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

Provided by: Academy & Industry Research Collaboration Center
Topic: Software
Format: PDF
In this paper, the authors give a novel concept of what they 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 (structuring elements) 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, and use structuring elements.

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