A Qualitative Model for Space

Most geometric models are quantitative, making it diffiiult to abstract the underlying spatial information needed for tasks such as planning, learning or vision. Furthermore, the precision used in a typical quantitative system often exceeds the actual accuracy of the data. In this work we describe a systematic representation that builds spatial maps based on local qualitative relations between objects. It derives relations that are more “functionally relevanr i.e. those that involve acckfental aiignments. or can be described based on such alignments. In one dimension, interval logic (Allen 331 provides a mechanism for representing these type of relations; in this work we propose a formalism that enables us to perform aiignment-based reasoning in two and higher dimensions with objects at angles. The principal advanmges of this representation is that a) it is free of subjective bias, and b) it is complete in the qualitative sense of distinguishing all overlap/ tangency/nocontact geometries. In addition, the model is capable of handling uncertainty in the initial system (e.g. “the fuse box is somewhere behind the compressor) by constructing bounded inferences from disjunctive input dam. Two kinds of uncertainty can be handled those arising from deliberate imprecision in the interest of compactness (“down the road from”), or those caused by an inadequacy of data (sensors, spatial descriptions, or maps).