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'''Randomized Hough transform''' is a probabilistic variant to the classical [[Hough transform]], which is a commonly used technique for detecting curves (straight line, circle, ellipse, etc.)<ref>D.H. Ballard, "Generalizing the Hough Transform to Detect Arbitrary Shapes", Pattern Recognition, Vol.13, No.2, p.111-122, 1981</ref> The basic idea of Hough transform (HT) is to implement a voting procedure for all potential curves in the image, and at the termination of the algorithm curves that do exist in the image will have relatively high voting scores. Randomized Hough transform (RHT) is different from HT in that it tries to avoid conducting the computationally expensive voting process for every nonzero pixel in the image by taking advantage of the geometric properties of analytical curves, and thus improve the time efficiency and reduce the storage requirement of the original algorithm.  
 
==Motivation==
 
Although Hough transform (HT) has been widely used in [[Edge detection|curve detection]], it has two major drawbacks:<ref>L. Xu, E. Oja, and P. Kultanan, "A new curve detection method: Randomized Hough transform (RHT)", ''Pattern Recog. Lett.'' 11, 1990, 331-338.</ref> First, for each nonzero pixel in the image, the parameters for the existing curve and redundant ones are both accumulated during the voting procedure. Second, the accumulator array (or Hough space) is predefined in a heuristic way. The more accuracy needed, the higher parameter resolution should be defined. These two needs usually result in a large storage requirement and low speed for real applications. Therefore, RHT was brought up to tackle this problem.
 
==Implementation==
 
In comparison with HT, RHT takes advantage of the fact that some [[analytical]] curves can be fully determined by a certain number of points on the curve. For example, a straight line can be determined by two points, and an [[ellipse]] (or a circle) can be determined by three points. The case of ellipse detection can be used to illustrate the basic idea of RHT. The whole process generally consists of three steps:
# Fit ellipses with randomly selected points.
# Update the accumulator array and corresponding scores.
# Output the ellipses with scores higher than some predefined threshold.
===Ellipse fitting===
 
One general equation for defining [[ellipse]]s is:
<math>a (x - p)^2+ 2b (x-p) (y-q) +  c (y-q)^2 + 1 = 0 </math>
 
with restriction: <math>ac-b^2>0</math>
 
However, an ellipse can be fully determined if one knows three points on it and the tangents in these points.
 
RHT starts by randomly selecting three points on the ellipse. Let them be X<sub>1</sub>, X<sub>2</sub> and X<sub>3</sub>. The first step is to find the tangents of these three points. They can be found by fitting a straight line using [[least squares]] technique for a small window of neighboring pixels.
 
The next step is to find the intersection points of the tangent lines. This can be easily done by solving the line equations found in the previous step. Then let the intersection points be T<sub>12</sub> and T<sub>23</sub>, the midpoints of line segments <math>X_1X_2</math> and <math>X_2X_3</math> be M<sub>12</sub> and M<sub>23</sub>. Then the center of the ellipse will lie in the intersection of <math>T_{12}M_{12}</math> and <math>T_{23}M_{23}</math>. Again, the coordinates of the intersected point can be determined by solving line equations and the detailed process is skipped here for conciseness.
 
Let the coordinates of ellipse center found in previous step be (x<sub>0</sub>, y<sub>0</sub>). Then the center can be translated to the origin with <math>x' = x-x_0</math> and <math>y' = y-y_0</math> so that the ellipse equation can be simplified to:
 
<math>ax'^2+2bx'y'+cy'^2=1</math>
 
Now we can solve for the rest of ellipse parameters: a, b and c by substituting the coordinates of X<sub>1</sub>, X<sub>2</sub> and X<sub>3</sub> into the equation above.
 
===Accumulating===
 
With the ellipse parameters determined from previous stage, the [[accumulator]] array can be updated correspondingly. Different from classical Hough transform, RHT does not keep "grid of buckets" as the accumulator array. Rather, it first calculates the similarities between the newly detected ellipse and the ones already stored in accumulator array. Different metrics can be used to calculate the similarity. As long as the similarity exceeds some predefined threshold, replace the one in the accumulator with the average of both ellipses and add 1 to its score. Otherwise, initialize this ellipse to an empty position in the accumulator and assign a score of 1.
 
===Termination===
 
Once the score of one candidate ellipse exceeds the threshold, it is determined as existing in the image (in other words, this ellipse is detected), and should be removed from the image and accumulator array so that the algorithm can detect other potential ellipses faster. The algorithm terminates when the number of iterations reaches a maximum limit or all the ellipses have been detected.
 
Pseudo code for RHT:<ref>S. Inverso, “Ellipse Detection Using Randomized Hough Transform”, www.saminverso.com/res/vision/EllipseDetectionOld.pdf, May 20, 2002</ref>
 
<source lang="cpp">
while (we find ellipses OR not reached the maximum epoch) {
    for(a fixed number of iterations) {
        Find a potential ellipse.
        if(the ellipse is similar to an ellipse in the accumulator)
            Replace the one in the accumulator with the average of two ellipses and add 1 to the score;
        else
            Insert the ellipse into an empty position in the accumulator with a score of 1;
    }
    Select the ellipse with the best score and save it in a best ellipse table;
    Elliminate the pixels of the best ellipse from the image;
    Empty the accumulator;
}
 
</source>
 
==References==
<references/>
 
[[Category:Image processing]]
[[Category:Computer vision]]

Latest revision as of 01:31, 22 June 2014

There's clearly a whole lot of use for one thing like this when driving or engaged on something which keeps your fingers away out of your phone, although you continue to have to have interaction the app physically, so we're not sure how much you'd get out of it in these situations. The entire concept appears one thing very much within the vein of Cover Move - a very spectacular part for the cellphone that simply would not have a ton of sensible use. Sure, your folks will assume it's pretty cool, however as a pragmatic group of gadget nerds, we do not see an incredible need for this performance.

At a mere 3.0 ounces, this knife just melts into your pocket and is hardly seen. It's a nice every single day carry or light responsibility knife, although slightly small and light-weight to succeed in a survival role. Overall, it seems to be ok to be thought of a gentleman’s knife and it performs well sufficient that I can strongly recommend one. Take into accout, lighter doesn’t always mean higher. Aluminium saves weight, but metal is stronger. Titanium could be very sturdy and light-weight, but prices a bit additional. Compare weights of different models after which research the development or reviews to make sure it may stand up to some day by day abuse.

Lastly, a number of notes on blade form and leading edge design. All however the Smith and Wesson Extreme Ops have some kind of drop-level formed blade. This is essentially the most versatile blade shape. The tanto-formed blade of the Smith And Wesson sacrifices some versatility in change for a slight improve in strength and significant increase in the Zero Tolerance Knives 0350 Review intimidating look. Additionally, word that blades in our check and elsewhere could be both straight or serrated. Neither is in any way better than the other. Serrated blades lower powerful supplies more simply while straight blades are simpler to sharpen. The OutdoorGearLab workforce prefers, generally, straight blades.

Buck a hundred and ten is a basic knife that has been round for a few decades now. It has a 3.25” carbon steel blade that is extremely resistant to corrosion and rust. The deployment is the outdated system of pulling the blade out with no reliance on shifting parts or expertise. Of all of the knives on this checklist, the Benchmade Mini Griptilian is the finest folding knife in our opinion. It has the best mix of excellent design and a sturdy blade that makes it straightforward to make use of and comfy on the same time.

Ka-Bar Mule Field Folder Knife - Wow, we merely cannot consider this knife is below $50.00. This undoubtedly deserves to be considered one of the best folding knives for the worth. You'll be able to put this knife up to any check, and it'll pass your expectations by far. This knife weighs a little Zero Tolerance 200 Knife Review less than half of a pound – which is an efficient thing as a result of this knife will final you awhile! The KA-BAR mule knife is perfect for any labor activity, and great for being in the wilderness. The opening and shutting technique of this knife will ensure you don’t have any unintended closures in your finger.

Though the critiques are primarily constructive, a number of pink flags have been unfurled by prospects. The most common is in the initial that is in section 1 of the weight loss plan. For the reason that carb intake is nearly nil in part 1, it may possibly result in a common feeling of fatigue. Nevertheless, this drawback is taken care of sooner or swiss army pocket knife later of the weight loss program itself. Few clients also report minor problems or complaints like constipation. However, such reports are uncommon. Also in case of such problems, the official web site has contact details of execs and doctors that provide one-on-one help that may enable you to type out the issue you might be dealing with.

I chosen a center price vary of approximately $25 to $50 in order to keep away from a budget stuff while overlooking the very costly. I filtered out only the four-star rankings or greater and then logged the variety of evaluations for every knife which indicates the popularity of the knife itself. What I came up with is the following list. I selected this knife to be on my record for several completely different causes. It is actually light weight, coming in at simply over 2.5 ounces. With a knife that mild, you received’t discover it sitting in your pocket. Essentially, that could be a big perk for some individuals when choosing an EDC.

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