We present a novel method to differentiate integrals of discontinuous functions, which are common in inverse graphics, computer vision, and machine learning applications. Previous methods either require specialized routines to sample the discontinuous boundaries of predetermined primitives, or use reparameterization techniques that suffer from high variance. In contrast, our method handles general discontinuous functions, expressed as shader programs, without requiring manually specified boundary sampling routines. We achieve this through a program transformation that converts discontinuous functions into piecewise constant ones, enabling efficient boundary sampling through a novel segment snapping technique, and accurate derivatives at the boundary by simply comparing values on both sides of the discontinuity. Our method handles both explicit boundaries (polygons, ellipses, Bézier curves) and implicit ones (neural networks, noise-based functions, swept surfaces). We demonstrate that our system supports a wide range of applications, including painterly rendering, raster image fitting, constructive solid geometry, swept surfaces, mosaicing, and ray marching.

In recent years, reconstruction methods have been developed that can recover strand-level hair geometry from images. However, these methods recover a vast number of individual hair strands that are difficult to edit and simulate. Many methods also rely on neural priors to infer non-visible inner hair, which can result in poor inner hair structure for complex hairstyles, such as curly hair. We propose an inverse hair grooming pipeline that transforms the imperfect 3D strands from these reconstruction methods into procedural hair grooms that consist of a small set of guide strands and hair grooming operators, inspired by pipelines used by artists in popular 3D modeling tools such as Blender and Houdini. We take a probabilistic view of these hair grooms and design various optimization strategies and loss functions to optimize for the guide strands and operator parameters. Due to the proceduralism, our resulting grooms can naturally represent challenging hairstyles, have structurally sound inner hair, and are easily editable.

Variance reduction techniques are widely used for reducing the noise of Monte Carlo integration. However, these techniques are typically designed with the assumption that the integrand is scalar-valued. Recognizing that rendering and inverse rendering broadly involve vector-valued integrands, we identify the limitations of classical variance reduction methods in this context. To address this, we introduce ratio control variates, an estimator that leverages a ratio-based approach instead of the conventional difference-based control variates. Our analysis and experiments demonstrate that ratio control variables can significantly reduce the mean squared error of vector-valued integration compared to existing methods and are broadly applicable to various rendering and inverse rendering tasks.

We propose a real-time path guiding method, Voxel Path Guiding (VXPG), that significantly improves fitting efficiency under limited sampling budget. Our key idea is to use a spatial irradiance voxel data structure across all shading points to guide the location of path vertices. For each frame, we first populate the voxel data structure with irradiance and geometry information. To sample from the data structure for a shading point, we need to select a voxel with high contribution to that point. To importance sample the voxels while taking visibility into consideration, we adapt techniques from offline many-lights rendering by clustering pairs of shading points and voxels. Finally, we unbiasedly sample within the selected voxel while taking the geometry inside into consideration. Our experiments show that VXPG achieves significantly lower perceptual error compared to other real-time path guiding and virtual point light methods under equal-time comparison. Furthermore, our method does not rely on temporal information, but can be used together with other temporal reuse sampling techniques such as ReSTIR to further improve sampling efficiency.

Ray tracing has been used for years in motion picture to generate photorealistic images while faster raster-based shading techniques have been preferred for video games to meet real-time requirements. However, recent Graphics Processing Units (GPUs) incorporate hardware accelerator units designed for ray tracing. These accelerator units target the process of traversing hierarchical tree data structures used to test for ray-object intersections. Distinct rays following similar paths through these structures execute many redundant ray-box intersection tests. We propose a ray intersection predictor that speculatively elides redundant operations during this process and proceeds directly to test primitives that the ray is likely to intersect. A key aspect of our predictor strategy involves identifying hash functions that preserve enough spatial information to identify redundant traversals. We explore how to integrate our ray prediction strategy into existing GPU pipelines along with improving the predictor effectiveness by predicting nodes higher in the tree as well as regrouping and scheduling traversal operations in a low cost, judicious manner. On a mobile class GPU with a ray tracing accelerator unit, we find the addition of a 5.5KB predictor per streaming multiprocessor improves performance for ambient occlusion workloads by a geometric mean of 26%.