Spatial-scaling-compatible morphological granulometries on locally convex topological vector spaces
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abstract
Granulometries are defined on function classes over topological vector spaces. The usual Euclidiean property for scaling compatibility, set scaling in the binary case and graph scaling in the gray-scale case, is changed so that it is with respect to spatial (domain) scaling for function spaces. As in the binary case, scaling compatible granulometries possess representations as double suprema over scaled generating elements. Without further constraint on the generating elements, the double supremum involves, for each generating element, all scalings exceeding the parameter of the particular granulometric operator. The salient theorem of this paper concerns necessary and sufficient conditions under which there is a reduction of the double-supremum representation to a single supremum over singularly scaled generating functions.
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Image Algebra and Morphological Image Processing III
