A qualitative model for space

TLDR

Most geometric models are quantitative, making it difficult to abstract underlying spatial information needed for planning, learning, or vision, and their precision often exceeds the actual accuracy of data. This work proposes a systematic representation that builds spatial maps from local qualitative relations between objects. The representation derives functionally relevant relations based on accidental alignments, employs interval logic for one‑dimensional cases and a formalism for alignment‑based reasoning in two or more dimensions, and handles uncertainty by constructing bounded inferences from disjunctive input data. Its principal advantages are that it is free of subjective bias and is qualitatively complete in distinguishing all overlap, tangency, and no‑contact geometries.

Abstract

Most geometric models are quantitative, making it difficult to abstract underlying spatial information needed for tasks such as planning, learning or vision. Furthermore, precision used in a typical quantitative system often exceeds actual accuracy of 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 relevant - i.e. those that involve accidental alignments, or can be described based on such alignments. In one dimension, interval logic (Allen 83] provides a mechanism for representing these type of relations; in this work we propose a formalism that enables us to perform alignment-based reasoning in two and higher dimensions with objects at angles. The principal advantages of this representation is that a) it is free of subjective bias, and b) it is complete in qualitative sense of distinguishing all overlap/ tangency/nocontact geometries. In addition, model is capable of handling uncertainty in initial system (e.g. the fuse box is somewhere behind compressor) by constructing bounded inferences from disjunctive input data. two kinds of uncertainty can be handled - those arising from deliberate imprecision in interest of compactness (down road from), or those caused by an inadequacy of data (sensors, spatial descriptions, or maps).