Digital or analog Hough transform?

doi:10.1016/0167-8655(91)90412-F

Pattern Recognition Letters

Volume 12, Issue 5, May 1991, Pages 291-297

https://doi.org/10.1016/0167-8655(91)90412-F Get rights and content

Abstract

A variation of the Hough Transform that is aimed at detecting digital lines has been recently suggested. Other Hough algorithms are intended to detect straight lines in the analog pre-image. These approaches are analyzed and compared in terms of the relation between the achievable resolution and the required number of accumulators, using a definition of resolution that is based on the Geometric Probability measure of straight lines. It is shown that the ‘analog’ approach is greatly superior in high resolution applications, where a ‘digital’ Hough Transform would generally require an infeasibly large number of accumulators.

References (17)

IllingworthJ. et al.
A survey of the Hough transform
Computer Vision, Graphics and Image Processing
(1988)
MelterR.A. et al.
New views of linearity and connectedness in digital geometry
Pattern Recognition Letters
(1989)
RisseT.
Hough transform for line recognition: complexity of evidence accumulation and cluster detection
Computer Vision, Graphics and Image Processing
(1989)
ThriftP.R. et al.
Approximating point-set images byline segments using a variation of the Hough transform
Computer Vision, Graphics and Image Processing
(1983)
Van VeenT.M. et al.
Discretization errors in the Hough transform
Pattern Recognition
(1981)
CyganskiD. et al.
The analytic Hough transform
DudaR.O. et al.
Use of the Hough transform to detect lines and curves in pictures
Conunun. ACM
(1972)
DorstL. et al.
Discrete representation of straight lines
IEEE Trans. Pattern Anal. Machine Intell.
(1984)

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However, the voting process always produces false positives on complicated regions. There have been several approaches to improve drawbacks of HT, such as Generalized Hough Transform (GHT) [5], Randomized Hough Transform (RHT) [6], Binary Hough Transform (BHT) [7], Digital Hough Transform (DHT) [8], Progressive Probabilistic Hough Transform (PPHT) [9] and Kernel-based Hough Transform (KHT) [10]. GHT makes use of the template matching to detect predefined shapes.
Line segments play an important role in the perception and representation of images by providing the geometry information about the scene. These segments can also be used as low-level features to analyze and detect more elaborated shapes. A length-based line segment detector is proposed in this paper. Based on the edge proportion statistics, an adaptive, robust and effective edge detection method is presented to extract edge segments from the image. Each of the segments is a clean, contiguous, 1-pixel wide chain of pixels. The line segment detector then approximates all the edge segments in a way that the curve satisfies a criterion of length condition. The detection result is a series of piecewise-linear segments with some dominant corners. Experimental results indicate that the proposed detector has a good detection accuracy and outperforms the state-of-the-art methods in terms of execution time.
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The paper contributes to a multiscale theory of digital shapes by presenting novel methods for a multiscale representation of digital lines and their intersections according to the Stern-Brocot tree. We give a new definition of the intersection (main connected part) of two specific digital straight lines on the same quadrant (First quadrant). More precisely, we give some new results about the minimal set of parameters (i.e. slope (a, b), shift (μ), parity (even or odd), and the coordinates of the upper leaning points) for each line and their intersections.
A survey of Hough Transform
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Citation Excerpt :
The distribution of lines in the natural set determines the precision and reliability with which straight lines can be measured on a discrete imaging array. Kiryati et al. [64] have compared and analyzed Digital HT (they have mainly considered the Analytic HT [49]) and the conventional, i.e. Analog HTs . Resolution has been defined as the worst case ambiguity in the location of straight lines that intersect opposite sides of the image and set all pixels in between.
In 1962 Hough earned the patent for a method [1], popularly called Hough Transform (HT) that efficiently identifies lines in images. It is an important tool even after the golden jubilee year of existence, as evidenced by more than 2500 research papers dealing with its variants, generalizations, properties and applications in diverse fields. The current paper is a survey of HT and its variants, their limitations and the modifications made to overcome them, the implementation issues in software and hardware, and applications in various fields. Our survey, along with more than 200 references, will help the researchers and students to get a comprehensive view on HT and guide them in applying it properly to their problems of interest.
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However, in the realization of SHT, there arise some issues: (i) digital image is by nature discrete; (ii) when mapped into (ρ, θ) space, θ also has to be sampled in a limited resolution and ρ has to be quantized; (iii) H(ρ, θ) is also represented on a discrete grid where only integer coordinates have values; and (iv) the original image can suffer from various noises. These issues could cause problems of aliasing, peak spreading or peak extension (Kiryati and Bruckstein 1991; Van Veen and Groen 1981; Brown 1983; Kiryati et al. 1991; Yuen and Ma 1997; Lam et al. 1994). To test the feasibility of using HT methods for the line orientation detection in musculoskeletal sonograms that are usually degraded by speckle noises, a modified HT named as revoting Hough transform (RVHT) was adopted in this paper.
Ultrasound imaging has been used frequently for the study of muscle contraction, including measurements of pennation angles and fascicle orientations. However, these measurements were traditionally conducted by manually drawing lines on the ultrasound images. In this study, we proposed a modified Hough transform (HT), aiming at automatically estimating orientations of straight line–shaped patterns, such as muscle fibers and muscle–bone interface in ultrasound images. The new method first located the global maximum in the HT accumulator matrix, which corresponded to the most dominant collinear feature points globally, using the standard HT; then the pixels close to the detected line were removed from the edge map, the HT accumulator matrix was calculated again, i.e., revoting, and a new line was detected. The iteration was repeated until the predefined termination conditions were satisfied. The performance of the algorithm was tested using computer-generated images with different levels of noises, as well as clinical ultrasound images, and compared with that of the conventional method. It was found that the orientation estimation results obtained by the new algorithm were well correlated (R² = 0.965), with those obtained using the traditional method, i.e., drawing lines manually and reading the angles with the assistance of software. Further mean-difference plots revealed a difference of 0.18 ± 2.41° between the two methods at the 95% confidence level. Compared with the traditional method, the new algorithm was more capable of handling with highly noisy data and could avoid the aliasing problem, i.e., reporting multiple lines instead of single expected line. The results of this study suggested that the proposed revoting HT can be potentially used for the reliable and nonsubjective automatic estimation of the orientations of muscle fibers in musculoskeletal ultrasound images. (E-mail: [email protected])
The fuzzy local-global duality in detecting pictorial patterns
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The Hough transform is recognized as being a powerful tool in shape analysis which gives good results even in the presence of noise and occlusion. Major shortcomings of the technique are excessive storage requirements and computational complexity. Solutions to these problems form the bulk of contributions to the literature concerning the Hough transform. An excellent comprehensive review of available methods up to and partially including 1988 is given by Illingworth and Kittler (Comput. Vision Graphics Image Process. 44, 1988, 87-116). In the years following this survey much new literature has been published. The present work offers an update on state of the art Hough techniques. This includes comparative studies of existing techniques, new perspectives on the theory, very many novel algorithms, parallel implementations, and additions to the task-specific hardware. Care is taken to distinguish between research that aims to further basic understanding of the technique without necessarily being computationally realistic and research that may be applicable in an industrial context. A new trend in Hough transform work, that of the probabilistic Houghs, is identified and reviewed in some detail. Attempts to link the low level perceptive processing offered by the Hough transform to high level knowledge driven processing are also included, together with the many recent successful applications appearing in the literature.

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Digital or analog Hough transform?

Abstract

Computer Vision, Graphics and Image Processing

Pattern Recognition Letters

Computer Vision, Graphics and Image Processing

Computer Vision, Graphics and Image Processing

Pattern Recognition

The analytic Hough transform

Use of the Hough transform to detect lines and curves in pictures

Conunun. ACM

Discrete representation of straight lines

IEEE Trans. Pattern Anal. Machine Intell.