Approximating point set images by line segments using a variation of the hough transform

Thrift, Philip; Dunn, Stanley M.

doi:10.1016/0146-664x(82)90149-6

Cited by 7 publications

(11 citation statements)

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“…Generalizations of the HT that involve replacing the kernel p by a smoother function have been suggested by Thrift and Dunn [21] and are discussed in [22]. To be more specific, if we consider the simple HT defined by H(8, p) = 2 p(p -zi cos 0 -yi sin Q), (32) i=l it can be seen that by using a rectangular function we obtain the standard HT.…”

Section: Generalized Maximum-likelihood Methodsmentioning

confidence: 99%

A formal definition of the Hough transform: Properties and relationships

1992

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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 defined implicitly 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). © 1992 Kluwer Academic Publishers

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Section: Generalized Maximum-likelihood Methodsmentioning

confidence: 99%

A formal definition of the Hough transform: Properties and relationships

1992

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“…In particular, it has been suggested [6,15] that the indicator function (9) be replaced by where C(-) is an "influence function" to be discussed in the sequel. This results with a modified continuous-support Hough Transform (12) z(p,9) can be point-sampled by assigning accumulators to a discrete set of sampling points, and evaluating (12) only at these points.…”

Section: Variants Of the Houghmentioning

confidence: 99%

“…A unit square circumscribes a circle of radius 0.5 and is inscribed in a circle of radius ^2/2. Reasonably assuming r m « 1, it immediately follows that A A , the minimum required number of samples in this "analogtype" Hough Transform satisfies A A =a 2n (15) where 0.5 < a < 1 is a constant. Using the influence function (13) and the convention that its effective bandwidth is triple the square root of the normalized second order energy moment of its Fourier Transform,…”

Section: Variants Of the Houghmentioning

confidence: 99%

“…Modern forms of the Hough Transform, e.g. [6,10,15], provide some compensation for location errors in the data, thus improving the performance of the algorithm. These variants do not provide special treatment for location errors which are due to image digitization; this is justified by the ability of modern edge detection schemes to offer sub-pixel accuracy when the levels of other sources of image noise are low.…”

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confidence: 99%

“…These variants do not provide special treatment for location errors which are due to image digitization; this is justified by the ability of modern edge detection schemes to offer sub-pixel accuracy when the levels of other sources of image noise are low. In this paper, [6,10,15] and related versions arc referred to as "Analog Hough Transforms", since they are intended to detect straight lines in the analog "pre-image".…”

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Digital or analog Hough transform?

Kiryati

Lindenbaum

Bruckstein

1991

Pattern Recognition Letters

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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 arc 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. The Hough Transform [2,4] is a well known technique for recognizing predefined features in edge maps. In this paper, the Hough Transform for detecting straight lines is considered.

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Generation of synthetic documents for performance evaluation of symbol recognition & spotting systems

Delalandre¹,

Valveny²,

Pridmore³

et al. 2010

IJDAR

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In this paper we present a robust system of symbol recognition using a structural approach. Our key objective here is to provide a system, equaling the statistical ones in robustness concerning the recognition, to apply next to localization. To do it we have investigated two particular structural methods: the straight line detection using Hough Transform and the vector templates matching. Experiments done on the GREC2003 database show how their combination allows to obtain high recognition results.

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Approximating point set images by line segments using a variation of the hough transform

Cited by 7 publications

References 0 publications

A formal definition of the Hough transform: Properties and relationships

A formal definition of the Hough transform: Properties and relationships

Digital or analog Hough transform?

Generation of synthetic documents for performance evaluation of symbol recognition & spotting systems

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