Salient spectral geometric features for shape matching and retrieval

This paper introduces a new method for extracting salient features from surfaces that are represented by triangle meshes. Our method extracts salient geometric feature points in the Laplace-Beltrami spectral domain instead of usual spatial domains. Simultaneously, a spatial region is determined as a local support of each feature point, which is correspondent to the "frequency" where the feature point is identified. The local shape descriptor of a feature point is the Laplace-Beltrami spectrum of the spatial region associated to the points which are stable and distinctive. Our method leads to the salient spectral geometric features invariant to spatial transforms such as translation, rotation, and scaling. The properties of the discrete Laplace-Beltrami operator make them invariant to isometric deformations and mesh triangulations as well. With the scale information transformed from the "frequency", the local supporting region always maintains the same ratio to the original model no matter how it is scaled. This means that the spatial region is scale-invariant as well. Therefore, both global and partial matching can be achieved with these salient feature points. We demonstrate the effectiveness of our method with many experiments and applications.