Warped-Area Reparameterization of Differential Path Integrals
Peiyu Xu1, Sai Bangaru2, Tzu-Mao Li3, and Shuang Zhao1
1University of California, Irvine          2MIT CSAIL          3University of California, San Diego
ACM Transactions on Graphics (SIGGRAPH Asia 2023), 42(6), 2023

Physics-based differentiable rendering is becoming increasingly crucial for tasks in inverse rendering and machine learning pipelines. To address discontinuities caused by geometric boundaries and occlusion, two classes of methods have been proposed: 1) the edge-sampling methods that directly sample light paths at the scene discontinuity boundaries, which require nontrivial data structures and precomputation to select the edges, and 2) the reparameterization methods that avoid discontinuity sampling but are currently limited to hemispherical integrals and unidirectional path tracing.

We introduce a new mathematical formulation that enjoys the benefits of both classes of methods. Unlike previous reparameterization work that focused on hemispherical integral, we derive the reparameterization in the path space. As a result, to estimate derivatives using our formulation, we can apply advanced Monte Carlo rendering methods, such as bidirectional path tracing, while avoiding explicit sampling of discontinuity boundaries. We show differentiable rendering and inverse rendering results to demonstrate the effectiveness of our method.

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Bibtex citation
        title={Warped-Area Reparameterization of Differential Path Integrals},
        author={Xu, Peiyu and Bangaru, Sai and Li, Tzu-Mao and Zhao, Shuang},
        journal={ACM Trans. Graph.},

We thank the anonymous reviewers for their constructive comments and Guangyan Cai, Wesley Chang, and Cheng Zhang for proofreading the paper. This project was partially funded by NSF grants 1900927 and 2105806.