Distance functions in digital geometry

Das, Partha Pratim; Chakrabarti, P. P.; Chatterji, B. N.

doi:10.1016/0020-0255(87)90019-3

Cited by 79 publications

(87 citation statements)

References 6 publications

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“…The literature on distances based on neighborhood sequences is rich; a theory for periodic neighborhood sequences not connected to any specific neighborhood relations in Z n is presented in the article by Yamashita and Honda (1984) and Yamashita and Ibaraki (1986) and further developed for the natural neighborhood structure, by the so-called octagonal neighborhood sequences in studies by Das and Chakrabarti (1987a) and Das et al (1987b). Results for general (not necessarily periodic) neighborhood sequences are presented in the article by Nagy (2003).…”

Section: Introductionmentioning

confidence: 97%

Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Nagy

Strand

2009

Int J Imaging Syst Tech

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In the digital image processing, digital distances are useful; distances based on neighborhood sequences are widely used. In this article, the diamond grid is considered, that is, the threedimensional grid of carbon atoms in the diamond crystal. An algorithm to compute a shortest path defined by a neighborhood sequence between any two points in the diamond grid is presented. A formula to compute the distance based on neighborhood sequences with two neighborhood relations is given. The metric and nonmetric properties of some distances based on neighborhood sequences are also discussed. Finally, the constrained distance transformation is shown. V

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Section: Introductionmentioning

confidence: 97%

Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Nagy

Strand

2009

Int J Imaging Syst Tech

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“…The use of the disc shape is motivated by the property that the (Euclidean) distance of the disc center is the same from all points on its border. Since one could use other types of distance, especially for digital images [2], [3], [4], [5], [6], [7], one could use other kinds of "discs," e.g., squares.…”

Section: The Matmentioning

confidence: 99%

Shape representation using a generalized potential field model

Ahuja

Chuang

1997

IEEE Trans. Pattern Anal. Machine Intell.

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Abstract-This paper is concerned with efficient derivation of the medial axis transform of a two-dimensional polygonal region. Instead of using the shortest distance to the region border, a potential field model is used for computational efficiency. The region border is assumed to be charged and the valleys of the resulting potential field are used to estimate the axes for the medial axis transform. The potential valleys are found by following force field, thus, avoiding twodimensional search. The potential field is computed in closed form using the equations of the border segments. The simple Newtonian potential is shown to be inadequate for this purpose. A higher order potential is defined which decays faster with distance than as inverse of distance. It is shown that as the potential order becomes arbitrarily large, the axes approach those computed using the shortest distance to the border. Algorithms are given for the computation of axes, which can run in linear parallel time for part of the axes having initial guesses. Experimental results are presented for a number of examples.

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“…By allowing arbitrary mixture of the basic motions, Das, Chakrabarti and Chatterji introduced the concept of periodic neighbourhood sequences in [2] and in [5]. The concept of neighbourhood sequences was extended to the infinite dimension also in [6].…”

Section: Introductionmentioning

confidence: 98%

Distance with generalized neighbourhood sequences innDand∞D

Nagy¹

2008

Discrete Applied Mathematics

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In this paper we generalize some former results of Das et al. about distances with n-dimensional periodic neighbourhood sequences. We use a more general definition of neighbourhood sequences, which does not require periodicity. As an extension of the earlier results, we give a formula to calculate the distance between two arbitrary points with general neighbourhood sequences in an arbitrary finite dimension. Moreover we extend the result to the infinite-dimensional digital space.

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Distance functions in digital geometry

Cited by 79 publications

References 6 publications

Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Neighborhood sequences in the diamond grid: Algorithms with two and three neighbors

Shape representation using a generalized potential field model

Distance with generalized neighbourhood sequences innDand∞D

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