Research On The Spatially-Variant Gray-Scale Morphological Operators

Based on the theory of umbra transform and surface operator, this paper studies the building way of spatially-variant gray-scale morphological operators, from the theory of spatially-variant binary morphology, in terms of the theory of kernel representation for the spatially-variant binary morphological operators, it discusses the theory of kernel representation for the spatially-variant gray-scale morphological operators, and made some innovative achievements. This paper will discuss the main content from the following three aspects:Firstly, it proves relevant conclusions about umbra sets, presents the spatially-variant gray-scale morphological opening and closing through umbra transform and surface operator, and demonstrates three operators(erosion, dilation, opening) with their corresponding algebraic forms, studies the properties of erosion, dilation, opening and closing, there are adjunction, increasing, composition, extensivity and anti-extensivity, idempotence etc, which are almostly consistent with the properties of spatially-variant binary morphological corresponding operators.Secondly, the duality is the important propery of the mathematical morphological operators.This paper studies the duality of the Spatially-Variant gray-scale morphological operators( erosion and dilation) on the basis of umbra transform from the duality of Spatially-Variant binary morphological operators( erosion and dilation).Finally, based on the theory of kernel representation for the spatially-variant binary morphological operators, this paper studies the theory of kernel representation for the spatially-variant gray-scale morphological operators from the theory of umbra transform and surface operator.