An algorithm for deciding similarities of 3-D objects

Abstract

A new algorithm for deciding the similarity of polyhedral objects is presented. The method consists of the following five sub-procedures.A polyhedron is decomposed into only convex components and represented as a hierarchical tree structure with those convex components, which has already been developed by the authors.From the tree structure, a new data structure called two layer structure, which consists of convex components separated into two layers, i.e., the first layer includes only positive convex components to be added and the second layer represents negative convex components to be subtracted from positive ones, is constructed.The two layer structure of an object is compared with that of another object.Each component of an object is compared with the corresponding convex component of the other object.Similarity of those two polyhedral objects is decided. In addition, similar and dissimilar parts can be recognized, even if two objects are totally not similar.The algorithm is implemented in C language and numerical similarities are calculated for various concave polyhedrons, and the correlation coefficient between numerical similarities and our feeling is calculated. The result is over 0.8. This means that the numerical similarities closely match our expectation.