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.

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
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