Pattern Representation by Minimum String Array Approach

Abstract

This paper is concerned with the intrinsic complexity of patterns. Previous works on the decomposition of pictures into their basic building blocks form the basis upon which the current work is based. However, the work presented here will look at the simplest description over all other descriptions. For a given domain the program complexity of Kolmogorov is to represent an image pattern in minimum length according to its pixel occurrence probability. Thus, the Kolmogorov complexity program is performed so that each 2-D image pattern is reduced into minimum resolution forooptimal storage, pattern recognition, or data communication purpose. The complexity of an image pattern is defined as the number of symbols in a given domain. For a binary image pattern, only two symbols are used which are ”0” and ”1” for object pixel or background. If the occurrence probability of a symbol in a block is the same, then it may be compacted together into a simple subblock to reduce its complexity. The complexity reduction algorithm can be performed by an automaton which reads the input pattern, measures its complexity, and transfers it into a new string array of the least complexity for data communication.