Distances with neighbourhood sequences in cubic and triangular grids

Nagy, Benedek

doi:10.1016/j.patrec.2006.06.007

Cited by 33 publications

(25 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The diamond grid is not a point-lattice (Conway and Sloane, 1988), because there are p, q [ D, such that p 1 q = 2 D. The grid has two types of points (such as the 2D triangular grid that is also not a point-lattice, but the theory of neighborhood sequences is developed for this grid as well (Nagy, 2002(Nagy, , 2004(Nagy, , 2007). …”

Section: Notation and Definitionsmentioning

confidence: 99%

“…Distances based on neighborhood sequences are examined and analyzed in the triangular grid by Nagy (2002Nagy ( , 2004Nagy ( , 2007. The generalizations of the hexagonal grid in three dimensions are the face-centered cubic (FCC) and body-centered cubic (BCC) grids, whereas the generalization of the triangular grid in three dimensions is the diamond grid, as mentioned in the work of Nagy and Strand (2008b).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Nagy

Strand

2009

Int J Imaging Syst Tech

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Notation and Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Nagy

Strand

2009

Int J Imaging Syst Tech

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the fourth section we give a formula which gives the distance between any two points with a given neighbourhood sequence in Z n or Z ∞ . We note here, that in [12] for the special case Z 3 our formula is proved to be equivalent to Das' formula. In the last section we summarize our results.…”

Section: Introductionmentioning

confidence: 64%

“…It is only a simple calculation to check that our formula gives the same result as Das' formula [2] in the case of periodic sequences in nD. The calculation for the cubic grid can be found in [12].…”

Section: Lemma 10 the Finite Path Exists (Ie The B-distance Is Finmentioning

confidence: 80%

Distance with generalized neighbourhood sequences innDand∞D

Nagy¹

2008

Discrete Applied Mathematics

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…The theory for ns-distances with periodic neighborhood sequences was further developed in [12][13][14][15], where for example formulas for point-to-point distance and conditions for metricity were given. In [16][17][18][19][20], ns-distances for the non-periodic case were considered for standard and non-standard grids.…”

mentioning

confidence: 99%

Weighted distances based on neighborhood sequences for point-lattices

Strand

2009

Discrete Applied Mathematics

View full text Add to dashboard Cite

a b s t r a c tA path-based distance is defined as the minimal cost-path between two points. One such distance function is the weighted distance based on a neighborhood sequence. It can be defined using any number of neighborhood relations and weights in conjunction with a neighborhood sequence. The neighborhood sequence restricts some steps in the path to a smaller neighborhood. We give formulas for computing the point-to-point distance and conditions for metricity for weighted distances based on neighborhood sequences with two neighborhood relations for the general case of point-lattices.

show abstract

Distances with neighbourhood sequences in cubic and triangular grids

Cited by 33 publications

References 13 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

Distance with generalized neighbourhood sequences innDand∞D

Weighted distances based on neighborhood sequences for point-lattices

Contact Info

Product

Resources

About