Research on Similarity Measurements of 3D Models Based on Skeleton Trees

There is a growing need to be able to accurately and efficiently recognize similar models from existing model sets, in particular, for 3D models. This paper proposes a method of similarity measurement of 3D models, in which the similarity between 3D models is easily, accurately and automatically calculated by means of skeleton trees constructed by a simple rule. The skeleton operates well as a key descriptor of a 3D model. Specifically, a skeleton tree represents node features (including connection and orientation) that can reflect the topology and branch features (including region and bending degree) of 3D models geometrically. Node feature distance is first computed by the dot product between node connection distance, which is defined by 2-norm, and node orientation distance, which is defined by tangent space distance. Then branch feature distances are computed by the weighted sum of the average regional distances, as defined by generalized Hausdorff distance, and the average bending degree distance as defined by curvature. Overall similarity is expressed as the weighted sum of topology and geometry similarity. The similarity calculation is efficient and accurate because it is not necessary to perform other operations such as rotation or translation and it considers more topological and geometric information. The experiment demonstrates the feasibility and accuracy of the proposed method