<title>Linear programming solutions to problems in logical inference and space-variant image restoration</title>

Abstract

Image Understanding is a cross-disciplinary field, drawing on concepts and algorithms from image processing, pattern recognition and artificial intelligence. An integrated system for image understanding may require a variety of capabilities that appear quite disparate, such as image restoration to compensate for degradations detected in the data, followed by logical inference to interpret features extracted from the restored data. In this paper we will establish that constrained optimization provides a uniform formulation for two such apparently disparate problems: restoration of blurred imagery, and logical deduction or mechanized inference. We shall show how to formulate problems in each of these categories as linear programming (LP) problems. The "deblurred" image is regained by minimizing a linear objective function subject to the constraints imposed by the blur. The degree of truth or falsity of a consequent proposition is established by maximizing a linear objective function subject to the constraints iniposed by the premises.