DDSL: Deep Differentiable Simplex Layer for Learning Geometric Signals

Understand

We present a Deep Differentiable Simplex Layer (DDSL) for neural networks for geometric deep learning.

• The DDSL is a differentiable layer compatible with deep neural networks for bridging simplex mesh-based geometry representations (point clouds, line mesh, triangular mesh, tetrahedral mesh) with raster images (e.g., 2D/3D grids).
• The DDSL uses Non-Uniform Fourier Transform (NUFT) to perform differentiable, efficient, anti-aliased rasterization of simplex-based signals.
• We present a complete theoretical framework for the process as well as an efficient backpropagation algorithm.