LBONet: Supervised Spectral Descriptors for Shape Analysis
This addresses the problem of performance breakdown in real-world shape analysis applications for researchers and practitioners in computer vision and graphics, though it is incremental as it builds on existing spectral descriptors.
The paper tackles the limitation of the Laplace-Beltrami operator (LBO) in shape analysis, which only works well under isometric deformations, by proposing a supervised method to learn task-specific operators that optimize the LBO eigenbasis, resulting in enormous improvements in tasks like retrieval, classification, segmentation, and correspondence.
The Laplace-Beltrami operator has established itself in the field of non-rigid shape analysis due to its many useful properties such as being invariant under isometric transformation, having a countable eigensystem forming an orthornormal basis, and fully characterizing geodesic distances of the manifold. However, this invariancy only applies under isometric deformations, which leads to a performance breakdown in many real-world applications. In recent years emphasis has been placed upon extracting optimal features using deep learning methods,however spectral signatures play a crucial role and still add value. In this paper we take a step back, revisiting the LBO and proposing a supervised way to learn several operators on a manifold. Depending on the task, by applying these functions, we can train the LBO eigenbasis to be more task-specific. The optimization of the LBO leads to enormous improvements to established descriptors such as the heat kernel signature in various tasks such as retrieval, classification, segmentation, and correspondence, proving the adaption of the LBO eigenbasis to both global and highly local learning settings.