Algebra of Three Dimensional Geometric Filters and its Relevance in 3-D Image Processing

This paper gives a novel concept of what we call as Geometric Filters defined over a 3-D rectangular grid of pixels. These G-Filters have potential applications to processing of volumetric images. In addition, the paper describes in brief the algebra of G-Filters by formulating a lattice of convex polyhedrons (structuringelements) constructed in a 3X3X3 grid of pixels. The results are visualized as a distributive lattice. Mathematical morphology is an application of lattice theory .Many applications of mathematical morphology like erosion, dilation etc, use structuring elements. The work discussed in this paper is systematically generating the 3-D structuring elements by using geometric filters (G-Filters) for mathematical, morphological operations.