Results 261 to 270 of about 174,404 (306)

Counting minimal paths in digital geometry

Pattern Recognition Letters, 1991
Abstract In this paper recursive formulae are derived for determining the number of the minimal cityblock, chessboard or octagonal paths in the two-dimensional digital plane.
Partha Pratim Das
exaly   +2 more sources

Digital geometry

Information Sciences, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Azriel Rosenfeld, Reinhard Klette
openaire   +2 more sources

Hyperspheres in digital geometry

Information Sciences, 1990
For two points x,y of the k-dimensional rectangular grid, their distance may be defined as \[ d_ m(x,y)=\max \{L_{\infty}(x,y),\frac{1}{m}L_ 1(x,y)\}, \] where \(L_ p\) denotes the standard \(L_ p\)-norm in k- space. The volume (or surface) of a digitized k-dimensional sphere with radius r around grid point x is measured by the number of grid points y ...
Partha Pratim Das, Biswanath N. Chatterji   +1 more
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Digital geometry

The Mathematical Intelligencer, 1989
This article introduces the basic concepts of digital geometry in the plane, which studies geometric properties of sets of lattice points produced by digitizing regions or curves. Some open questions and generalizations are discussed and it is given a brief guide to the literature.
Rosenfeld, Azriel, Melter, Robert A.
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Generalized distances in digital geometry

Information Sciences, 1987
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
Partha Pratim Das 0001, P. P. Chakrabarti 0001, Biswanath N. Chatterji   +2 more
openaire   +2 more sources

Metric bases in digital geometry

Computer Vision, Graphics, and Image Processing, 1984
The authors consider the set D of all points in the Euclidean plane with integral coordinates (digital plane). Given a metric d on \(A\subset D\), a subset \(S\subset A\) is called a metric basis for A if \(d(x,s)=d(y,s)\) for all \(s\in S\) implies \(x=y.\) It is well known that a minimal metric basis for the Euclidean plane with respect to the ...
Robert A. Melter, Ioan Tomescu
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A digital geometry for hexagonal pixels

Image and Vision Computing, 1989
Abstract Comparison of hexagonal and square pixels and arrays for image processing shows that the former have many advantages. However, squares can be addressed with integers and orthogonal axes, while for hexagons the axes must be at an oblique angle of 60°. This paper describes a general method of producing geometrical algorithms for such axes.
Sarah B. M. Bell, Fred C. Holroyd, David C. Mason   +2 more
openaire   +1 more source

Distance functions in digital geometry

Information Sciences, 1987
An analysis of paths and distances in n dimensions is carried out using variable neighborhood sequences. A symbolic expression for the distance function between any two points in this quantized space is derived. An algorithm for finding the shortest path is presented.
Partha Pratim Das 0001, P. P. Chakrabarti 0001, Biswanath N. Chatterji   +2 more
openaire   +2 more sources

Geometry in digital molecular arrays

Organic & Biomolecular Chemistry, 2006
The development of digital molecular devices arises through the appropriate geometric positioning of a molecular assay. A detailed evaluation of the digital media reveals the critical aspects of geometric positioning in terms of developing an analytically-robust system for molecular analysis.
James J, La Clair, Michael D, Burkart
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The t-Cost distance in digital geometry

Information Sciences, 1992
The authors define certain distance functions in an \(n\)-D grid. There the distances of neighbour points may be unequal to unity. They derive a characterisation of such distance functions to define a metric. These distances then are called \(t\)-cost distances.
Partha Pratim Das 0001, Jayanta Mukherjee 0001, B. N. Chatterji   +2 more
openaire   +1 more source