Adaptive Bayesian Classification of Spatial Data

Abstract

Abstract A two-dimensional scene is analyzed statistically by superimposing on it a rectangular grid and studying each square picture element (pixel) as one unit of the entire picture. With each pixel we want to associate one of K labels, but the label must be determined. Labels may be related to one another spatially, reflecting an underlying pattern in the scene. There is a noisy observation vector associated with each pixel, and these vectors are used contextually to classify the pixels; that is, to determine their labels in an effort to reconstruct the true scene. The discretized picture and the K labels constitute a lattice structure. We assume there is prior information available to assist in the reconstruction. The adaptive Bayesian classification (ABC) procedure proposed is iterative. It starts with a formal predictive contextual Bayesian classification of the entire map, then proceeds by adaptively reclassifying all of the labels in the map at each iteration using an empirical Bayesian updating algorithm. The ABC algorithm provides an approximation to a local maximum for the joint posterior classification probability of all pixels in the map. The procedure attempts to improve on other such iterative procedures by reestimating parameters and reclassifying pixels by conditioning initially on prior information via the predictive Bayesian paradigm. It is “adaptive Bayesian” in that its initial reconstruction stage is formal Bayesian, and it also uses a Bayes theorem-type argument for updating the data at each iteration. Applications include image processing of remotely sensed satellite data, photon emission tomography, and computer vision.