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Boundary Tracing Algorithm usning Abstract Cell Complexes

ABSTRACT
In this project we introduced the concept of Abstract Cell Complexes (ACC)on non-Euclidean spaces and some of its properties. Further we studied the concept of connectivity using notion of ACC. Also we established the result that every finite topological space with the separation property is isomorphic to an abstract cell complex. Finally we develop an algorithm for tracing the boundaries of the images.

INTRODUCTION

Geometry is an important tool for the study of digital images. However there are many geometrical problems in image analysis which cannot be solved on the basis of classical Euclidean geometry.
In this project we introduced a new notion of Abstract Cell Complex (ACC) which is independent of Euclidean geometry and based on locally finite T0 topological space. Further, we introduced the boundary, frontier and connectivity among the abstract elements using the notion of closed set, open set and more importantly smallest neighborhood of elements in cell complexes. Finally we established the result every finite topological space with separation property is isomorphic to an Abstract Cell Complex (ACC).
Using the ACC we encode the image with 0-cell, 1-cell, 2-cel and we developed an algorithm to trace the boundary of the images.