Abstract Rendering:  Certified Rendering Under 3D Semantic Uncertainty
Yangge Li, Chenxi Ji, Xiangru Zhong, Huan Zhang, Sayan Mitra
The rendering process, which generates 2D images from 3D scene representations, has been extensively studied, yet the impact of camera pose and scene uncertainty on rendered outputs and downstream tasks remains underexplored. We propose **Abstract Rendering**, a framework that computes provable bounds on all images rendered under continuously varying camera poses and scene configurations. The resulting **Abstract Image**, defined by constraints over the image matrix, enables rigorous uncertainty propagation through rendering and downstream neural networks, offering a principled way to certify models under realistic 3D semantic perturbations—beyond traditional pixel-level noise models. Our approach propagates camera pose uncertainty through each rendering step using efficient piecewise linear bounds, including custom abstractions for three rendering-specific operations—matrix inversion, sorting-based aggregation, and cumulative product summation—not supported by standard tools. Our implementation, AbstractRender, targets two state-of-the-art photorealistic scene representations—Gaussian Splatting and Neural Radiance Fields (NeRF)—and scales to complex scenes with up to 1M Gaussians. Our computed provable image bounds achieves up to  3% over-approximation error comparing with sampling results (baseline) and enables certified robustness for downstream tasks, including classification (ResNet), object detection (YOLO), and pose estimation (GATENet) under camera pose uncertainty.