用于查找曲线段的霍夫变换 [英] Hough Transform for finding curve segments

问题描述

霍夫变换可用于从图像中提取线条.它也可以用来提取曲线——虽然这有点困难，因为更高维的霍夫变换会消耗资源.我想知道是否如何将霍夫变换限制为 3 阶曲线的 2D 投票空间，即 x^{3}+ax^{2}+bx+c ?

Hough Transform can be used to extract lines from images. It can also be used to extract curves - this is a little harder though because higher dimensional Hough transforms are resource consuming. I was wondering whether how one restricts the Hough transform to 2D voting space for a curve of order 3 i.e. x^{3}+ax^{2}+bx+c ?

任何人都知道任何解释这一点的好网站(似乎找不到任何网站).或者如果没有，请在此处解释:).

Anyone know any good sites explaining this (can't seem to find any). Or an explanation here if there isn't one :).

推荐答案

广义霍夫变换的精髓在于，累加器的边"就是你要找的答案.如果您尝试匹配椭圆或任意曲线 - 在您的情况下为 a、b、c 参数，那么您应该构建 3D 累加器并在那里寻找最大值.谷歌使用霍夫变换的椭圆检测"或使用霍夫变换的任意形状检测".

The essence of the Generalised Hough Transform that the "sides" of the accumulator is the answer you are looking for. If you are trying to match ellipses or arbitrary curves - in your case a, b, c parameters then you should build 3D accumulator and look for maximum there. Google "ellipse detection using hough transform" or "arbitrary shape detection using hough transform".

在多维累加器中有很多方法可以优化您的搜索，所以不要害怕构建多维 HT 参数化空间 - 它可以让您很好地了解您的问题.

There are many way to optimise your search in multi dimensional accumulator, so don't be afraid to build multidimensional HT parameterised space - it can give you good overview of your problem.

您可能希望将搜索分为两个阶段 - 例如为您的 a 和 b 参数构建一个经典的 2D，然后使用非常简单的 1D 累加器来查找 c，这已在边缘检测中完成，但请注意，这如果 a、b、c 相互依赖，拆分可能会引入大错误.

You may want to split your search into two stage - for example build a classic 2D for your a and b parameters, then use very simple 1D accumulator for finding c, this has been done in edge detection, but be aware that this split can introduce large errors if you a,b,c interdependent.

优化多维霍夫变换的方法:(概率)随机霍夫变换、混合和多维霍夫变换.

Ways to optimise multidimensional Hough Transform: (Probabilistic) Randomised Hough transform, Hybrid and Multidimensional Hough Transform.

此外，广义霍夫变换和 Radon 变换几乎是同义词，因此对于任意形状检测，Radon 变换"可能会给您更好的想法:Hough 变换是连续 Radon 变换的离散版本.

Also Generalised Hough Transform and Radon Transform are nearly synonymous, so for arbitrary shape detection "Radon transform" may give you better ideas: Hough Transform is a discrete version of continuous Radon Transform.

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