Interpreting three-dimensional shape distributions

Effective content-based shape retrieval systems would allow engineers to search data-bases of three-dimensional computer-aided design (CAD) models for objects with specific geometries or features. Much of the academic work in this area has focused on the development of indexing schemes based on different types of three-dimensional to two-dimensional 'shape functions'. Ideally, the shape function used to generate a distribution should be easy to compute and permit the discrimination of both large and small features. The work reported in this paper describes the properties of three new shape distributions based on computationally simple shape functions. The first shape function calculates the arithmetic difference between distributions derived (using the original D2 distance shape function) from both a three-dimensional model and its convex hull. The second shape function is obtained by sampling the angle between random pairs of facets on the object. The third shape function uses the surface orientation to filter the results of a distance distribution. The results reported in this paper suggest that these novel shape functions improve significantly the ability of shape distributions to discriminate between complex engineering parts. © IMechE 2005.