max , min -convolution and Mathematical MorphologyReport as inadecuate

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1 CMM - Centre de Morphologie Mathématique

Abstract : A formal denition of morphological operators in max, min-algebra is introduced and their relevant properties from an algebraic viewpoint are stated. Some previous works in mathematical morphology have already encountered this type of operators but a systematic study of them has not yet been undertaken in the morphological literature. It is shown in particular that one of their fundamental property is the equivalence with level set processing using Minkowski addition and subtraction. Theory of viscosity solutions of the Hamilton-Jacobi equation with Hamiltonians containing u and Du is summarized, in particular, the corresponding Hopf-Lax-Oleinik formulas as max, min-operators. Links between max, min-convolutions and some previous approaches of unconventional morphology, in particular fuzzy morphology and viscous morphology, are reviewed.

Keywords : Minkowski addition adjunction HamiltonJacobi PDE fuzzy morphology viscous morphology

Author: Jesus Angulo -



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