基于Hough变换的椭圆检测方法

椭圆检测在图像、图形识别与计算机视觉领域中有着重要的应用,而基于Hough变换的椭圆检测是其中常见的方法之一。本文对基于Hough变换的椭圆检测算法进行了综述,其中包括利用三点确定椭圆的提取方法、基于弦中心Hough变换的提取算法和基于椭圆几何对称性算法等,着重对不同方法的原理、实现和优缺点进行了讨论。     

一种基于随机Hough变换的椭圆检测算法研究

提出了一种有效的基于随机Hough变换的椭圆检测算法(RED).该算法首先在图像中随机选择三个边缘点,并分别以这三个点为中心选取相同大小的窗口.利用最小二乘法对这三个窗口中的所有边缘点进行椭圆拟合,然后在图像中随机选取第四个边缘点,以判断图像中是否存在一个可能的椭圆.在找到一个可能的椭圆后,通过证据收集以进一步验证这个可能的椭圆是否真实存在.仿真实验和实际图像的实验表明本文算法比其它的算法具有速度快和精度高的优点.     

基于最大内切圆的椭圆孔组检测

针对当前一些椭圆孔组工件检测成本高、时效低等问题,提出了一种基于最大内切圆的椭圆孔组检测方法。首先对椭圆孔组图像进行去噪、二值化和边缘检测等预处理;再根据椭圆的几何性质,结合椭圆中心估计方法和最值距离选取方法,求出椭圆最大内切圆,从而确定椭圆的中心坐标、长短轴长和倾斜角。实验数据表明,该方法能对椭圆孔组进行快速精确检测,在估计出椭圆中心的基础上能快速截取有效椭圆弧,大幅减少无效采样;与基于中心估计Hough椭圆检测算法和基于最小二乘改进椭圆检测算法相比,具有耗时短、精度高等优点,可有效应用于椭圆孔组工件的自动化检测。     

一种识别SAR图像中椭圆目标的方法

提出了一种对SAR图像中的椭圆形目标进行自动识别的综合方法。它利用SAR图像所具有的统计特性、CFAR检测对SAR图像进行预处理。根据中心椭圆算法构造椭圆并计算以此灰度占空比系数,采用马氏距离从背景中识别出目标。实际SAR图像实验结果表明了该方法的有效性。     

一种新的不基于Hough变换的随机椭圆检测算法

椭圆检测在模式识别领域中占据着非常重要的位置。常见的基于Hough变换的椭圆检测算法(如RHT算法)存在着占用大量存储空间及计算耗时等缺点。本文提出一种高效随机的椭圆检测算法(RED)。该算法不基于Hough变换,其原理是:首先从一幅图像中随机地挑选出6个点,并定义一个约束距离以确定在此图像中是否存在一个可能的椭圆;当可能椭圆确定之后,引入椭圆点收集过程以进一步确定可能椭圆是否是待检测的真实椭圆。通过对具有不同噪声的合成图像以及真实图像进行测试,结果表明RED算法在低噪声与适度噪声的情况下,速度明显快于RHT算法。     

PCB检测中圆Mark的快速精确定位

高密度电路板在缺陷检测时获取的圆形标志有时会变形,从而影响检测精度。为此,提出一种求取最圆椭圆度的Mark点精确定位算法。该算法将检测的彩色图像转换成灰度图,采用Otus的阈值分割技术使Mark区域与背景相分离,对图像进行二值化,求取边缘点(图像轮廓)。对图像轮廓进行椭圆拟合后求取椭圆的外接矩形,将矩形长与宽之差与矩形宽之比小于0.1作为判据,判断所求的是否为最圆的椭圆,输出Mark点中心。仿真测试结果表明,该算法具有高速、抗干扰能力强和鲁棒性高的特点。     

一种随机多椭圆检测的快速算法

针对多椭圆检测问题提出了一种快速随机检测算法。该算法利用在图像中随机采样到的一个边缘点和局部搜索到的两个边缘点以及这三个点的邻域信息确定候选椭圆,再将候选椭圆变换为对应圆,通过确认真圆来确认真椭圆。在确定候选椭圆时,最大限度地减少随机采样点数﹑剔除更多的非椭圆点,降低了无效采样,减少了无效计算。数值实验结果表明：该算法具有良好的鲁棒性,其检测速度比同类算法快。     

基于边界的最小二乘椭圆拟合改进算法

由于变电站巡检机器人停靠位置和云台转动的偏差,拍摄所获得的图像中仪表位置会有较大不同。为解决图像中仪表的定位问题,文中提出了一种快速地利用边界提取椭圆形目标的方法,可有效地解决图像中圆形目标的提取。原有最小二乘椭圆拟合算法对图像边界上所有样本点都参与运算,所以会对椭圆拟合的最后结果产生偏差且耗时较长。针对这种情况,采取边界的最小二乘拟合算法,依次取图像边缘提取后的边界,逐段拟合椭圆,并对拟合出的椭圆进行评估,选取适合待检测目标的椭圆区域,具有快速高效、定位准确等特点。最后,通过合成图像和实际图像的应用验证了算法能够拟合出具有高精度的椭圆,能够有效地处理仪表表盘的提取。     

瞳孔亚像素边缘检测与中心定位

为提高视线跟踪系统的分辨率和精确度,提出了一种亚像素精度的边缘检测与中心定位算法。利用设计的一维边缘检测算子对瞳孔像素级边缘点进行提取,然后利用边缘点小邻域内梯度方向上图像信息,进行亚像素边缘位置检测,最后经椭圆拟合确定瞳孔中心的精确位置及瞳孔形状参数。仿真实验验证了算法的有效性,提出的算法已被成功应用于实时视线跟踪系统中。     

基于局部搜索的多椭圆随机检测算法

随机采样2个图像点后再分别在这2点相关的3条线段上搜索1个图像点。利用采样的2个图像点和搜索的3个图像点决定侯选椭圆。当采样和搜索图像点时,通过识别和剔除孤立、半连续噪声和不在同一个真椭圆上的图像点,显著地减少了无效采样及无效计算。在确认真椭圆时,文中方法将椭圆变换成对应圆,通过确认真圆来确认真椭圆并直接控制椭圆的检测精度。数值实验结果表明:该文算法在检测多个椭圆时的检测效率和鲁棒性等方面都具有良好的性能。     

A fast and effective ellipse detector for embedded vision applications

Several papers addressed ellipse detection as a first step for several computer vision applications, but most of the proposed solutions are too slow to be applied in real time on large images or with limited hardware resources. This paper presents a novel algorithm for fast and effective ellipse detection and demonstrates its superior speed performance on large and challenging datasets. The proposed algorithm relies on an innovative selection strategy of arcs which are candidate to form ellipses and on the use of Hough transform to estimate parameters in a decomposed space. The final aim of this solution is to represent a building block for new generation of smart-phone applications which need fast and accurate ellipse detection also with limited computational resources.     

一种基于变形模板的椭圆提取算法

针对普通的动态轮廓算法对曲线仅提供有限的连续与正则性约束,虽然带来了局部的灵活性,却丧失了全局的完整性,从而导致轮廓提取结果强烈敏感于图像噪声及邻近边缘点,针对这一问题,给出了一种基于椭圆变形模板的椭圆提取新算法。该算法使用一种基于椭圆形状约束的变形模板,由于其能量最小化过程直接在椭圆的参数空间中进行,从而可保证提取的结果一定是椭圆。此外,算法还容许同时提取多个椭圆,并可充分利用各个椭圆参数及其相关性(例如同心椭圆)等先验知识来实现快速、准确、鲁棒的椭圆提取。仿真结果与实际图像应用表明,该新算法是有效的。     

Application of the Fisher-Rao Metric to Ellipse Detection

The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm.     

基于边界曲线弧分割的多椭圆检测

不同于传统的Hough变换算法,提出一种基于边界弧分割的椭圆检测方法。首先将边界从交点处分割成弧段,将得到弧段划分为长弧和短弧两组并按长度降序排序,然后从两组中找出属于某个椭圆的若干弧段,利用最小二乘法拟合得到候选椭圆并验证是否为真正椭圆。实验表明该算法能快速检测出图中椭圆,运行时间远小于采用随机Hough变换算法,在具有噪声、椭圆残缺的情况下仍能有较好的检测结果。     

Multi-ellipses detection on images inspired by collective animal behavior

This paper presents a novel and effective technique for extracting multiple ellipses from an image. The approach employs an evolutionary algorithm to mimic the way animals behave collectively assuming the overall detection process as a multi-modal optimization problem. In the algorithm, searcher agents emulate a group of animals that interact with each other using simple biological rules which are modeled as evolutionary operators. In turn, such operators are applied to each agent considering that the complete group has a memory to store optimal solutions (ellipses) seen so far by applying a competition principle. The detector uses a combination of five edge points as parameters to determine ellipse candidates (possible solutions), while a matching function determines if such ellipse candidates are actually present in the image. Guided by the values of such matching functions, the set of encoded candidate ellipses are evolved through the evolutionary algorithm so that the best candidates can be fitted into the actual ellipses within the image. Just after the optimization process ends, an analysis over the embedded memory is executed in order to find the best obtained solution (the best ellipse) and significant local minima (remaining ellipses). Experimental results over several complex synthetic and natural images have validated the efficiency of the proposed technique regarding accuracy, speed, and robustness.     

局部PCA参数约束的Hough多椭圆分层检测算法

针对随机Hough变换(RHT)在复杂图像中检测圆及椭圆时随机采样所造成的大量无效采样、无效累积以及运算时间长等问题,提出基于局部PCA感兴趣参数约束Hough多椭圆分层检测思路。首先利用边缘检测算子获得边缘信息并去除边缘交叉点,在边缘图像中标记并提取出满足一定长度的连续曲线段;其次利用线段PCA方向分析确定是否属于有效曲线段;然后,对所有感兴趣曲线段按照标记顺序依次利用椭圆拟合办法初步得到感兴趣椭圆粗略参数,根据拟合结果进而模糊约束Hough变换参数搜索范围,得到精确椭圆参数;最后利用检测结果更新图像空间,删除已经检测到的椭圆,依次进行,直到所有椭圆检测完毕。实验结果表明,该算法在计算、存储消耗上均大大减少。     

Projective reconstruction of ellipses from multiple images

This paper presents a new approach for reconstructing 3D ellipses (including circles) from a sequence of 2D images taken by uncalibrated cameras. Our strategy is to estimate an ellipse in 3D space by reconstructing N(≥5) 3D points (called representative points) on it, where the representative points are reconstructed by minimizing the distances from their projections to the measured 2D ellipses on different images (i.e., 2D reprojection error). This minimization problem is transformed into a sequence of minimization sub-problems that can be readily solved by an algorithm which is guaranteed to converge to a (local) minimum of the 2D reprojection error. Our method can reconstruct multiple 3D ellipses simultaneously from multiple images and it readily handles images with missing and/or partially occluded ellipses. The proposed method is evaluated using both synthetic and real data.     

基于中点提取的椭圆检测算法

针对Hough变换检测椭圆时存在运算速度慢、需要大量储存空间的问题,提出一种快速的随机椭圆检测算法。该算法随机采样2点并搜索第3点,再利用椭圆极径性质求出椭圆中心坐标,接着通过坐标变换得到简化的椭圆方程,解方程组求出椭圆剩下的参数。在证据收集确认候选椭圆时,只选取椭圆外切矩形内的边缘点,同时利用特殊的累积记录函数对候选椭圆参数进行进一步判别。实验结果表明,该算法具有检测速度快、精度高、抗椭圆部分缺失的能力强等优点。