M-Idempotent and self-dual morphological filters

Nidhal Bouaynaya, Mohammed Charif-Chefchaouni, Dan Schonfeld

    Research output: Contribution to journalArticlepeer-review

    4 Scopus citations

    Abstract

    In this paper, we present a comprehensive analysis of self-dual and m-idempotent operators. We refer to an operator as m-idempotent if it converges after m iterations. We focus on an important special case of the general theory of lattice morphology: spatially variant morphology, which captures the geometrical interpretation of spatially variant structuring elements. We demonstrate that every increasing self-dual morphological operator can be viewed as a morphological center. Necessary and sufficient conditions for the idempotence of morphological operators are characterized in terms of their kernel representation. We further extend our results to the representation of the kernel of m-idempotent morphological operators. We then rely on the conditions on the kernel representation derived and establish methods for the construction of m-idempotent and self-dual morphological operators. Finally, we illustrate the importance of the self-duality and m-idempotence properties by an application to speckle noise removal in radar images.

    Original languageEnglish (US)
    Article number6109268
    Pages (from-to)805-813
    Number of pages9
    JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
    Volume34
    Issue number4
    DOIs
    StatePublished - 2012

    All Science Journal Classification (ASJC) codes

    • Software
    • Computer Vision and Pattern Recognition
    • Computational Theory and Mathematics
    • Artificial Intelligence
    • Applied Mathematics

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