A tunable distance measure for coloured solid models

Abstract

People are willing to rank simple objects of different shape and colour on the basis of “similarity”. If machines are to reason about structure, this comparison process must be formalized. That is, a distance measure between formal object representations must be defined. If the machine is reasoning with information to be presented to a human, the distance measure needs to accord with human notions of object similarity. Since our perception of similarity is subjective and strongly influenced by situation, the measure should be tunable to particular users and contexts. This paper describes a distance measure between solid models which incorporates heuristics of the mental mappings humans use to compare objects. The first step is to formally represent objects in a way that reflects human visual segmentations. We use a modified boundary representation scheme in colour + physical space. The next step is to define a family of maps between these representations, motivated by considerations of how humans match shapes. The distance between two objects is essentially the cost of the lowest-cost map between them. The cost of a map incorporates a geometric measure of the smooth deformation required of edges and faces, a feature measure based on visually significant singular points, and a topological measure based on correspondence of visually significant vertices, edges and faces. Tunable features of the match are: the relative cost of ignoring parts of objects; the treatment of colour; and whether or not the distance measure is required to be rotation invariant. An important application for such distance measures is to the development of user-friendly query of CAD and image databases. Query-by-example depends on implementation of a concept of likeness between object models in the database which, to be useful, must reflect the user's concepts. Another important application for distance measures is in automatic recognition of objects into classes whose members are not identical, so that the concept that “this object is like object X” is required. In the common situation that classes are based on human perceptions of visual similarity, the distance measure between the class prototype and the object to be classified should reflect those human perceptions.