In various applications, we often haveto deal with sets of images of a certain type; for example,X-rayimages, traffic sceneimages, in the set may be different from all the others, but at the same time all images may share certain common characteristics. We need the statistical description of images so that we capture these common characteristics and use them in order to represent an image with fewer bits and reconstruct it with the minimum error “on average”. | Image Processing The Fundamentals. Maria Petrou and Panagiota Bosdogianni Copyright 1999 John Wiley Sons Ltd Print ISBN 0-471-99883-4 Electronic ISBN 0-470-84190-7 Chapter 3 Statistical Description of Images What is this chapter about This chapter provides the necessary background for the statistical description of images from the signal processing point of view. Why do we need the statistical description of images In various applications we often haveto deal with sets of images of a certain type for example X-ray images traffic scene images etc. Each image in the set may be different from all the others but at the same time all images may share certain common characteristics. We need the statistical description of images so that we capture these common characteristics and use them in order to represent an image with fewer bits and reconstruct it with the minimum error on average . The first idea is then to try to minimize the mean square error in the reconstruction of the image if the same image or a collection of similar images were to be transmitted and reconstructed several times as opposed to minimizing the square error of each image separately. The second idea is that the data with which we would like to r present the image must be uncorrelated. Both these ideas lead to the statistical description of images. Is there an image transformation that allows its representation in terms of uncorrelated data that can be used to approximate the image in the least mean square error sense Yes. It is called Karhunen-Loeve or Hotelling transform. It is derived by treating the image as an instantiation of a random field. 90 Image Processing The Fundamentals What is a random field A random field is a spatial function that assigns a random variable at each spatial position. What is a random variable A random variable is the value we assign to the outcome of a random experiment. How do we describe random variables Random variables are described in terms of their distribution
