Rank-based decompositions of morphological templates

Author

Sussner, Peter ; Ritter, Gerhard X.

Author_Institution

Int. of Math., Stat. & Sci. Comput., State Univ. of Campinas, Brazil

Volume

9

Issue

8

fYear

2000

fDate

8/1/2000 12:00:00 AM

Firstpage

1420

Lastpage

1430

Abstract

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for these investigations is the new theory of rank within minimax algebra. Thus far, only minimax decompositions of rank 1 and rank 2 matrices into outer product expansions are known to the image processing community. We derive a heuristic algorithm for the decomposition of matrices having arbitrary rank

Keywords

convolution; image processing; mathematical morphology; matrix decomposition; matrix multiplication; minimax techniques; convolution; heuristic algorithm; image processing; matrix decomposition; minimax algebra; minimax decompositions; morphological templates; nonlinear domain; outer product expansions; rank 1 matrix; rank 2 matrix; rank-based decompositions; template decomposition; Algebra; Computational efficiency; Costs; Heuristic algorithms; Image processing; Matrix decomposition; Minimax techniques; Morphology; Nonlinear filters; Pixel;

fLanguage

English

Journal_Title

Image Processing, IEEE Transactions on

Publisher

ieee

ISSN

1057-7149

Type

jour

DOI

10.1109/83.855436

Filename

855436