A Contraction Mapping Method in Digital Image Processing

Abstract

The topological features of the objects or digital image pictures are characterized by digital topology. A digital image picture is a distinctive arrangement of numbers which are non negative. Decomposing an image picture into its constituent components and investigating its several characteristics with fundamental elements is generally coined as digital image processing. In investigating the fundamental constituents of images, the separation of connected segments are established to enquire the adjacency relationship. During this course of tracking, thinning and coding them, it is kept in mind that the specification of connectedness of the pictures remains unaltered. The characteristics of the constituent subsets and relationships may be stipulated when the image is fragmented into its elementary constituents. Some features of the subsets of these constituent parts are based on their respective positions. Thus, the basic idea for image processing is the primary topological characteristics of digital images like adjacency, connectedness, etc. The fixed point theorems associated to certain kinds of contraction mappings can be utilised in the field of engineering science and technology as computational technique to provide an exclusive programme to explore various problems. Parallel and distributed computation, modeling, simulation and digital image processing are few notables among these techniques. In digital image processing digital contraction mapping is defined and then existence of the solution and its uniqueness is obtained using the fixed point theorem concerned, which is the mathematical basis of border following, thinning and contour filling of a digital image picture. In digital image processing the applicability of fixed point theorem and contraction mappings as a computational technique has been grazed well. To further broaden its pertinency in image processing our interest is to delve into some of contraction mappings as a significant mechanism.