Morphology on Convolution Lattices with Applications to the Slope Transform and Random Set Theory

Authors:
Henk J. A. M. Heijmans;Ilya S. Molchanov
Affiliations:
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands;Department of Statistics, University of Glasgow, Glasgow G12 8QW, Scotland, U.K.
Venue:
Journal of Mathematical Imaging and Vision
Year:
1998

Citing 8
Cited 2

The algebraic basis of mathematical morphology. I. dilations and erosions

Computer Vision, Graphics, and Image Processing
Why mathematical morphology needs complete lattices

Signal Processing
The algebraic basis of mathematical morphology

CVGIP: Image Understanding
Morphological systems: slope transforms and max-min difference and differential equations

Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Morphological signal processing and the slope transform

Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Lattice calculus of the morphological slope transform

Signal Processing
Image Analysis and Mathematical Morphology

Image Analysis and Mathematical Morphology
Slope transforms: theory and application to nonlinear signalprocessing

IEEE Transactions on Signal Processing

Inverses and quotients of mappings between ordered sets

Image and Vision Computing
What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

SIAM Review

Quantified Score

Hi-index	0.00

Visualization

Abstract

This paper develops an abstract theory for mathematical morphologyon complete lattices. It differs from previous work in this direction in thesense that it does not merely assume the existence of a binary operation onthe underlying lattice. Rather, the starting point is the recognition of thefact that, in general, objects are only known through information resultingfrom a given collection of measurements, called evaluations. Such anabstract approach leads in a natural way to the concept of convolutionlattice, where ‘convolution’ has to be understood in the senseof an abstract Minkowski addition. The paper contains various examples. Twoapplications are treated in great detail, the morphological slope transformand random set theory.