<title>Applications Of Moments To Image Understanding</title>

Abstract

AbstractSeveral problems in image understanding can be solved by applying the mathematical con­ cept of moments. In this presentation a review of the moment concept will be given, followed by a discussion of the applications of moments to image pattern recognition, change detection, quality evaluation and data compression.IntroductionThe mathematical concept of moments has been around for many years and has found useful applications in many diverse fields. In mechanics, the radius of gyration of a rigid body, its center of gravity and its moment of inertia are important parameters in establishing structural strength and equilibrium position. In statistics, the mean, variance, skewness and kurtosis help to define the probability density function of a random process. All of these parameters mentioned take on some form of the moment. It is not too surprising then, to find that moments have useful applications in other fields as well, such as in image understanding.This paper will discuss those properties of moments that make them highly suitable for solving problems in the image understanding areas of pattern recognition, image change detection, data compression, and image quality evaluation. Aside from its intrinsic value, it is felt that investigating these four seemingly disparate problems from a common per­ spective, allows one to more clearly grasp the interrelationships that really do exist between different areas of image understanding.Basic moment conceptsSeveral properties of moments will be particularly useful in the applications to be discussed and only these properties will be emphasized. We start out with a definition of moments and their properties in only one- di men si on (1-D), because of the easier conveyance of the underlying concepts involved. An extension to the physically more appropriate two- dimensional moments is fairly straightforward.The 1-D moment of order n is defined as