基于Hough变换的圆检测方法

总结了圆检测的几种常用方法,如经典HT、随机HT和广义HT.结合几种方法的优缺点,提出了一种基于经典HT的改进Hough变换圆检测方法.该方法先对图像进行预处理,如灰度化、去噪滤波、边缘检测以及运用数学形态学等,然后进行Hough变换.其主要思想是用多维数组来代替经典的循环过程.把Hough变换应用到织物防水性能自动测试的真实图像中,通过对经典Hough变换与改进后的Hough变换的比较,可以看出检测速度有所提高,检测精度也达到了令人满意的程度.     

A formal definition of the Hough transform: Properties and relationships

Shape, in both 2D and 3D, provides a primary cue for object recognition and the Hough transform (P.V.C. Hough, U.S. Patent 3,069,654, 1962) is a heuristic procedure that has received considerable attention as a shape-analysis technique. The literature that covers application of the Hough transform is vast; however, there have been few analyses of its behavior. We believe that one of the reasons for this is the lack of a formal mathematical definition. This paper presents a formal definition of the Hough transform that encompasses a wide variety of algorithms that have been suggested in the literature. It is shown that the Hough transform can be represented as the integral of a function that represents the data points with respect to a kernel function that is definedimplicitly through the selection of a shape parameterization and a parameter-space quantization. The kernel function has dual interpretations as a template in the feature space and as a point-spread function in the parameter space. A novel and powerful result that defines the relationship between parameterspace quantization and template shapes is provided. A number of interesting implications of the formal definition are discussed. It is shown that the Radon transform is an incomplete formalism for the Hough transform. We also illustrate that the Hough transform has the general form of a generalized maximum-likelihood estimator, although the kernel functions used in estimators tend to be smoother. These observations suggest novel ways of implementing Hough-like algorithms, and the formal definition forms the basis of work for optimizing aspects of Hough transform performance (see J. Princen et. al.,Proc. IEEE 3rd Internat. Conf. Comput. Vis., 1990, pp. 427–435).This work was supported by the Ministry of Defence, Royal Aerospace Establishment, U.K.     

随机Hough变换实现角点检测

为实现角点的有效检测,提高检测速度,提出一种基于随机 Hough变换的角点检测方法。利用随机 Hough变换求取出直线参数;根据角点在 Hough空间中的特征,利用反 Hough变换的反演原理对参数空间中的峰值进行反变换,定位图像空间中的直线交点;为避免虚假角点,将那些附近不包含任何边缘的交点删除,得到正确的角点。实验结果表明,该方法相对于 Harris算法和SUSAN具有更好的准确性、鲁棒性和稳定性,实时性也有一定提高。     

The 3-D Hough shape transform

The 3-D Hough shape transform is described which is used for the localization in space of 3-D objects defined in terms of the spatial organization of their features.     

Discretization errors in the Hough transform

Straight line-segments in a two-dimensional image can be detected with the Hough transform by searching peaks in a parameter space. The influence on the Hough transform of the quantization of the parameter space, the quantization of the image and the width of the line-segment is investigated in this paper.

The Hough transform was improved by O'Gorman and Clowes by taking into account the gradient direction. The resulting scatter of the peaks can be reduced by using a weighting function in the transform. Examples of asbestos preparations are given.     

Accurate and efficient curve detection in images: the importance sampling Hough transform

The Hough transform is a well known technique for detecting parametric curves in images. We place a particular group of Hough transforms, the probabilistic Hough transforms, in the framework of importance sampling. This framework suggests a way in which probabilistic Hough transforms can be improved: by specifying a target distribution and weighting the sampled parameters accordingly to make identification of curves easier. We investigate the use of clustering techniques to simultaneously identify multiple curves in the image. We also use probabilistic arguments to develop stopping conditions for the algorithm. Results from applying our method and two popular versions of the Hough transform to both simulated and real data are shown.     

An unsupervised generalized Hough transform for natural shapes

The Hough transform was originally designed to recognize artifical objects in images. A Hough transform for natural shapes (HTNS) was subsequently proposed, but necessitates the supervised learning of the class of shapes. Here, we extend HTNS to unsupervised pattern recognition, the variability of the object class being coded with tools originating from mathematical morphology (erosion, dilation and distance functions).     

Analysis of textual images using the Hough transform

The analysis of images of printed pages of text is considered. Since printed text can be viewed as textured line, the use of the Hough transform for detecting straight lines is proposed as an analysis tool. Methods for handling several discretization problems that arise in mapping the rectangular image space to the (, ) accumulator array are described. Several applications of analyzing the accumulator array are proposed. They include detecting the text skew angle, determining the signature of a text line so as to accept or reject a block as containing only text, using profile analysis to segment text into lines, and determining whether a textual block is rightside-up or otherwise.     

基于Hough变换的煤岩界面识别方案

根据煤层与岩石层分界明显且呈线状的煤岩图像特征,提出一种基于Hough变换的煤岩界面识别方案。首先对煤岩图像进行去噪与增强预处理,然后去除煤与岩石边缘的孤立点与虚假边缘,最后采用Hough变换识别煤岩分界线。实验结果表明,该方案能够较快、较准确地检测出煤岩分界线。     

Computing the Hough transform on a pyramid architecture

An algorithm to implement the Hough transform for the detection of a straight line on a pyramidal architecture is presented. The algorithm consists of two phases. The first phase, called block-projection, takes constant time. The second phase, called block-combination, is repeated logn times and takes a total ofO(n ^1/2) time for the detection of all straight lines having a given slope on an n×n image; if there arep different slopes to be detected, then the total time becomesO(pn ^1/2).     

Extended Hough transform for linear feature detection

Improving the accuracy of line segment detection reduces the complexity of subsequent high-level processing common in cartographic feature detection. We developed a new extension to the Hough transform and reported on its application to building extraction. We expanded the Hough space by a third parameter, the horizontal or vertical coordinate of the image space, to provide incremental information as to the length of the lineal feature being sought. Using this extended HT transform allowed us to more accurately detect the true length of a line segment. In addition, we used a Bayesian probabilistic approach to process our extended Hough space that further increased the accuracy of our extended Hough transform.     

Hough transform for feature detection in panoramic images

Omni-directional sensors are useful in obtaining a 360° field-of-view. With a radially symmetric mirror and conventional lens system this can be achieved with a single camera. There are several proposed profiles for the mirror, but most violate the single viewpoint (SVP) criteria necessary to allow functional equivalence to the standard perspective projection, posing challenges that have not yet been addressed in the literature. Such a imaging system with a non-SVP optical system do not benefit from the affine quality of straight line features being represented as collinear points in the image plane. To utilize these non-SVP mirrors, a new method to recognize such features is required. This work describes an approach to detecting features in panoramic non-SVP images using a modified Hough transform. A mathematical model for this feature extraction process is given. Experimental results are presented to validate this model and show robust performance in identifying line features with only estimated calibration.     

On improving the accuracy of the Hough transform

The subject of this paper is very high precision parameter estimation using the Hough transform. We identify various problems that adversely affect the accuracy of the Hough transform and propose a new, high accuracy method that consists of smoothing the Hough arrayH(, ) prior to finding its peak location and interpolating about this peak to find a final sub-bucket peak. We also investigate the effect of the quantizations and ofH(, ) on the final accuracy. We consider in detail the case of finding the parameters of a straight line. Using extensive simulation and a number of experiments on calibrated targets, we compare the accuracy of the method with results from the standard Hough transform method of taking the quantized peak coordinates, with results from taking the centroid about the peak, and with results from least squares fitting. The largest set of simulations cover a range of line lengths and Gaussian zero-mean noise distributions. This noise model is ideally suited to the least squares method, and yet the results from the method compare favorably. Compared to the centroid or to standard Hough estimates, the results are significantly better—for the standard Hough estimates by a factor of 3 to 10. In addition, the simulations show that as and are increased (i.e., made coarser), the sub-bucket interpolation maintains a high level of accuracy. Experiments using real images are also described, and in these the new method has errors smaller by a factor of 3 or more compared to the standard Hough estimates.     

Generalizing the Hough transform to detect arbitrary shapes

The Hough transform is a method for detecting curves by exploiting the duality between points on a curve and parameters of that curve. The initial work showed how to detect both analytic curves^(1,2) and non-analytic curves,⁽³⁾ but these methods were restricted to binary edge images. This work was generalized to the detection of some analytic curves in grey level images, specifically lines,⁽⁴⁾ circles⁽⁵⁾ and parabolas.⁽⁶⁾ The line detection case is the best known of these and has been ingeniously exploited in several applications.^(7,8,9)We show how the boundaries of an arbitrary non-analytic shape can be used to construct a mapping between image space and Hough transform space. Such a mapping can be exploited to detect instances of that particular shape in an image. Furthermore, variations in the shape such as rotations, scale changes or figure ground reversals correspond to straightforward transformations of this mapping. However, the most remarkable property is that such mappings can be composed to build mappings for complex shapes from the mappings of simpler component shapes. This makes the generalized Hough transform a kind of universal transform which can be used to find arbitrarily complex shapes.     

A method for detection of circular arcs based on the Hough transform

The circular arc is a very useful feature for object detection and recognition in industrial environments. In this paper, a method for detection of circular arcs is described that is based on the Hough transform. The method estimates all five arc parameters and is robust in the presence of a moderate amount of noise. It has a computational and memory complexity ofO(n·m·R) andO(n·m) respectively, wheren andm are the sizes in thex andy directions andR is the maximum expected arc radius in pixels. Arcs as small as 45 degrees and radii down to 4 pixels can be detected. The computing time is almost independent of the number of circular arcs in the image.This work was supported by the Swedish Board for Technical Development, Grant No. 87-01954P.     

A Hough transform based line recognition method utilizing both parameter space and image space

Hough Transform (HT) is recognized as a powerful tool for graphic element extraction from images due to its global vision and robustness in noisy or degraded environment. However, the application of HT has been limited to small-size images for a long time. Besides the well-known heavy computation in the accumulation, the peak detection and the line verification become much more time-consuming for large-size images. Another limitation is that most existing HT-based line recognition methods are not able to detect line thickness, which is essential to large-size images, usually engineering drawings. We believe these limitations arise from that these methods only work on the HT parameter space. This paper therefore proposes a new HT-based line recognition method, which utilizes both the HT parameter space and the image space. The proposed method devises an image-based gradient prediction to accelerate the accumulation, introduces a boundary recorder to eliminate redundant analyses in the line verification, and develops an image-based line verification algorithm to detect line thickness and reduce false detections as well. It also proposes to use pixel removal to avoid overlapping lines instead of rigidly suppressing the N×N neighborhood. We perform experiments on real images with different sizes in terms of speed and detection accuracy. The experimental results demonstrate the significant performance improvement, especially for large-size images.     

An improved generalized Hough transform for the recognition of overlapping objects

The generalized Hough transform (GHT) is a powerful method for recognizing arbitrary shapes as long as the correct match accounts for both much of the model and much of the sensory object. For moderate levels of occlusion, however, the GHT can hypothesize many false solutions. In this paper, we present an improved two-stage GHT procedure for the recognition of overlapping objects. Each boundary point in the image is described by three features including the concavity, radius and normal direction of the curve segment in the neighborhood of the point. The first stage of the voting process determines the rotational angle of the sensory object with respect to the model by matching those points that have the same concavity and radii. The second stage then determines the centroid of the sensory object by matching those points that have the same concavity, radii and rotational angles. The three point features remove the false contribution of votes in the vote generation phase. Experimental results have shown that the proposed algorithm works well for complex objects under severely overlapping conditions.     

并行Hough变换快速航迹起始

Hough变换在航迹起始领域得到广泛应用,但在扫描次数较少时起始效果不佳。通过转变Hough变换处理结构和改变计数器累加方式,提出了一种并行Hough变换快速航迹起始算法。利用Hough变换将不同时刻的量测集合分别映射到参数空间,继而将空间中具有相同索引的各次累加结果构成累加向量,统计其非零元素的个数,如大于预先设定的门限,则用向量各元素求和作为累加结果,否则置零。将利用该方法获得最终的累加结果进行门限检测来确定是否起始航迹。仿真实验表明,该算法可在密集环境下快速准确地起始航迹。     

基于Hough变换的植物叶脉检测新方法

针对植物叶脉的特点,提出了利用灰度拉伸、Hough变换与边缘生长、图像腐蚀与膨胀进行植物叶脉检测的新方法。在该方法中,Hough变换检测植物叶脉图像的同时也较好的消除了图像噪声,该方法应用到植物叶脉检测中效果较好。     

Geometrically invariant watermarking: synchronization through circular Hough transform

This paper addresses a geometrically invariant watermarking method for digital images. Most previous watermarking algorithms perform weakly against geometric distortions, which desynchronize the location for the inserted watermark. Watermark synchronization, which is a process for finding the location for watermark insertion and detection, is crucial for robust watermarking. In this paper, we propose a watermarking method that is robust to geometric distortions. In order to synchronize the location for watermark insertion and detection, we use circular Hough transform, which extracts circular features that are invariant to geometric distortions. The circular features are then watermarked using additive way on the spatial domain. Our method belongs to the category of blind watermarking techniques, because we do not need the original image during detection. Experimental results support the contention that our method is useful and considerably robust against both geometric distortion attacks and signal processing attacks as listed in Stirmark 3.1.