( max , min )-convolution and Mathematical Morphology
International audience 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...
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Other Authors: | , , |
Format: | Conference Object |
Language: | English |
Published: |
HAL CCSD
2015
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Subjects: | |
Online Access: | https://hal.science/hal-01257501 https://hal.science/hal-01257501/document https://hal.science/hal-01257501/file/MaxMinConvolution_ISMM15_final.pdf https://doi.org/10.1007/978-3-319-18720-4_41 |
Summary: | International audience 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. |
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