Lattice of octagonal distances in digital geometry

Das, Partha Pratim

doi:10.1016/0167-8655(90)90099-n

Cited by 51 publications

(29 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Originally, the relation * was introduced by Das [3] in the two dimensional digital space, and by Fazekas et al in [4] for higher dimensions. We will use it for infinite sequences (R ∞ ).…”

Section: Definition 23 a Function Dmentioning

confidence: 99%

Generalised distances of sequences II: B-distances with weight sequences

Nagy

2019

Filomat

View full text Add to dashboard Cite

In this paper, we investigate the weighted B-distances of infinite sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Z n), and the theory was recently extended for application to sequences. By assigning various weights to the elements of the sequences the concept is further generalized. An algorithm is presented which provides a shortest path between two sequences. Formula is also provided to calculate the weighted B-distance of any two sequences with a neighbourhood sequence B and a weight sequence. There are several neighbourhood sequences, which do not generate metrics. We prove a necessary and sufficient condition for a B-distance to define a generalized metric space above the sequences. Moreover, our results can be applied if the elements of the sequences used with various weights. In case of weight functions used B-distances we present also the metric conditions.

show abstract

Section: Definition 23 a Function Dmentioning

confidence: 99%

Generalised distances of sequences II: B-distances with weight sequences

Nagy

2019

Filomat

View full text Add to dashboard Cite

show abstract

“…Originally, the relation w was introduced by Das [4] in the two dimensional digital space, and by Fazekas et al in [7] for higher dimensions. We will use it for infinite sequences (R 1 ).…”

Section: Notations and Definitionsmentioning

confidence: 99%

Generalised distances of sequences I: $B$-distances

Nagy¹

2018

MMN

View full text Add to dashboard Cite

In this paper, we investigate the B-distances of infinite sequences. For this purpose we use generalized neighbourhood sequences. The general neighbourhood sequences were introduced for measuring distances in digital geometry (Z n). We extend their application to sequences, and present an algorithm which provides a shortest path between two sequences. We also present a formula to calculate the B-distance of any two sequences for a neighbourhood sequence B. We also investigate the concept of k-convergent sequences for k 2 N, that concept is generally weaker than the convergence. We will use the term k-sequence which is a kind of generalization of the concept of 0-sequence. We also show some connection between the B-distances of sequences and the properties of their difference sequences.

show abstract

“…In our structural investigations we examine some subsets of S n with respect to two partial orderings, * and [1,2]. These orderings are defined in the following way.…”

Section: Basic Concepts and Notationmentioning

confidence: 99%

“…Such sequences are dealt with in many papers, see e.g. [1,6,5,7,8] and the references given there. Fazekas, Hajdu and Hajdu [2] extended the theory to the case of arbitrary octagonal neighborhood sequences, where any (not necessarily periodic) sequences are considered.…”

Section: Introductionmentioning

confidence: 99%

On the Lattice Structure of Subsets of Octagonal Neighborhood Sequences in ℤn

Hajdú

Hajdu

2006

Discrete Geometry for Computer Imagery

View full text Add to dashboard Cite

In this paper we investigate the lattice properties of several special, but important subsets of Sn, the set of nD octagonal neighborhood sequences in Z n , with respect to two ordering relations * and. Both orderings have some natural meaning, especially * compares the "speed" how neighborhood sequences spread in Z n. We summarize our and the previous related results in a table. In particular, our theorems can be considered as extensions of some results from [1, 2, 3].

show abstract

Lattice of octagonal distances in digital geometry

Cited by 51 publications

References 4 publications

Generalised distances of sequences II: B-distances with weight sequences

Generalised distances of sequences II: B-distances with weight sequences

Generalised distances of sequences I: $B$-distances

On the Lattice Structure of Subsets of Octagonal Neighborhood Sequences in ℤn

Contact Info

Product

Resources

About