Performance Prediction of the Hough Transform

Based on hree different implementation schemes,this paper strongly demonstrates that the performance of the Hough transform depends crucially on its implementation sceme when it is used for line detection.Moreover,the obtained results can be used as a theoretical basis to predict the performance of the Hough transform as well as to eliminate the noise in Hough space coming from image noise.     

基于Hough变换的圆形物体的检测

Hough变换在图像处理中占有重要地位,但本身具有存储空间大、计算时间长的缺点。利用圆的几何特性,针对Hough变换的缺点进行改进,并将其应用到图像中存在多个圆的情况。实验表明:该算法能较好地减少存储空间,并降低计算时间,同时,能很好地对图像中多个圆进行检测。     

O(log n) bimodality analysis

The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P₁ and P₂. If P is a mixture of two (approximately) Gaussian subpopulations, then P₁ and P₂ are good approximations to the original Gaussians, if their Fisher distance is great enough. Moreover, good approximations to P₁ and P₂ can be obtained by dividing P into small parts; finding the maximum-distance (MD) subdivision of each part; combining small groups of these subdivisions into (approximate) MD subdivisions of larger parts; and so on. This divide-and-conquer approach yields an approximate MD subdivision of P in O(log n) computational steps using O(n) processors, where n is the size of P.     

快速随机Hough变换多圆检测算法

随机Hough变换是检测圆的一种有效方法,但在处理多圆复杂图像时随机采样带来的大量无效累积会导致计算量过大。文中提出一种基于随机Hough变换的快速多圆检测算法,除去三类噪声点,通过随机采样到的一点按照一定规则搜索另外两点来确定候选圆,用原始图像对候选圆进行证据积累以判断是否为真圆。理论分析和实验结果表明：该算法较其他算法能更快地检测出图像中的多个圆,具有较好的应用价值。     

Fourier extension and hough transform for multiple component FM signal analysis

Conventional representations in the time or frequency domain are inadequate for non-stationary signals which have statistical properties varying with time. In particular the advent of pulse compression techniques and the use of time varying chirp-type signals widespread in radar, sonar and seismic technologies means there is a need for time-frequency representation. We present a technique which extends the Fourier transform to non-stationary signals. We call the technique Fourier Extension analysis. We show that the analysis extends naturally to a time-frequency representation using the Hough transform projection, and investigate the resolutions obtainable with regard to separation of chirp signals compared with the usual matched filter approach common in radar processing. A visual interpretation of the magnitude and phase of the analytic results is introduced allowing a range of transform orders to be viewed simultaneously. Using frequency modulated signals, we demonstrate significantly higher resolution both in rate and time separation. Examples are given using synthetic and real world chirp signals illustrating improvements in time-frequency resolution using the new approach compared to the commonly used quadratic transforms.     

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).     

Bridging across the log(n) Space Frontier

This paper establishes the importance of even the lowest possible level of space bounded computations. We show that DLOG does not coincide with NLOG if and only if there exists a tally set in NSPACE(log log n)\DSPACE(log log n). This result stands in perfect analogy to the related results concerning linear space or exponential time. Moreover, the above problem is equivalent to the existence of a functions(n), with arbitrarily slow or rapid growth rate, that is nondeterministically fully space constructible but cannot be constructed deterministically. We also present a “hardest” fully space constructibles(n)∈O(log log n), a functional counterpart of log-space complete languages. These nonrelativized results are obtained by the use of oracle machines consuming much larger amount of space, in range betweennand 2^d·n.     

Computing the Quartet Distance between Evolutionary Trees in Time O ( n log n )

Evolutionary trees describing the relationship for a set of species are central in evolutionary biology, and quantifying differences between evolutionary trees is therefore an important task. The quartet distance is a distance measure between trees previously proposed by Estabrook, McMorris, and Meacham. The quartet distance between two unrooted evolutionary trees is the number of quartet topology differences between the two trees, where a quartet topology is the topological subtree induced by four species. In this paper we present an algorithm for computing the quartet distance between two unrooted evolutionary trees of n species, where all internal nodes have degree three, in time O(n log n. The previous best algorithm for the problem uses time O(n ²).     

Computing the Quartet Distance between Evolutionary Trees in Time O( n log n)

Evolutionary trees describing the relationship for a set of species are central in evolutionary biology, and quantifying differences between evolutionary trees is therefore an important task. The quartet distance is a distance measure between trees previously proposed by Estabrook, McMorris, and Meacham. The quartet distance between two unrooted evolutionary trees is the number of quartet topology differences between the two trees, where a quartet topology is the topological subtree induced by four species. In this paper we present an algorithm for computing the quartet distance between two unrooted evolutionary trees of n species, where all internal nodes have degree three, in time O(n log n. The previous best algorithm for the problem uses time O(n ²).     

New memory- and computation-efficient hough transform for detecting lines

The slope-intercept Hough transform (SIHT) is one of the two types of line-detection methods. However, the disadvantage of the SIHT is its low memory utilization, say 50%. Based on the affine transformation, this paper presents a new method to improve the memory utilization of the SIHT from 50% to 100%. According to the proposed affine transformation, we first present a basic SIHT-based algorithm for detecting lines. Instead of concerning floating-point operations in the basic SIHT-based algorithm, an improved SIHT-based algorithm, which mainly concerns integer operations, is presented. Besides the memory utilization advantage, experimental results reveal that the improved SIHT-based algorithm has more than 60% execution time improvement ratio when compared to the basic SIHT-based algorithm and has more than 33% execution time improvement ratio when compared to another type of line-detection methods, such as the (r,θ)-based HT algorithm and its variant. The detailed complexity analyses for all the related algorithms are also investigated and we show that the time complexity required in the improved SIHT-based algorithm is the least.     

Randomised hough transform with error propagation for line and circle detection

In this paper, we introduce a new Randomised Hough Transform aimed at improving curve detection accuracy and robustness, as well as computational efficiency. Robustness and accuracy improvement is achieved by analytically propagating the errors with image pixels to the estimated curve parameters. The errors with the curve parameters are then used to determine the contribution of pixels to the accumulator array. The computational efficiency is achieved by mapping a set of points near certain selected seed points to the parameter space at a time. Statistically determined, the seed points are points that are most likely located on the curves and that produce the most accurate curve estimation. Further computational advantage is achieved by performing progressive detection. Examples of detection of lines using the proposed technique are given in the paper. The concept can be extended to non-linear curves such as circles and ellipses. ID="A1"Correspondance and offprint requests to: Q. Ji, Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180, USA. E-mail: qji@ecse.rpi.edu     

A hough transform technique for subgraph isomorphism

The Generalized Hough Transform is an established technique for geometric shape matching. An analogous technique is presented here for approximate solution of subgraph isomorphism problems. Its chief advantages are that it can also be used to find partial isomorphisms and that it can be readily implemented in parallel on a network of simple processors.     

An application of the hough transform to the recognition of printed hebrew characters

This paper describes computer recognition of printed Hebrew characters, in which the Hough Transform space is used as the feature domain. The sequentially built recognition scheme has a first stage coarse classification by end points of strokes and a second stage classifier divided into two parts: in one part the decision is based on matching features in the transform space and in the other part a structural classification is applied. The method was tested on a sample set of eighteen print-simulated alphabets and a recognition rate of 99.6% was achieved. A performance comparison with two other recognition methods is also given.     

基于Hough变换的地形图自动校正

利用Hough变换检测地形图中的方里网网点坐标,并由地形图图幅编号计算得到方里网网点的理论坐标,再把方里网网点的理论坐标与相应Hough变换搜索得到的方里网网点图像坐标进行最小二乘拟合,以纠正扫描地形图的误差得到精确的方里网网点坐标。结合该技术形成了自动扫描生成DRG的软件系统。     

改进随机Hough变换在虹膜定位中的应用

针对随机Hough变换(RHT)中随机采样造成的大量无效采样和无效积累问题，提出了基于连续曲线段检测的RHT(CRHT)算法并应用于虹膜定位中，它利用了边缘图像的连续特性来减少无效采样的数量。实验结果证明，改进的CRHT变换提高了虹膜定位速度。     

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).     

An iterative hough procedure for three-dimensional object recognition

This paper describes an iterative Hough procedure for recognizing images of three-dimensional objects. Straight line segments in the image are matched by finding the parameters of a viewing transformation of a three-dimensional model consisting of line segments. Assuming the scale of the object is known, there are three orientation and two translation parameters to be estimated. Initially a sparse, regular subset of parameters and transformations is evaluated for goodness-of-fit, then the procedure is repeated by successively subdividing the parameter space near current best estimates or peaks.     

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.     

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.     

Randomized or probabilistic Hough transform: unified performance evaluation

Rapid computation of the Hough transform is necessary in very many computer vision applications. One of the major approaches for fast Hough transform computation is based on the use of a small random sample of the data set rather than the full set. Two different algorithms within this family are the randomized Hough transform (RHT) and the probabilistic Hough transform (PHT). There have been contradictory views on the relative merits and drawbacks of the RHT and the PHT. In this paper, a unified theoretical framework for analyzing the RHT and the PHT is established. The performance of the two algorithms is characterized both theoretically and experimentally. Clear guidelines for selecting the algorithm that is most suitable for a given application are provided. We show that, when considering the basic algorithms, the RHT is better suited for the analysis of high quality low noise edge images, while for the analysis of noisy low quality images the PHT should be selected.