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。     

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。     

Ellipse,arc of ellipse and elliptic spline

A general method for generating ellipses by using conjugate radii is presented. Elliptical arcs are then defined based on this method for generating ellipses. A 90° arc of ellipse is then used to generate a number of curves with slope constraints. Other arc of ellipse interpolations are then discussed. Three of these interpolations are used to define local elliptic splines with first order derivative continuity.     

板材排样问题中不规则多边形优化组合策略研究

板材排样问题是从一组给定的矩形（或非矩形）板材上切割出一批规则的和不规则形状的零件，且使板材的耗费最低。本文研究不规则多边形优化组合策略，提出一种相同零件受限递归组合算法。     

基于直线段跟踪的手绘图元离线识别方法*

手绘图形是人类思维外化和表达意图的一种有效方式,如何有效地提取手绘在图纸上的图形元素是理解绘图者意图的关键问题。鉴于手绘图形是由基本图元组合构成,采用层次结构逐步实现图元提取的思想,提出了一种手绘基本图元（线段、弧、圆和椭圆）的离线识别方法。在提取图形笔画骨架像素的基础上,跟踪骨架像素得到图形的直线段描述;通过对直线段序列的分析,进行直线段序列的断开和连接处理,形成图元的曲线段描述,通过对图元曲线段描述的分析得出图元的几何参数。实验表明,该方法能够以高精确度快速识别出图像中包含的手绘图元,具有良好的稳定性     

Calculating ellipse overlap areas

We present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse. Overlap between two ellipses is calculated by combining the areas of appropriate segments and polygons in each ellipse. For four of the ten possible orientations of two ellipses, the method requires numerical determination of transverse intersection points. Approximate intersection points can be determined by solving the two implicit ellipse equations simultaneously. Alternative approaches for finding transverse intersection points are available using tools from algebraic geometry, e.g., based on solving an Eigen-problem that is related to companion matrices of the two implicit ellipse curves. Implementations in C of several algorithm options are analyzed for accuracy, precision and robustness with a range of input ellipses.     

Recognition of overlapping elliptical objects in a binary image

Recognition of overlapping objects is required in many applications in the field of computer vision. Examples include cell segmentation, bubble detection and bloodstain pattern analysis. This paper presents a method to identify overlapping objects by approximating them with ellipses. The method is intended to be applied to complex-shaped regions which are believed to be composed of one or more overlapping objects. The method has two primary steps. First, a pool of candidate ellipses are generated by applying the Euclidean distance transform on a compressed image and the pool is filtered by an overlaying method. Second, the concave points on the contour of the region of interest are extracted by polygon approximation to divide the contour into segments. Then, the optimal ellipses are selected from among the candidates by choosing a minimal subset that best fits the identified segments. We propose the use of the adjusted Rand index, commonly applied in clustering, to compare the fitting result with ground truth. Through a set of computational and optimization efficiencies, we are able to apply our approach in complex images comprised of a number of overlapped regions. Experimental results on a synthetic data set, two types of cell images and bloodstain patterns show superior accuracy and flexibility of our method in ellipse recognition, relative to other methods.

     

Edge curvature and convexity based ellipse detection method

In this paper, we propose a novel ellipse detection method for real images. The proposed method uses the information of edge curvature and their convexity in relation to other edge contours as clues for identifying edge contours that can be grouped together. A search region is computed for every edge contour that contains other edge contours eligible for grouping with the current edge contour. A two-dimensional Hough transform is performed in an intermediate step, in which we use a new ‘relationship score’ for ranking the edge contours in a group, instead of the conventional histogram count. The score is found to be more selective and thus more efficient. In addition, we use three novel saliency criteria, that are non-heuristic and consider various aspects for quantifying the goodness of the detected elliptic hypotheses and finally selecting good elliptic hypotheses. The thresholds for selection of elliptic hypotheses are determined by the detected hypotheses themselves, such that the selection is free from human intervention. The method requires a few seconds in most cases. So, it is suitable for practical applications. The performance of the proposed ellipse detection method has been tested on a dataset containing 1200 synthetic images and the Caltech 256 dataset containing real images. In both cases, the results show that the proposed ellipse detection method performs far better than existing methods and is close to the ideal results, with precision, recall, and F-measure, all very close to 1. Further, the method is robust to the increase in the complexity of the images (such as overlapping ellipses, occluded ellipses), while the performance of the contemporary methods deteriorates significantly.     

Ellipse Motion Estimation Using Parametric Snakes

In this paper we propose a multiscale parametric snake model for ellipse motion estimation across a sequence of images. We use a robust ellipse parameterization based on the geometry of the intersection of a cylinder and a plane. The ellipse parameters are optimized in each frame by searching for local minima of the snake model energy including temporal coherence in the ellipse motion. One advantage of this method is that it just considers the convolution of the image with a Gaussian kernel and its gradient, and no edge detection is required. A detailed study about the numerical evaluation of the snake energy on ellipses is presented. We propose a Newton–Raphson-type algorithm to estimate a local minimum of the energy. We present some experimental results on synthetic data, real video sequences and 3D medical images.     

Generation of anisotropic mesh by ellipse packing over an unbounded domain

With the advance of the finite element method, general fluid dynamic and traffic flow problems with arbitrary boundary definition over an unbounded domain are tackled. This paper describes an algorithm for the generation of anisotropic mesh of variable element size over an unbounded 2D domain by using the advancing front ellipse packing technique. Unlike the conventional frontal method, the procedure does not start from the object boundary but starts from a convenient point within an open domain. The sequence of construction of the packing ellipses is determined by the shortest distance from the fictitious centre in such a way that the generation front is more or less a circular loop with occasional minor concave parts due to element size variation. As soon as an ellipse is added to the generation front, finite elements are directly generated by properly connecting frontal segments with the centre of the new ellipse. Ellipses are packed closely and in contact with the existing ellipses by an iterative procedure according to the specified anisotropic metric tensor. The anisotropic meshes generated by ellipse packing can also be used through a mapping process to produce parametric surface meshes of various characteristics. The size and the orientation of the ellipses in the pack are controlled by the metric tensor as derived from the principal surface curvatures. In contrast to other mesh generation schemes, the domain boundary is not considered in the process of ellipse packing, this reduces a lot of geometrical checks for intersection between frontal segments. Five examples are given to show the effectiveness and robustness of anisotropic mesh generation and the application of ellipse packing to mesh generation over various curved surfaces.     

Detection of incomplete ellipse in images with strong noise by iterative randomized Hough transform (IRHT)

An iterative randomized Hough transform (IRHT) is developed for detection of incomplete ellipses in images with strong noise. The IRHT iteratively applies the randomized Hough transform (RHT) to a region of interest in the image space. The region of interest is determined from the latest estimation of ellipse parameters. The IRHT “zooms in” on the target curve by iterative parameter adjustments and reciprocating use of the image and parameter spaces. During the iteration process, noise pixels are gradually excluded from the region of interest, and the estimation becomes progressively close to the target. The IRHT retains the advantages of RHT of high parameter resolution, computational simplicity and small storage while overcoming the noise susceptibility of RHT. Indivisible, multiple instances of ellipse can be sequentially detected. The IRHT was first tested for ellipse detection with synthesized images. It was then applied to fetal head detection in medical ultrasound images. The results demonstrate that the IRHT is a robust and efficient ellipse detection method for real-world applications.     

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.     

Real-time system for elliptical-based face detection

In this paper, we present a real-time ellipse detector in gray scale images with a new multiple stage architecture based on a 3-accumulator version of the Fast Hough Transform with a previous Canny edge extraction. The system can be applied to detect different elliptical objects and is robust to incomplete ellipses, cluttered backgrounds and illumination changes. It achieves 12 frames per second on a PC Pentium 4, 2.80 GHz. Experimental results, focusing on faces, with both static and video images are showed. The presented ellipse detector can be used as a preprocessing module in a face tracking or recognition application.     

Projectively invariant decomposition and recognition of planar shapes

An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented. by ellipses. The method is invariant to projective transformations of the shape, and thus the conic primitives can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and it is based on finding ellipses with four points of contact to the given shape. The cross ratio computed from the four points on the ellipse can then be used as a projectively invariant index. It is demonstrated that a given shape has a unique parameter-free decomposition into a finite set of ellipses with unit cross ratio. For a given shape, each pair of ellipses can be used to compute two independent projective invariants. The set of invariants computed for each ellipse pair can be used as indexes to a hash table from which model hypothesis can be generated Examples of shape decomposition and recognition are given for synthetic shapes and shapes extracted from grey level images of real objects using edge detection.     

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。     

On the Use of Neural Networks and Geometrical Criteria for Localisation of Highly Irregular Elliptical Shapes

Detection of elliptical shapes is of extreme importance in several computer vision applications. In this paper a new method for irregular elliptical shapes localisation in multi-connected regions is described. This method first computes a set of elementary arc segments, which is then aggregated using geometrical decision criteria and a posteriori aggregation probabilities obtained from a neural network for Bayes classification. To identify and characterise the elementary arc segments, a cluster identification, a contour grouping strategy and some extensions to Fitzgibbon’s ellipse fitting method are introduced. These methods are applied successfully in the set-up of an automatic lime granule inspection system. The algorithm has proven to be very robust, since it is able to correctly detect elliptical shapes even when noisy data are present. Received: 2 November 1998, Received in revised form: 14 April 1999, Accepted: 6 May 1999     

基于中心估计的椭圆检测

椭圆检测在图像理解中有重要的作用。为克服标准Hough变换对时空需求高的缺点,设计了一种改进算法。通过椭圆对称特性估计图像中可能存在的椭圆中心,利用长轴确定椭圆中心及夹角参数只需一维累积数组对椭圆短轴的投票,采用聚类分析技术将检测到的虚椭圆归类到对应的真实椭圆。对合成图像和实际图像的实验表明算法的正确和高效。     

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.     

Splitting touching cells based on concave points and ellipse fitting

A new touching cells splitting algorithm based on concave points and ellipse fitting is proposed in this paper. The algorithm includes two parts: contour pre-processing and ellipse processing. The purpose of contour pre-processing is to smooth fluctuations of the contour, find concave points of the contour and divide the contour into different segments via the concave points. The purpose of ellipse processing is to process the different segments of the contour into possible single cells by using the properties of the fitted ellipses. Because concave points divide the whole contour of touching cells into different segments and different segments of one single cell have similar properties, the ellipse processing can separate the touching cells through ellipse fitting. This paper demonstrates a new way of using ellipse fitting to split the binary contour of touching cells. Experimental results show that our algorithm is efficient.     

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。