Generalized distances in digital geometry
type: Item
instance of: scholarly article
title: Generalized distances in digital geometry
zbMATH Open document ID: 0632.68067
DOI: 10.1016/0020-0255(87)90015-6
published in: Information Sciences
publication date: 1987-01-01T00:00:00Z
review text: This paper proposes a generalized distance measure called m-neighbour distance in quantized n-dimensional space. Given two points \(P=\{x_ i\}\) and \(Q=\{y_ i\}\) for \(1\leq i\leq n\), the m-neighbour distance is defined as: \[ d^ n_ m(P,Q)=\max (\max^{n}_{k=1}X_ k,\quad \lceil \sum^{n}_{k=1}X_ k/m\rceil)\quad, \] where \(X_ k=| x_ k-y_ k|\), \(1\leq k\leq n\) and m,n\(\in {\mathbb{N}}.\) Given a point \(P=\{x_ i\}\); an r-neighbour of P is defined as \(Q=\{y_ i\}:\) \(0\leq | x_ i-y_ i| \leq 1\) for \(1\leq i\leq n\) and \(\sum^{n}_{1}| x_ i-y_ i| =r\). An r-neighbour of P has `n-r' vertices in common with P. It is shown that \(d^ n_ m(P,Q)\) is a distance metric, and an algorithm is given to trace the shortest path composed of successive r- neighbours between points P and Q. It is shown that \(d^ n_ r(P,Q)\) is the length of the path.
Mathematics Subject Classification ID: 68R99
Mathematics Subject Classification ID: 68P10
zbMATH DE Number: 4028923
zbMATH Keywords: generalized distance measure
zbMATH Keywords: m-neighbour distance
zbMATH Keywords: quantized n- dimensional space
zbMATH Keywords: distance metric
zbMATH Keywords: shortest path
author: Partha Pratim Das
author: P. P. Chakrabarti
author: Biswa Nath Chatterji
MaRDI profile type: Publication
full work available at URL: 0020-0255(87)90015-6
OpenAlex ID: W1974763083
cites work: Distance functions in digital geometry
cites work: The m-dimensional grid point space
cites work: Paths and distance functions on three-dimensional digitized pictures
cites work: Digital geometry
cites work: Three-dimensional digital topology
description: scientific article; zbMATH DE number 4028923