Qualitative vision rules, combining theorems, and derivational algorithms

Abstract

Basic steps to 3-D scene analysis may be encoded by qualitative rules of reasoning specifying assumptions (a model description) and a list of some 2-D or 3-D features in the premise, and one or several feature(s) in the conclusion for which a certain constraint may be derived. In integrative approaches, cp. for example Aloimonos and Shulman (1989) and Kanatani (1990), the list in the premise consists of at least two features, as local displacement (optical flow), texture, or lighting direction. Such rules are verified by combining theorems which may also be used to design derivational algorithms. Rule, theorem, and algorithm constitute a derivational unit which has to be considered in detail for analyzing its potential power for complex solutions in Computer Vision. The evaluation of such a derivational unit, resp. its qualitative rule, is possible via the specified algorithm (time complexity, numeric stability, etc.), and its behavior for selected classes of scenes. In this paper, the proposed general approach of the study of derivational units is illustrated by the discussion of some integrative approaches for shape analysis using local displacement, intensity ratios, lighting direction, etc., as features in the premise.