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.     

Hough transform from the radon transform

An appropriate special case of a transform developed by J. Radon in 1917 is shown to have the major properties of the Hough transform which is useful for finding line segments in digital pictures. Such an observation may be useful in further efforts to generalize the Hough transform. Techniques for applying the Radon transform to lines and pixels are developed through examples, and the appropriate generalization to arbitrary curves is discussed.     

Antialiasing the Hough transform

The discretization of the Hough transform parameter plane is considered. It is shown that the popular accumulator method implies sampling of a nonbandlimited signal. The resultant aliasing accounts for several familiar difficulties in the algorithm. Bandlimiting the parameter plane would allow Nyquist sampling, thus aliasing could be avoided. An effectively alias-free Hough algorithm is presented and analyzed. The uncertainty principle of signal representation induces a compromise between image-space localization and parameter-space sampling density, as well as an upper bound on the performance of the algorithm. These results contribute to the development of a design methodology for hierarchical “coarse to fine” Hough algorithms.     

On the sensitivity of the Hough transform for object recognition

Object recognition from sensory data involves, in part, determining the pose of a model with respect to a scene. A common method for finding an object's pose is the generalized Hough transform, which accumulates evidence for possible coordinate transformations in a parameter space whose axes are the quantized transformation parameters. Large clusters of similar transformations in that space are taken as evidence of a correct match. A theoretical analysis of the behavior of such methods is presented. The authors derive bounds on the set of transformations consistent with each pairing of data and model features, in the presence of noise and occlusion in the image. Bounds are provided on the likelihood of false peaks in the parameter space, as a function of noise, occlusion, and tessellation effects. It is argued that haphazardly applying such methods to complex recognition tasks is risky, as the probability of false positives can be very high     

The vector-gradient Hough transform

The paper presents a new transform, called vector-gradient Hough transform, for identifying elongated shapes in gray-scale images. This goal is achieved not only by collecting information on the edges of the objects, but also by reconstructing their transversal profile of luminosity. The main features of the new approach are related to its vector space formulation and the associated capability of exploiting all the vector information of the luminosity gradient     

The Hough transform versus the UpWrite

This paper compares the Hough transform and the UpWrite for the detection of lines, circles, and ellipses. Both ideal and noisy images are tested. The UpWrite is found to be more robust for images containing perturbation noise. For ideal images and images with speckle noise, the results are found to depend on the complexity of the object being detected, with more complex objects favoring the UpWrite     

Error propagation for the Hough transform

In this paper, a statistically efficient Hough transform (HT) technique with improved performance in accuracy and robustness is described. The proposed technique analytically computes the uncertainty of each feature point based on image noise, the procedure used for estimating edge orientation, and the specific parametric representation scheme of a line. Using the estimated uncertainty of each feature point, a Bayesian probabilistic scheme is introduced to compute the contribution of each feature point to the accumulator. A performance evaluation of our technique reveals its improved performance, especially for noisy images.     

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.     

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.     

Lead-lag compensator design by the Hough transform

The frequency response of a compensator can be expressed as a curve in the complex plane. The Hough transform is very useful in finding a mathematical model which matches the curve in a plane very well. We combine these concepts to generate a new method of compensator design. Two examples are illustrated to explain the design procedure and results.     

A New Definition of the Hough Transform

This paper‘s main contributions are three-fold.Firstly,it is shown that the two existing template matching-like definitions of the Hough transform in the literature are inadequate.Secondly,an inherent probabilistic aspect of the Hough transform embedded in the transformation process from image space to parameter space is clarified.Thirdly,a new definition of the Hough transform is proposed which takes into account both the intersection scheme between the mapping curve(or mapping surface) and accumulator cells and the inherent probabilistic characteristics.     

A real-time processor for the Hough transform

The Hough transform method for recognition can cope effectively with noisy backgrounds and gaps in boundaries. However, long computation time and large memory requirements have prevented it from being used in real-time applications. An architecture devised to solve those problems, with a focus on detecting straight lines, is presented. Examples are given of the use of an experimental hardware model for automatic inspection and measurement of objects in factories and laboratories. It took less than one second from picture input to straight line parameter reproduction for these examples     

一种面向FPGA的快速Hough变换

在FPGA上设计并实现了一种用于直线检测的快速Hough变换方法。使用分类滤波器把直线目标分成多个方向,使多个方向上的运算在空间上实现了并行处理;在每个方向上,设计实现了一种用于Hough变换的流水线处理结构;提出了一种基于直方图统计的两阶段搜索算法。大量的实验验证了提出的Hough变换实现方法的可行性,结果证明该方法占用空间少,实时性高。     

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.     

An inherent probabilistic aspect of the Hough transform

In this paper,a new property of the Hough transform is discovered,namely an inherent probabilistic aspect which is independent of the input image and embedded in the transformation process from the image space to the parameter space.It is shown that such a probabilistic aspect has a wide range of implications concerning the specification of implementation schemes and the performance of Hough transform.In particular,it is shown that in order to make the Hough transform really meaningful,an appropriate curve(surface)density function must be,either explicitly or implicitly,supplied during its implementation process,and that the widely used approach to uniformly discretizing parameter space in the literature is generally inadequate.     

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.     

Mobile robot navigation using the range-weighted Hough transform

Accurate navigation of a mobile robot in cluttered rooms using a range-measuring laser as a sensor has been achieved. To extract the directions and distances to the walls of the room the range-weighted Hough transform is used. The following experimental results are emphasized: The robot extracts the walls of the surrounding room from the range measurements. The distances between parallel walls are estimated with a standard deviation smaller than 1 cm. It is possible to navigate the robot along any preselected trajectory in the room. One special case is navigation through an open door detected by the laser. The accuracy of the passage is 1 cm at a speed of 0.5 m/s. The trajectory is perpendicular to the wall within 0.5 degrees in angle. When navigating through corridors, the accuracy is better than 1 cm at 0.8 m/s-the maximum speed of the robot. Odometric data and laser measurements are combined using the extended Kalman filter. The size of the cluttered rectangular room and the position and orientation (pose) of the robot are estimated during motion. The extraction and the resulting navigation are very robust against both spurious measurements in the laser measurements and disturbing objects     

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.     

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).