Differentiable Heightfield Path Tracing with Accelerated Discontinuities

We investigate the problem of accelerating a physically-based differentiable renderer for heightfields based on path tracing with global illumination. On a heightfield with 1 million vertices (1024x1024 resolution), our differentiable renderer requires only 4 ms per sample per pixel when differentiating direct illumination, orders of magnitude faster than most existing general 3D mesh differentiable renderers. It is well-known that one can leverage spatial hierarchical data structures (e.g., the maximum mipmaps) to accelerate the forward pass of heightfield rendering. The key idea of our approach is to further utilize the hierarchy to speed up the backward pass-differentiable heightfield rendering. Specifically, we use the maximum mipmaps to accelerate the process of identifying scene discontinuities, which is crucial for obtaining accurate derivatives. Our renderer supports global illumination. we are able to optimize global effects, such as shadows, with respect to the geometry and the material parameters. Our differentiable renderer achieves real-time frame rates and unlocks interactive inverse rendering applications. We demonstrate the flexibility of our method with terrain optimization, geometric illusions, shadow optimization, and text-based shape generation.