Elements of Digital Geometry, Mathematical Morphology, and Discrete Optimization

10.1142/12584 ◽  
2022 ◽  
Author(s):  
Christer Oscar Kiselman
Keyword(s):  
Mathematical Morphology ◽  
Discrete Optimization ◽  
Digital Geometry

scholarly journals An extension problem of a connectedness preserving map between Khalimsky spaces

Filomat ◽  
2016 ◽  
Vol 30 (1) ◽  
pp. 15-28 ◽  
Author(s):  
Sang-Eon Han
Keyword(s):  
Computer Science ◽  
Mathematical Morphology ◽  
Digital Images ◽  
Digital Topology ◽  
Extension Problem ◽  
Topological Spaces ◽  
Digital Geometry ◽  
Applied Topology ◽  
Continuous Map ◽  
Connected Sets

The goal of the present paper is to study an extension problem of a connected preserving (for short, CP-) map between Khalimsky (K-for brevity, if there is no ambiguity) spaces. As a generalization of a K-continuous map, for K-topological spaces the recent paper [13] develops a function sending connected sets to connected ones (for brevity, an A-map: see Definition 3.1 in the present paper). Since this map plays an important role in applied topology including digital topology, digital geometry and mathematical morphology, the present paper studies an extension problem of a CP-map in terms of both an A-retract and an A-isomorphism (see Example 5.2). Since K-topological spaces have been often used for studying digital images, this extension problem can contribute to a certain areas of computer science and mathematical morphology.

Mathematical morphology for shape description

2002 ◽  
Vol 12 (1) ◽  
pp. 87-116 ◽  
Author(s):  
M. Schmitt
Keyword(s):  
Mathematical Morphology ◽  
Shape Description

Modern Approaches to Solving Complex Discrete Optimization Problems

2016 ◽  
Vol 48 (1) ◽  
pp. 15-24 ◽  
Author(s):  
Ivan V. Sergienko ◽  
Vladimir P. Shylo
Keyword(s):  
Discrete Optimization ◽  
Optimization Problems ◽  
Discrete Optimization Problems

Olive Tree Identification Method by Spatial Statistics Analysis and Mathematical Morphology

2008 ◽  
Vol 3 (3) ◽  
pp. 5-13
Author(s):  
Mounir Salhi ◽  
◽  
A. Kallel ◽  
N. Derbel ◽  
◽  
...  
Keyword(s):  
Spatial Statistics ◽  
Mathematical Morphology ◽  
Olive Tree ◽  
Statistics Analysis ◽  
Identification Method

Discrete optimization of semi-rigid steel frames in second-order analysis

2019 ◽  
Author(s):  
Marcos Henrique Bossardi Borges ◽  
Adelano Esposito ◽  
Herbert Gomes
Keyword(s):  
Discrete Optimization ◽  
Steel Frames ◽  
Second Order ◽  
Order Analysis

Applications of Mathematical Morphology to Range Imagery

1987 ◽  
Author(s):  
Thomas R. Esselman ◽  
Jacques G. Verly
Keyword(s):  
Mathematical Morphology

Combining Exact ad Heuristic Approaches for Discrete Optimization

2011 ◽  
Author(s):  
George L. Nemhauser
Keyword(s):  
Discrete Optimization ◽  
Heuristic Approaches
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