Three-Dimensional CAD Model Matching with Anisotropic Diffusion Maps

In modern manufacturing, retrieval and reuse of the pre-existed three-dimensional (3-D) computer-aided design (CAD) models would greatly save time and cost in the product development cycle. For the 3-D CAD model retrieval, one is confronted with the quality of searching in large databases with models in complex structure and high dimension. This paper proposes a new 3-D model matching approach that reduces the data dimension and matches the models effectively. It is based on diffusion maps which integrate the random walk and anisotropic kernel to extract intrinsic features of models with complex geometries. The high-dimensional data points in diffusion space are projected into low-dimensional space and the low-dimension embedding coordinates are extracted as features. They are then used with the Grovmov Hausdorff distance for model retrieval. These coordinates could capture multiscale spectral properties of the 3-D geometry and have shown good robustness to noise. In the experiments, the proposed algorithm has shown better performance compared to the celebrated eigenmap approach in the 3-D model retrieval from the aspects of precision and recall.