Discrete Representation of Straight Lines

Dorst, Leo; Smeulders, A.W.M.

doi:10.1109/tpami.1984.4767550

Cited by 153 publications

(66 citation statements)

References 5 publications

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“…Both, efficient algorithms for the decomposition of digital curves into maximal straight line segments and efficient coding scheme for digital straight line segments already exist -see [6,10] and [1,7]. Let us notice, that the coding scheme presented here is expected to be more robust because it is not based on the boundary points only, as it would be in the case of the coding based on the boundary decomposition into digital straight line segments.…”

Section: Comments and Conclusionmentioning

confidence: 98%

A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

Žunić

2003

Lecture Notes in Computer Science

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Abstract. For a given planar region P its discretization on a discrete planar point set S consists of the points from S which fall into P . If P is bounded with a convex polygon having n vertices and the number of points from P ∩ S is finite, the obtained discretization of P will be called discrete convex n-gon. In this paper we show that discrete moments having the order up to n characterize uniquely the corresponding discrete convex n-gon if the discretizing set S is fixed. In this way, as an example, the matching of discrete convex n-gons can be done by comparing 1 2 · (n + 1) · (n + 2) discrete moments what can be much efficient than the comparison "point-by-point" since a digital convex n-gon can consist of an arbitrary large number of points.

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Section: Comments and Conclusionmentioning

confidence: 98%

A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

Žunić

2003

Lecture Notes in Computer Science

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“…relations between irreducible rational fractions and digital lines (see [10,11] for a characterization with Farey series, and [12] for a link with decomposition into continuous fractions), but in [5], Debled first introduced the link between this tree and digital lines. She noticed that recognizing a piece of digital line is like going down the Stern-Brocot tree up to the directional vector of the line.…”

Section: Minimal Parametersmentioning

confidence: 99%

New Results about Digital Intersections

Sivignon¹,

Dupont

Chassery³

2003

Discrete Geometry for Computer Imagery

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Abstract. Digital geometry is very different from Euclidean geometry in many ways and the intersection of two digital lines or planes is often used to illustrate those differences. Nevertheless, while digital lines and planes are widely studied in many areas, very few works deal with the intersection of such objects. In this paper, we investigate the geometrical and arithmetical properties of those objects. More precisely, we give some new results about the connectivity, periodicity and minimal parameters of the intersection of two digital lines or planes.

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“…It is specifically aimed at detecting digital straight lines [3], and is thus referred to here as the "Digital Hough Transform". This version of the Hough Transform employs the slope-intercept paramctrization, and a non-uniform parameter space quantization scheme that, in principle, assigns an accumulator to each of the triangular or quadrilateral domains in the (m ,b) space that correspond to distinct digital lines.…”

Section: A Variation Of the Hough Transform That Is Aimed At Detectinmentioning

confidence: 99%

Digital or analog Hough Transform?

Kiryati¹,

Lindenbaum²,

Bruckstein³

1990

Procedings of the British Machine Vision Conference 1990

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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 anaThe 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.Most Hough algorithms consist of an incrementation stage, in which each edge point "votes" for the parameter-pairs of all possible straight lines on which it can lie, and an exhaustive search for peaks. These correspond to large collinear sets of edge-points.Originally, the slope-intercept (m,b) parametrization of straight lines had been employed in the Hough Transform. It has the advantage that an edge point corresponds to a straight line in the parameter space, thus voting is simple. Its drawback is that the parameter space is unbounded, implying some theoretical and practical difficulties. With normal (p,0) parametrization of straight lines, as suggested by [2], an edge point corresponds to a sinusoid in the parameter space, thus voting is somewhat more complex. The normal parametrization has the advantage that a bounded image leads to a bounded parameter space. Other straight-line parametrizations have also been suggested, see [4,11,17].In most implementations of the Hough algorithm the parameter space is represented by a rectangular accumulator array, such that each accumulator corresponds to a rectangular, constant size domain in the parameter space. The quantization of the parameter space greatly influences the resolution and detection capabilities of the algorithm, as well as the computational and storage requirements; see [6,16].

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Discrete Representation of Straight Lines

Cited by 153 publications

References 5 publications

A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

A Characterization of Discretized Polygonal Convex Regions by Discrete Moments

New Results about Digital Intersections

Digital or analog Hough Transform?

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