Classification of fuzzy mathematical morphologies based on concepts of inclusion measure and duality

Autor(es)

Sussner, Peter ^[1] ; Valle, Marcos Eduardo ^[2]

Afiliação do(s) autor(es)

^[1] Univ Estadual Campinas, Inst Math Stat & Sci Computat, BR-13081970 Campinas, SP - Brazil

^[2] Univ Estadual Londrina, Ctr Exact Sci, BR-86051990 Londrina, PR - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Imaging and Vision; v. 32, n. 2, p. 139-159, OCT 2008.
• Citações Web of Science: 42

Resumo

Mathematical morphology was originally conceived as a set theoretic approach for the processing of binary images. Extensions of classical binary morphology to gray-scale morphology include approaches based on fuzzy set theory. This paper discusses and compares several well-known and new approaches towards gray-scale and fuzzy mathematical morphology. We show in particular that a certain approach to fuzzy mathematical morphology ultimately depends on the choice of a fuzzy inclusion measure and on a notion of duality. This fact gives rise to a clearly defined scheme for classifying fuzzy mathematical morphologies. The umbra and the level set approach, an extension of the threshold approach to gray-scale mathematical morphology, can also be embedded in this scheme since they can be identified with certain fuzzy approaches. (AU)

• Processo FAPESP: 06/06818-1 - Uma classe geral de memórias associativas morfológicas nebulosas
• Beneficiário: Marcos Eduardo Ribeiro Do Valle Mesquita
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado