The algebraic basis of mathematical morphology. I. dilations and erosions
Computer Vision, Graphics, and Image Processing
Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
ISMM '98 Proceedings of the fourth international symposium on Mathematical morphology and its applications to image and signal processing
Geometric partial differential equations in image analysis: past, present, and future
ICIP '95 Proceedings of the 1995 International Conference on Image Processing (Vol. 3)-Volume 3 - Volume 3
Planar Shape Enhancement and Exaggeration
ICPR '96 Proceedings of the 1996 International Conference on Pattern Recognition (ICPR '96) Volume I - Volume 7270
Algebraic framework for linear and morphological scale-spaces
Algebraic framework for linear and morphological scale-spaces
Inf-semilattice approach to self-dual morphology
Inf-semilattice approach to self-dual morphology
Nonlinear multiresolution signal decomposition schemes. I. Morphological pyramids
IEEE Transactions on Image Processing
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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, 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.