-Idempotent and Self-Dual Morphological Filters

In this paper, we present a comprehensive analysis of selfdual and m-idempotent operators. We refer to an operator as midempotent if it converges after m iterations. We focus on an important special case of the general theory of lattice morphology: Spatiallyvariant 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 midempotence properties by an application to speckle noise removal in radar images.