Spatially-variant mathematical morphology for color images

In this paper, we present an approach of the generalization of the Spatially-Variant Morphological Operators to the color images, that preserves the concept of the structuring function. Two methods are suggested. The first method is based on total ordering and the second on marginal treatment of each component of the image. For each method, we define the notion of Spatially-Variant (SV) structuring elements, the basic color operators (dilation, erosion, opening and closing). The former operators allow the construction of morphological filters obtained by infimum, supremum and composition operations. Examples are provided through simulations to show the potential power of the defined operators for image filtering.