Research Article

# Algebra of Geometric Filters Defined over Three Dimenisonal Rectangular Lattice-PartI

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@INPROCEEDINGS{10.1007/978-3-642-27317-9_11, author={Towheed Sultana and E. Rajan}, title={Algebra of Geometric Filters Defined over Three Dimenisonal Rectangular Lattice-PartI}, proceedings={Advances in Computer Science and Information Technology. Computer Science and Information Technology. Second International Conference, CCSIT 2012, Bangalore, India, January 2-4, 2012. Proceedings, Part III}, proceedings_a={CCSIT PART III}, year={2012}, month={11}, keywords={Geometric Filters 3-D image processing Image Algebra Extended Topology Topological Filters}, doi={10.1007/978-3-642-27317-9_11} }

- Towheed Sultana

E. Rajan

Year: 2012

Algebra of Geometric Filters Defined over Three Dimenisonal Rectangular Lattice-PartI

CCSIT PART III

Springer

DOI: 10.1007/978-3-642-27317-9_11

## Abstract

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 constructed in a 3X3X3 grid of pixels. The results are visualized as a distributive lattice. The lattice also contains its proper envelopes as its successors.

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