Mutational equations of the morphological dilation tubes

The present paper provides some differential results dealing with the morpho-logical dilation of a compact set in the nonregular case. Indeed the evolution of dilated sets with respect to time is characterized through mutational equa-tions which are new mathematical tools extending the concept of di...

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Bibliographic Details
Published in:Journal of mathematical imaging and vision 1995, Vol.5 (3), p.219-230
Main Authors: Doyen, Luc, Najman, Laurent, Mattioli, Juliette
Format: Article
Language:English
Subjects:
Analysis of PDEs
Differential Geometry
Dynamical Systems
Mathematics
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Summary:The present paper provides some differential results dealing with the morpho-logical dilation of a compact set in the nonregular case. Indeed the evolution of dilated sets with respect to time is characterized through mutational equa-tions which are new mathematical tools extending the concept of differential equations to the metric space of all nonempty compact sets of IR n . Using this new tool, we prove that the mutation of the dilation is the normal cone which is a generalization of the classical notion of normal. This result clearly establishes that the dilation transforms this initial set in the direction of the normal at any point of the set. Furthermore, it does not require any regularity assumptions on the compact set.
ISSN:0924-9907
1573-7683
DOI:10.1007/BF01248373