霍夫变换用于查找曲线段 [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。它也可以用于提取曲线 - 这是一个有点困难，但是因为更高维度的霍夫变换是资源消耗。我想知道如何将一个限制Hough变换的二维投票空间为一个3阶的曲线即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 ?

任何人都知道任何好的网站解释这（似乎找不到任何）。

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

通用霍夫变换的本质是侧面的累加器是你正在寻找的答案。如果你试图匹配椭圆或任意曲线 - 在你的情况下，a，b，c参数，那么你应该建立3D累加器，寻找最大值。 Google使用hough变换的椭圆检测或使用hough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".

有很多方法可以优化多维累加器中的搜索，害怕建立多维的HT参数化空间 - 它可以给你良好的概述你的问题。

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.

你可能想把搜索分成两个阶段 - 例如构建一个经典2D为您的a和b参数，然后使用非常简单的1D累加器找到c，这已经在边缘检测，但要注意，如果你a，b，c相互依赖，这种分裂可能会引入大的错误。

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.

通用Hough变换和Radon变换几乎是同义词，因此对于任意形状检测，Radon变换可能给你更好的想法：Hough变换是连续Radon的离散版本转变。

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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