbf{n}\log{\mathbf{n}})</math> for solve [[Linear system of equations|system]], <math>\mathbf{O}(\mathbf{m}+\mathbf{n}\log{\mathbf{n}})</math> for determine surface)
 
==Hierarchical algorithm==
An idea of [[hierarchical]] [[Algorythm|algorithm]] is an acceleration of calculations due to [[Decomposition (computer science)|decomposition]] of intricate problem on the great number of simple (see picture). [[File:Hierarchical algorithm flow chart.gif]]
 
In this case [[hierarchical]] division of space containing points on elementary parts, the [[Linear system of equations|system]] of small dimension solves in each of which. The calculation of surface in this case is taken to the [[hierarchical]] (on the basis of [[Tree (data structure)|tree-structure]]) calculation of interpolant. A method for a [[2D computer graphics|2D]] case is offered Pouderoux J. et al.<ref>Pouderox, J. et al. (2004), “Adaptive hierarchical RBF interpolation for creating smooth digital elevathion models”, Proc. 12-th ACM Int. Symp. Advances in Geographical information Systems 2004, ACP Press, P. 232&ndash;240</ref> For a [[3D computer graphics|3D]] case a method is used in the tasks of [[3D computer graphics|3D graphics]] by W. Qiang et al.<ref>Qiang, W.; Pan, Z.; Chun, C.; Jiajun, B. (2007), “Surface rendering for parallel slice of contours from medical imaging”, Computing in science & engineering, 9(1), January&ndash;February 2007, P 32&ndash;37</ref> and modified by Babkov V.<ref>Babkov, V.S. (2008) “Modification of hierarchical RBF method for 3D-modelling based on laser scan result”. Proc. Int. Conference “Modern problems and achievement of radio, communication
and informatics”, Zaporizhzhya National Technical University, [http://babkov.name/article/2008-08.pdf] (in Ukrainian)</ref>
 
==References==
{{reflist}}
 
{{DEFAULTSORT:Hierarchical Rbf}}
[[Category:Geometric algorithms]]
[[Category:Computer graphics]]
[[Category:Interpolation]]

Revision as of 06:37, 2 March 2014

http://news.goldgrey.org/silver/ The recent optimism asserted itself again Friday supported by U.S.corporate earnings and some blind faith the Europeans can fix their debt crisis. At least they appear to be working on it with some harmony from recent rhetoric.



Everyone is eager to make money so that we can get more out of this world. Go traveling, shopping with your loved ones and having good food. Whether it is by doing business, investing in stocks or real estate, we all dream of making it big. Our aim is to make money. Some also turn to gambling to make a living but there is nothing wrong with it as long as it is not illegal. Professional poker players are earning more than you and me now. The same theory applies to sports betting, many people would try their 'luck' to earn cash from it. And fortunately for some, they are very well at it.

Develop a Strategy - Have a goal and a plan. Identify the reasons that make you want to trade stocks. Include how much profit you expect to make and how much loss you can take. Put a time frame for your objectives as well. This helps you identify if you are a risk-taker or a conservative investor and adjust your approach appropriately.

That's understandable. The beginnings can be, and usually are, challenging. But it's easy to handle this if you simplify things. Simple things are not necessarily worse than complex ones, so before you decide to embark on using the top notch trading technology, I suggest that you explore some really simple options, some basic yet solid elements that has been around for a very long time and are here to stay.

Bear in mind, every stock trading strategy comes with its own set of advantages and risks', knowing these is vital to determining the stock trading you want to do. Let's take a look at some of the stock traders out there and what kind of stock trading they do.

The number one thing to keep in mind if you are new to trading stocks is to start small and work your way up. The last thing you want is to jump into a shark tank unprepared and lose thousands of dollars. Start with low lots of shares such as 100 as this is much easier to take in if the shares go against you.

Of course, you will not always be able to predict the future correctly unless you are clairvoyant or are engaging in illegal insider trading. If neither of these two is true of you then it's obvious that you'll make mistakes sometimes. After all, you're working under sub-optimal conditions. You're using conflicting information to guide your decision making process. Your brain isn't meant to work under these conditions but yet here you are, slogging through and doing the best you can.

One of the reasons more and more people are trading stocks using stock trading systems has been the need to have more control over risk. After the sharp decline in stock prices starting about April 2000 we all started to realize that maybe there is more to making money in the stock market than "buy and hold".

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