Paper Info
Title
Adjunctions in Pyramids, Curve Evolution and Scale-Spaces
Abstract
We have been witnessing lately a convergence among mathematical morphology and other nonlinear fields, such as curve evolution, PDE-based geometrical image processing, and scale-spaces. An obvious benefit of such a convergence is a cross-fertilization of concepts and techniques among these fields. The concept of adjunction however, so fundamental in mathematical morphology, is not yet shared by other disciplines. The aim of this paper is to show that other areas in image processing can possibly benefit from the use of adjunctions. In particular, a strong relationship between pyramids and adjunctions is presented. We show how this relationship may help in analyzing existing pyramids, and construct new pyramids. Moreover, it will be explained that adjunctions based on a curve evolution scheme can provide idempotent shape filters. This idea is illustrated in this paper by means of a simple affine-invariant polygonal flow. Finally, the use of adjunctions in scale-space theory is also addressed.
Year
DOI
Venue
2003
10.1023/A:1022952007509
International Journal of Computer Vision
Keywords
Field
DocType
adjunctions,mathematical morphology,curve evolution,scale-spaces,pyramids,partially ordered sets,image processing
Convergence (routing),Nonlinear system,Computer science,Image processing,Artificial intelligence,Adjunction,Discrete mathematics,Polygon,Algebra,Mathematical morphology,Idempotence,Machine learning,Partially ordered set
Journal
Volume
Issue
ISSN
52
2-3
1573-1405
Citations 
PageRank 
References 
1
0.35
11
Authors
2
Name
Order
Citations
PageRank
Renato Keshet133827.26
Henk J. A. M. Heijmans265966.31