Neural Descriptors: Self-Supervised Learning of Robust Local Surface Descriptors Using Polynomial Patches
This work addresses the need for more reliable shape descriptors in 3D shape analysis, particularly for applications involving noisy or incomplete data, though it is incremental as it builds on existing shape correspondence frameworks.
The paper tackles the problem of classical shape descriptors being sensitive to mesh connectivity, sampling patterns, and topological noise by introducing a self-supervised learning approach for robust local surface descriptors, resulting in improved performance on benchmarks like FAUST, SCAPE, TOPKIDS, and SHREC'16 with enhanced robustness to topological noise and partial shapes.
Classical shape descriptors such as Heat Kernel Signature (HKS), Wave Kernel Signature (WKS), and Signature of Histograms of OrienTations (SHOT), while widely used in shape analysis, exhibit sensitivity to mesh connectivity, sampling patterns, and topological noise. While differential geometry offers a promising alternative through its theory of differential invariants, which are theoretically guaranteed to be robust shape descriptors, the computation of these invariants on discrete meshes often leads to unstable numerical approximations, limiting their practical utility. We present a self-supervised learning approach for extracting geometric features from 3D surfaces. Our method combines synthetic data generation with a neural architecture designed to learn sampling-invariant features. By integrating our features into existing shape correspondence frameworks, we demonstrate improved performance on standard benchmarks including FAUST, SCAPE, TOPKIDS, and SHREC'16, showing particular robustness to topological noise and partial shapes.