A comparative study of spectral embedding methods for triangle meshes

In order to have a better understanding and use of the strengths and weaknesses of different spectral approaches in the field of geometry processing and analysis, this preliminary comparative study investigates the behaviors of four spectral embedding methods: Global Point Signatures Embedding (GPSE), Heat Kernel Signature Embedding (HKSE), Multi-Dimensional Scaling Embedding (MDSE), and Spectral Embedding using Gaussian-filtered affinity matrices (SEG), by applying them onto three applications. Therefore experimental observations are obtained based on the limited test cases. For the mesh segmentation, HKSE and GPSE tend to outperform MDSE and SEG with better segments and boundaries. For the symmetry detection, all the embedding methods produce similar results. For the shape correspondence, MDSE and SEG show better performance and more stability than GPSE and HKSE. All in all, there is no single one embedding method that clearly outperforms the others across all three applications.