Statistical Modeling of Photographic Images

The set of all possible visual images is huge, but not all of these are equally likely to be encountered by an imaging device such as the eye. Knowledge of this nonuniform probability on the image space is known to be exploited by biological visual systems, and can be used to advantage in the majority of applications in image processing and machine vision. For example, loosely speaking, when one observes a visual image that has been corrupted by some sort of noise, the process of estimating the original source image may be viewed as one of looking for the highest-probability image that is “close to ” the noisy observation. The problem of compression essentially boils down to using a larger proportion of the available bits to encode those regions of the image space that are more likely. And problems such as resolution enhancement or image synthesis involve selecting (sampling) a highprobability image from the distribution, perhaps subject to some set of constraints. Precise developments of such applications can be found in many chapters throughout this book. In order to develop a probability model for visual images, we first must decide which images to model. In a practical sense, this means we must (a) decide on imaging conditions, such as the field of view, resolution, sensor or postprocessing nonlinearities, etc, (b) decide what kind of scenes, under what kind of lighting, are to be captured in the images. It may seem odd, if one has not encountered such models, to imagine that all images are drawn from a single universal probability urn. In particular, the features and properties in any given image are often specialized. For example, outdoor nature scenes contain structures that are quite different from city streets, which in turn are nothing like human faces. There are two means by which this dilemma is resolved. First, the statistical properties that we will examine are basic enough that they are relevant for essentially all visual scenes. Second, we will use parametric models, in which a set of hyperpa