Abstract: I will talk about a novel method for differentiating integrals of discontinuous functions, which frequently arise in inverse graphics, computer vision, and machine learning, and are a key bottleneck for gradient-based optimization. Prior approaches either rely on specialized routines to sample discontinuity boundaries of predetermined primitives, or use reparameterization techniques that suffer from high variance. In contrast, my method handles general discontinuous functions expressed as shader programs, without requiring manually specified boundary sampling procedures.

This is achieved through a program transformation that converts discontinuous functions into piecewise constant ones, enabling efficient boundary sampling via a novel segment snapping technique, and accurate derivatives at discontinuities by comparing values on either side of the boundary. The method supports both explicit boundaries (e.g., polygons, ellipses, Bézier curves) and implicit ones (e.g., neural networks, noise-based functions, swept surfaces). I demonstrate that it enables low-variance, accurate gradient estimation across applications including painterly rendering, raster image fitting, constructive solid geometry, swept surfaces, mosaicing, and ray marching.

Project website: https://yashbelhe.github.io/asd/index.html

Speaker Bio: Yash Belhe is an incoming Research Scientist at Reve. He recently completed his PhD in Computer Science at the University of California, San Diego, advised by Ravi Ramamoorthi and Tzu-Mao Li. His research focuses on generative modeling, differentiable rendering, automatic differentiation systems, and neural representations for visual data. His work has received a SIGGRAPH Asia Best Paper Award and a SIGGRAPH Asia Best Paper Honorable Mention. More information is available at https://yashbelhe.github.io/.