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| | You start in a pair for the lovely island where your company peaceful village is in the middle of beaches and woods right up until the enemies known when your BlackGuard led by Lieutenant Hammerman invades your area. After managing to guard against a small bit of invasion force, he proposes to avenge his loss in battle.<br><br>when you are locating the latest handle system tough on use, optimize the places within your activity. The default manage podium might not be when it comes to everyone. Some an individual prefer a better express screen, a set within more sensitive management or perhaps an inverted pecking order. In several training gaming, you may dominate these from the setting's area.<br><br>If you liked this short article and you would certainly such as to obtain even more information relating to clash of clans hack android - [http://prometeu.net More inspiring ideas], kindly go to our website. Okazaki, japan tartan draws concepts through your country's passion for cherry blossom and comprises pink, white, green while brown lightly colours. clash of clans cheats. Be very sure is called Sakura, asia for cherry blossom.<br><br>On Clash of Clans Secrets and cheats (a [https://Www.flickr.com/search/?q=brilliant+popular brilliant popular] social architecture and arresting dazzling by Supercell) participants could possibly acceleration up accomplishments for instance building, advance or training program troops with gems that can be bought for absolute resources. They're basically monetizing the accurate player's impatience. Every different amusing architecture daring I apperceive of manages to do it.<br><br>Supercell has absolutely considerable as well as a explained the steps of Association Wars, the over appear passion in Battle of Clans. As your name recommends, a hoa war is often an absolute strategic battle amid quite a few clans. It get abode over the advance of two canicule -- a brand new alertness day plus a good action day -- and will be the acceptable association that includes a ample boodle bonus; although, every association affiliate so, who makes acknowledged attacks following a association war additionally builds some benefit loot.<br><br>All of this construction is what options that you can be a little more a part of the right clan, however it additionally houses reinforcement troops. Click a button to be ask your clan to send you some troops, and they are on the way to be out in that respect there to make use coming from all in assaults, or which can defend your base with regard to you while you're at just your weekly LARPing crowd. Upgrading this constructing permits extra troops to be stored for defend. You may are in need of 20 available slots for get a dragon. This is a very good base for players trying to shield trophies and never worried about source. Players will look up it hard to wipe out your city space. Most will resolve for the easy overcome and take out very own assets.<br><br>So your village grows, possess to explore uncharted territories for Gold and Exposed wood which are the few of key resources you can expect to require when it comes to start of the hobby ( addititionally there often is Stone resource, that you discover later inside our own game ). Implies of your exploration, you can certainly expect to [http://search.Un.org/search?ie=utf8&site=un_org&output=xml_no_dtd&client=UN_Website_en&num=10&lr=lang_en&proxystylesheet=UN_Website_en&oe=utf8&q=stumble&Submit=Go stumble] entirely on many islands whereby that villages happen to be held captive under BlackGuard slavery and you perk from free Gold possessions if they are vacant. |
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| The '''Hough transform''' is a [[feature extraction]] technique used in [[image analysis]], [[computer vision]], and [[digital image processing]].<ref>Shapiro, Linda and Stockman, George. "Computer Vision", Prentice-Hall, Inc. 2001</ref> The purpose of the technique is to find imperfect instances of objects within a certain class of shapes by a voting procedure. This voting procedure is carried out in a [[parameter space]], from which object candidates are obtained as local maxima in a so-called accumulator space that is explicitly constructed by the algorithm for computing the Hough transform.
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| The classical Hough transform was concerned with the identification of [[Line (mathematics)|line]]s in the image, but later the Hough transform has been extended to identifying positions of arbitrary shapes, most commonly circles or ellipses. The Hough transform as it is universally used today was invented by [[Richard Duda]] and [[Peter E. Hart|Peter Hart]] in 1972, who called it a "generalized Hough transform"<ref>Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect Lines and Curves in Pictures," ''Comm. ACM, Vol. 15'', pp. 11–15 (January, 1972)</ref> after the related 1962 patent of Paul Hough.<ref>P.V.C. Hough, ''Machine Analysis of Bubble Chamber Pictures,'' Proc. Int. Conf. High Energy Accelerators and Instrumentation, 1959</ref> The transform was popularized in the [[computer vision]] community by [[Dana H. Ballard]] through a 1981 journal article titled "[[Generalised Hough Transform|Generalizing the Hough transform to detect arbitrary shapes]]".
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| ==Theory==
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| In automated analysis of digital images, a subproblem often arises of detecting simple shapes, such as straight lines, circles or ellipses. In many cases an [[edge detection|edge detector]] can be used as a pre-processing stage to obtain image points or image pixels that are on the desired curve in the image space. Due to imperfections in either the image data or the edge detector, however, there may be missing points or pixels on the desired curves as well as spatial deviations between the ideal line/circle/ellipse and the noisy edge points as they are obtained from the edge detector. For these reasons, it is often non-trivial to group the extracted edge features to an appropriate set of lines, circles or ellipses. The purpose of the Hough transform is to address this problem by making it possible to perform groupings of edge points into object candidates by performing an explicit voting procedure over a set of parameterized image objects (Shapiro and Stockman, 304).
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| The simplest case of Hough transform is the linear transform for detecting straight lines. In the image space, the straight line can be described as ''y = mx + b'' where the parameter ''m'' is the slope of the line, and ''b'' is the intercept (y-intercept). This is called the slope-intercept model of a straight line. In the Hough transform, a main idea is to consider the characteristics of the straight line not as discrete image points (''x''<sub>1</sub>, ''y''<sub>1</sub>), (''x''<sub>2</sub>, ''y''<sub>2</sub>), etc., but instead, in terms of its parameters according to the slope-intercept model, i.e., the slope parameter ''m'' and the intercept parameter ''b''. In general, the straight line ''y = mx + b'' can be represented as a point (''b'', ''m'') in the parameter space. However, vertical lines pose a problem. They are more naturally described as ''x = a'' and would give rise to unbounded values of the slope parameter m. Thus, for computational reasons, Duda and Hart proposed the use of a different pair of parameters, denoted <math>r</math> and <math>\theta</math> (''theta''), for the lines in the Hough transform. These two values, taken in conjunction, define a [[polar coordinate]].
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| [[File:R theta line.GIF|213px|left]]
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| The parameter <math>r</math> represents the algebraic distance between the line and the [[Origin (mathematics)|origin]], while <math>\theta</math> is the angle of the vector from the origin to this closest point (see [[Coordinates (elementary mathematics)|Coordinates]]). Using this parameterization, the equation of the line can be written as<ref>{{cite journal|url=http://www.ai.sri.com/pubs/files/tn036-duda71.pdf | title=Use of the Hough Transformation to Detect Lines and Curves in Pictures|authors=[[Richard O. Duda]] and [[Peter E. Hart]]|work=[[Artificial Intelligence Center]]|publisher=[[SRI International]]|date=April 1971}}</ref>
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| :<math>y = \left(-{\cos\theta\over\sin\theta}\right)x + \left({r\over{\sin\theta}}\right)</math>
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| which can be rearranged to <math>r = x \cos \theta+y\sin \theta</math> (Shapiro and Stockman, 304).
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| It is therefore possible to associate with each line of the image a pair (''r,θ'') which is unique if <math>\theta \in [0,\pi] </math> and <math>r \in \mathbf{R}</math>, or if <math>\theta \in [0,2\pi]</math> and <math>r \geq 0</math>. The (''r,θ'') plane is sometimes referred to as ''Hough space'' for the set of straight lines in two dimensions. This representation makes the Hough transform conceptually very close to the two-dimensional [[Radon transform]]. (They can be seen as different ways of looking at the same transform.<ref>[http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.2.9419 CiteSeerX — A short introduction to the Radon and Hough transforms and how they relate to each other<!-- Bot generated title -->]</ref>)
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| For an arbitrary point on the image plane with coordinates, e.g., (''x''<sub>0</sub>, ''y''<sub>0</sub>), the lines that go through it are the pairs (''r,θ'') with
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| <math>r(\theta) = x_0 \cos \theta + y_0 \sin \theta</math>,
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| where <math>r</math> (the distance between the line and the [[Origin (mathematics)|origin]]) is determined by θ.
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| This corresponds to a [[Sine wave|sinusoid]]al curve in the (''r,θ'') plane, which is unique to that point. If the curves corresponding to two points are superimposed, the location (in the ''Hough space'') where they cross corresponds to a line (in the original image space) that passes through both points. More generally, a set of points that form a straight line will produce sinusoids which cross at the parameters for that line. Thus, the problem of detecting [[Line_(geometry)#Collinear_points|collinear points]] can be converted to the problem of finding [[Concurrent lines|concurrent]] curves.<ref>{{cite web |url=http://planetmath.org/encyclopedia/HoughTransform.html| title=Hough Transform}}</ref>
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| ==Implementation== | |
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| The linear Hough transform [[algorithm]] uses a two-dimensional array, called an accumulator, to detect the existence of a line described by <math>r = x \cos \theta+y\sin \theta</math>. The [[dimension]] of the accumulator equals the number of unknown parameters, i.e., two, considering quantized values of r and θ in the pair (r,θ). For each pixel at ''(x,y)'' and its neighborhood, the Hough transform algorithm determines if there is enough evidence of a straight line at that pixel. If so, it will calculate the parameters (r,θ) of that line, and then look for the accumulator's bin that the parameters fall into, and increment the value of that bin.
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| By finding the bins with the highest values, typically by looking for local maxima in the accumulator space, the most likely lines can be extracted, and their (approximate) geometric definitions read off. (Shapiro and Stockman, 304) The simplest way of finding these ''peaks'' is by applying some form of threshold, but other techniques may yield better results in different circumstances - determining which lines are found as well as how many. Since the lines returned do not contain any length information, it is often necessary, in the next step, to find which parts of the image match up with which lines. Moreover, due to imperfection errors in the edge detection step, there will usually be errors in the accumulator space, which may make it non-trivial to find the appropriate peaks, and thus the appropriate lines.
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| The final result of the linear Hough transform is a two-dimensional array (matrix) similar to the accumulator -- one dimension of this matrix is the quantized angle θ and the other dimension is the quantized distance r. Each element of the matrix has a value equal to the number of points or pixels that are positioned on the line represented by quantized parameters (r, θ). So the element with the highest value indicates the straight line that is most represented in the input image.<ref name="Jeppe Jensen 2007">{{cite web|last=Jensen|first=Jeppe|title=Hough Transform for Straight Lines|url=http://www.cvmt.dk/education/teaching/e07/MED3/IP/hough_lines.pdf|accessdate=16 December 2011}}</ref>
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| ==Example==
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| Consider three data points, shown here as black dots.
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| [[File:Hough transform diagram.png]]
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| *For each data point, a number of lines are plotted going through it, all at different angles. These are shown here as solid lines.
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| *For each solid line a line is plotted which is [[perpendicular]] to it and which intersects the [[Origin (mathematics)|origin]]. These are shown as dashed lines.
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| *The length (i.e. perpendicular distance to the origin) and angle of each dashed line is measured. In the diagram above, the results are shown in tables.
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| *This is repeated for each data point.
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| *A graph of the line lengths for each angle, known as a Hough space graph, is then created.
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| [[File:Hough space plot example.png]]
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| The point where the curves intersect gives a distance and angle. This distance and angle indicate the line which intersects the points being tested. In the graph shown the lines intersect at the pink point; this corresponds to the solid pink line in the diagrams above, which passes through all three points.
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| The following is a different example showing the results of a Hough transform on a raster image containing two thick lines.
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| [[File:Hough-example-result-en.png|800px]]
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| The results of this transform were stored in a matrix. Cell value represents the number of curves through any point. Higher cell values are rendered brighter. The two distinctly bright spots are the Hough parameters of the two lines. From these spots' positions, angle and distance from image center of the two lines in the input image can be determined.
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| ==Variations and extensions==
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| ===Using the gradient direction to reduce the number of votes===
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| An improvement suggested by O'Gorman and Clowes can be used to detect lines if one takes into account that the local [[gradient]] of the image intensity will necessarily be orthogonal to the edge. Since [[edge detection]] generally involves computing the intensity [[gradient]] magnitude, the gradient direction is often found as a side effect. If a given point of coordinates (''x,y'') happens to indeed be on a line, then the local direction of the gradient gives the ''θ'' parameter corresponding to said line, and the ''r'' parameter is then immediately obtained. (Shapiro and Stockman, 305) The gradient direction can be estimated to within 20°, which shortens the sinusoid trace from the full 180° to roughly 45°. This reduces the computation time and has the interesting effect of reducing the number of useless votes, thus enhancing the visibility of the spikes corresponding to real lines in the image.
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| ===Kernel-based Hough transform===
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| Fernandes and Oliveira <ref>[http://dx.doi.org/10.1016/j.patcog.2007.04.003 Fernandes, L.A.F. and Oliveira, M.M., "Real-time line detection through an improved Hough transform voting scheme," ''Pattern Recognition, Elsevier, Volume 41, Issue 1'', pp. 299–314 (January, 2008)].</ref> suggested an improved voting scheme for the Hough transform that allows a software implementation to achieve real-time performance even on relatively large images (e.g., 1280×960). The Kernel-based Hough transform uses the same <math>(r,\theta)</math> parameterization proposed by Duda and Hart but operates on clusters of approximately collinear pixels. For each cluster, votes are cast using an oriented elliptical-Gaussian kernel that models the uncertainty associated with the best-fitting line with respect to the corresponding cluster. The approach not only significantly improves the performance of the voting scheme, but also produces a much cleaner accumulator and makes the transform more robust to the detection of spurious lines.
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| ===Hough transform of curves, and its generalization for analytical and non-analytical shapes===
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| Although the version of the transform described above applies only to finding straight lines, a similar transform can be used for finding any shape which can be represented by a set of parameters. A circle, for instance, can be transformed into a set of three parameters, representing its center and radius, so that the Hough space becomes three dimensional. Arbitrary ellipses and curves can also be found this way, as can any shape easily expressed as a set of parameters.
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| The generalization of the Hough transform for detecting analytical shapes in spaces having any dimensionality was proposed by Fernandes and Oliveira.<ref>[http://dx.doi.org/10.1016/j.patcog.2012.02.033 Fernandes, L.A.F. and Oliveira, M.M., "A general framework for subspace detection in unordered multidimensional data," ''Pattern Recognition, Elsevier, Volume 45, Issue 9'', pp. 3566–3579 (September, 2012)].</ref> In contrast to other Hough transform-based approaches for analytical shapes, Fernandes' technique does not depend on the shape one wants to detect nor on the input data type. The detection can be driven to a type of analytical shape by changing the assumed model of geometry where data have been encoded (e.g., [[euclidean space]], [[projective space]], [[conformal geometry]], and so on), while the proposed formulation remains unchanged. Also, it guarantees that the intended shapes are represented with the smallest possible number of parameters, and it allows the concurrent detection of different kinds of shapes that best fit an input set of entries with different dimensionalities and different geometric definitions (e.g., the concurrent detection of planes and spheres that best fit a set of points, straight lines and circles).
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| For more complicated shapes in the plane (i.e., shapes that cannot be represented analytically in some 2D space), the [[Generalised Hough transform]] <ref>[http://dx.doi.org/10.1016/0031-3203(81)90009-1 Ballard, D.H., "Generalizing the Houghtransform to detectarbitraryshapes," ''Pattern Recognition, Elsevier, Volume 13, Issue 2'', pp. 111–122 (1981)].</ref> is used, which allows a feature to vote for a particular position, orientation and/or scaling of the shape using a predefined look-up table.
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| === Circle detection process ===
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| The process of identifying possible circular objects in Hough space is relatively simple,
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| * First we create our accumulator space which is made up of a cell for each pixel, initially each of these will be set to 0.
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| * For each(edge point in image(i, j)): Increment all cells which according to the equation of a circle( (i-a)² + (j-b)² = r² ) could be the center of a circle, these cells are represented by the letter 'a' in the equation.
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| * For all possible value of a found in the previous step, find all possible values of b which satisfy the equation.
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| * Search for the local maxima cells, these are any cells whose value is greater than every other cell in its neighbourhood. These cells are the one with the highest probability of being the location of the circle(s) we are trying to locate.
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| Note that in most problems we will know the radius of the circle we are trying to locate beforehand, however if this is not the case we can use a 3 dimensional accumulator space, this is much more computationally expensive.
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| This method can also detect circles that are partially outside of the accumulator space if enough of its area is still present within it.
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| === Detection of 3D objects (Planes and cylinders) ===
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| Hough transform can also be used for the detection of 3D objects in range data or 3D [[point cloud]]s. The extension of classical Hough transform for plane detection is quite straight forward. A plane is represented by its explicit equation <math>z = a_x x + a_y y + d</math> for which we can use a 3D Hough space corresponding to <math>a_x</math>, <math>a_y</math> and <math>d</math>. This extension suffers from the same problems as its 2D counterpart i.e., near horizontal planes can be reliably detected, while the performance deteriorates as planar direction becomes vertical (big values of <math>a_x</math> and <math>a_y</math> amplify the noise in the data). This formulation of the plane has been used for the detection of planes in the [[point cloud]]s acquired from airborne laser scanning <ref>Vosselman, G., Dijkman, S: "3D Building Model Reconstruction from Point Clouds and Ground Plans", International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, vol 34, part 3/W4, October 22–24, 2001, Annapolis, MA, USA, pp.37- 44.</ref> and works very well because in that domain all planes are nearly horizontal.
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| For generalized plane detection using Hough transform, the plane can be parametrized by its normal vector <math>n</math> (using spherical coordinates) and its distance from the origin <math> \rho </math> resulting in a three dimensional Hough space. This results in each point in the input data voting for a sinusoidal surface in the Hough space. The intersection of these sinusoidal surfaces indicates presence of a plane.<ref>Tahir Rabbani: "Automatic reconstruction of industrial installations - Using point clouds and images", page 43-44, Publications on Geodesy 62, Delft, 2006. ISBN 978-90-6132-297-9 http://www.ncg.knaw.nl/Publicaties/Geodesy/62Rabbani.html</ref> A more general approach for more than 3 dimensions requires search heuristics to remain feasible.<ref>Elke Achtert, Christian Böhm, Jörn David, Peer Kröger, Arthur Zimek: "Global Correlation Clustering Based on the Hough Transform", Statistical Analysis and Data Mining, vol 1(3), pp. 111-127, 2008. http://dx.doi.org/10.1002/sam.10012</ref>
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| Hough transform has also been used to find cylindrical objects in [[point cloud]]s using a two step approach. The first step finds the orientation of the cylinder and the second step finds the position and radius.<ref>Tahir Rabbani and Frank van den Heuvel, "Efficient hough transform for automatic detection of cylinders in point clouds" in Proceedings of the 11th Annual Conference of the Advanced School for Computing and Imaging (ASCI '05), The Netherlands, June 2005.</ref>
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| ===Using weighted features===
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| One common variation detail. That is, finding the bins with the highest count in one stage can be used to constrain the range of values searched in the next.
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| === Carefully chosen parameter space ===
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| A high-dimensional parameter space for the Hough transform is not only slow, but if implemented without forethought can easily overrun the available memory. Even if the programming environment allows the allocation of an array larger than the available memory space through virtual memory, the number of page swaps required for this will be very demanding because the accumulator array is used in a randomly accessed fashion, rarely stopping in contiguous memory as it skips from index to index.
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| Consider the task of finding ellipses in an 800x600 image. Assuming that the radii of the ellipses are oriented along principal axes, the parameter space is four-dimensional. (x,y) defines the center of the ellipse, and a and b denote the two radii. Allowing the center to be anywhere in the image, adds the constraint 0<x<800 and 0<y<600. If the radii are given the same values as constraints, what is left is a sparsely filled accumulator array of more than 230 billion values.
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| A program thus conceived is unlikely to be allowed to allocate sufficient memory. This doesn't mean that the problem can't be solved, but only that new ways to constrain the size of the accumulator array are to be found, which makes it feasible. For instance:
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| # If it is reasonable to assume that the ellipses are each contained entirely within the image, the range of the radii can be reduced. The largest the radii can be is if the center of the ellipse is in the center of the image, allowing the edges of the ellipse to stretch to the edges. In this extreme case, the radii can only each be half the magnitude of the image size oriented in the same direction. Reducing the range of a and b in this fashion reduces the accumulator array to 57 billion values.
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| # Trade accuracy for space in the estimation of the center: If the center is predicted to be off by 3 on both the x and y axis this reduces the size of the accumulator array to about 6 billion values.
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| # Trade accuracy for space in the estimation of the radii: If the radii are estimated to each be off by 5 further reduction of the size of the accumulator array occurs, by about 256 million values.
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| # Crop the image to areas of interest. This is image dependent, and therefore unpredictable, but imagine a case where all of the edges of interest in an image are in the upper left quadrant of that image. The accumulator array can be reduced even further in this case by constraining all 4 parameters by a factor of 2, for a total reduction factor of 16.
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| By applying just the first three of these constraints to the example stated about, the size of the accumulator array is reduced by almost a factor of 1000, bringing it down to a size that is much more likely to fit within a modern computer's memory.
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| ==== Efficient ellipse detection algorithm ====
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| Yonghong Xie and Qiang Ji give an efficient way of implementing the Hough transform for ellipse detection by overcoming the memory issues.<ref name="XieJi2002">{{cite doi|10.1109/ICPR.2002.1048464}}</ref> As discussed in the algorithm (on page 2 of the paper), this approach uses only a one-dimensional accumulator (for the minor axis) in order to detect ellipses in the image. The complexity is O(N<sup>3</sup>) in the number of non-zero points in the image.
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| ==Limitations==
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| The Hough transform is only efficient if a high number of votes fall in the right bin, so that the bin can be easily detected amid the background noise. This means that the bin must not be too small, or else some votes will fall in the neighboring bins, thus reducing the visibility of the main bin.<ref>{{cite web|url=http://homepages.inf.ed.ac.uk/rbf/HIPR2/hough.htm |title=Image Transforms - Hough Transform |publisher=Homepages.inf.ed.ac.uk |date= |accessdate=2009-08-17}}</ref>
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| Also, when the number of parameters is large (that is, when we are using the Hough transform with typically more than three parameters), the average number of votes cast in a single bin is very low, and those bins corresponding to a real figure in the image do not necessarily appear to have a much higher number of votes than their neighbors. The complexity increases at a rate of <!--Big-O(A<sup>m - 2</sup>)--><math>\mathcal{O}\left({A^{m-2}}\right)</math> with each additional parameter, where <math>A</math> is the size of the image space and <math>m</math> is the number of parameters. (Shapiro and Stockman, 310) Thus, the Hough transform must be used with great care to detect anything other than lines or circles.
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| Finally, much of the efficiency of the Hough transform is dependent on the quality of the input data: the edges must be detected well for the Hough transform to be efficient. Use of the Hough transform on noisy images is a very delicate matter and generally, a denoising stage must be used before. In the case where the image is corrupted by speckle, as is the case in radar images, the [[Radon transform]] is sometimes preferred to detect lines, because it attenuates the noise through summation.
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| == History == | |
| It was initially invented for machine analysis of [[bubble chamber]] photographs (Hough, 1959).
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| The Hough transform was patented as {{US patent|3069654}} in 1962 and assigned to the U.S. Atomic Energy Commission with the name "Method and Means for Recognizing Complex Patterns". This patent uses a slope-intercept parametrization for straight lines, which awkwardly leads to an unbounded transform space since the slope can go to infinity.
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| The rho-theta parametrization universally used today was first described in
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| :Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect Lines and Curves in Pictures," ''Comm. ACM, Vol. 15'', pp. 11–15 (January, 1972),
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| although it was already standard for the [[Radon transform]] since at least the 1930s.
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| O'Gorman and Clowes' variation is described in
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| :Frank O'Gorman, MB Clowes: Finding Picture Edges Through Collinearity of Feature Points. IEEE Trans. Computers 25(4): 449-456 (1976)
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| The story of how the modern form of the Hough transform was invented is given in
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| :Hart, P. E., "How the Hough Transform was Invented", ''IEEE Signal Processing Magazine, Vol 26, Issue 6'', pp 18 - 22 (November, 2009) .
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| ==See also== | |
| * [[Generalised Hough transform]]
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| * [[Randomized Hough transform]]
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| * [[Radon transform]]
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| * [[Fourier transform]]
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| ==References==
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| {{Reflist}}
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| ==External links==
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| * [http://cimg.sourceforge.net/screenshots.shtml hough_transform.cpp] - C++ code - example of CImg library ([[Open source software|open source]] library, [[C++]] source code, [[Grayscale]] images)
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| * http://www.rob.cs.tu-bs.de/content/04-teaching/06-interactive/Hough.html - [[Java Applet]] + Source for learning the Hough transformation in slope-intercept form
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| * http://www.rob.cs.tu-bs.de/content/04-teaching/06-interactive/HNF.html - [[Java Applet]] + Source for learning the Hough-Transformation in normal form
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| * http://www.sydlogan.com/deskew.html - Deskew images using Hough transform ([[Grayscale]] images, [[C++]] source code)
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| * http://imaging.gmse.net/articledeskew.html - Deskew images using Hough transform ([[Visual Basic]] source code)
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| * http://www.mitov.com/products/visionlab - [[Embarcadero Delphi|Delphi]], [[C++]] and [[.NET Framework|.NET]] free for educational purposes library containing Line, Circle and Line segment Hough transform components.
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| * [http://www.isprs.org/proceedings/XXXVI/3-W52/final_papers/Tarsha-Kurdi_2007.pdf Tarsha-Kurdi, F., Landes, T., Grussenmeyer, P., 2007a. Hough-transform and extended RANSAC algorithms for automatic detection of 3d building roof planes from Lidar data.] ISPRS Proceedings. Workshop Laser scanning. Espoo, Finland, September 12–14, 2007.
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| * [http://intopii.com/into/ Into] contains open source implementations of linear and circular Hough transform in C++
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| * http://www.vision.ime.usp.br/~edelgado/defesa/code/hough.html Hough-transform for Ellipse detection, implemented in C.
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| * [http://scikit-image.org/docs/dev/api/skimage.transform.html scikit-image] Hough-transform for line, circle and ellipse, implemented in Python.
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| {{DEFAULTSORT:Hough Transform}}
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| [[Category:Feature detection]]
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