NeRF Revisited: Fixing Quadrature Instability in Volume Rendering

• URL: http://arxiv.org/abs/2310.20685v2
• Date: Fri, 19 Jan 2024 18:53:13 GMT
• Title: NeRF Revisited: Fixing Quadrature Instability in Volume Rendering
• Authors: Mikaela Angelina Uy, Kiyohiro Nakayama, Guandao Yang, Rahul Krishna Thomas, Leonidas Guibas, Ke Li
• Abstract summary: Volume rendering requires evaluating an integral along each ray, which is numerically approximated with a finite sum. The rendered result is unstable w.r.t. the choice of samples along the ray, a phenomenon that we dub quadrature instability. We propose a mathematically principled solution by reformulating the sample-based rendering equation so that it corresponds to the exact integral under piecewise linear volume density.
• Score: 8.82933411096762
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural radiance fields (NeRF) rely on volume rendering to synthesize novel views. Volume rendering requires evaluating an integral along each ray, which is numerically approximated with a finite sum that corresponds to the exact integral along the ray under piecewise constant volume density. As a consequence, the rendered result is unstable w.r.t. the choice of samples along the ray, a phenomenon that we dub quadrature instability. We propose a mathematically principled solution by reformulating the sample-based rendering equation so that it corresponds to the exact integral under piecewise linear volume density. This simultaneously resolves multiple issues: conflicts between samples along different rays, imprecise hierarchical sampling, and non-differentiability of quantiles of ray termination distances w.r.t. model parameters. We demonstrate several benefits over the classical sample-based rendering equation, such as sharper textures, better geometric reconstruction, and stronger depth supervision. Our proposed formulation can be also be used as a drop-in replacement to the volume rendering equation of existing NeRF-based methods. Our project page can be found at pl-nerf.github.io.

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