Qualitative Spatial Representation Based on Connection Pattern and Convexity

Contents

We present an extended PLCA that represents the shape of an object qualitatively. PLCA, a framework for qualitative reasoning, is based on the simple components: points(P), lines(L), circuits(C) and areas(A), and the entire figure is represented as a combination of these components. The entire space is considered to be partitioned into disjoint regions, and the connection patterns of regions can be distinguished. We extend PLCA to represent the qualitative shape of a region with a hierarchy of convex hulls. We formalize our approach, present an algorithm to generate the symbolic expression for a given figure, and discuss the properties that should be satisfied by this expression. Our goal is to represent not only the shapes of the outer circuits of single regions, but also those of the boundaries between regions.