Introduction

Abstract

A fundamental task of knowledge representation and processing is to infer properties of real objects or situations given their representations. In spatial knowledge representation, and in particular, in computer vision, real objects are represented in a pictorial way as finite sets (also called discrete sets), since computers only can handle finite structures. The discrete sets result from a quantization process, in which real objects are approximated by discrete sets. This is a standard process in finite element models in engineering. In computer vision, this process is called sampling or digitization and is naturally realized by technical devices like CCD cameras or scanners. Consequently, a fundamental question addressed in spatial knowledge representation is: which properties inferred from discrete representations of real objects correspond to properties of their originals, and under what conditions is this the case? In this book, we present a comprehensive answer to this question with respect to important topological and certain geometrical properties.