Image processing and pattern recognition by polynomial approach

This thesis describes a polynomial approach to the representation of binary, gray and color images for machine vision. First, we develop an algebraic system and show that most of the standard image processing can be done by our method. Further, we develop some operators which rely on the intrinsic properties of polynomials. In particular, we develop an algorithm to decompose a template by the separability property of polynomial to reduce the time complexity in parallel processing. In Chapter 1 we investigate an algebra system based on the finite field GF(2) and show how to implement most of the standard binary image processing operations. In Chapter 2 we extend the algebra described in chapter 1 to process gray, color and 3-D images. In Chapter 3 we generalize polynomial algebra and introduce algebraic operators to perform certain basic image processings. In Chapter 4, we apply the template polynomial approach to pattern recognition to label the connected components of a binary image, to decompose the shape of the image, to match a picture with a template and to find the skeleton of the gray image. We also develop a method to decompose the template which reduces the time complexity significantly for a large sized template. We obtain a necessary and sufficient condition for the decomposability of a template. Polynomial approach can be used to develop a standardized algebra-based image processing language, which is capable of expressing a wide variety of image transformation