An Approach of Similarity Analysis for Non-Rigid Models Based on Diffusion Map with Thin-Plate Spline

Isometric transformation with geodesic distance is widely used in similarity analysis or 3D retrieval of non-rigid objects. However, geodesic distance is sensitive to topology noise and can be problematic in cases where objects topology is changed locally. In order to solve the problem, a new method based on diffusion map was proposed. We used diffusion map to compute embedded models and utilized thin-plate spline (TPS) to match the embedded models to obtain the similarity error of original objects. The method was tested on some examples, the results show that the new method is suitable to similarity analysis or 3D retrieval of non-rigid objects, moreover, our method is robust to the deformed objects with topology noise.