NeRF Revisited: Fixing Quadrature Instability in Volume Rendering

Fuente: arXiv
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Main Authors: Uy, Mikaela Angelina, Nakayama, Kiyohiro, Yang, Guandao, Thomas, Rahul Krishna, Guibas, Leonidas, Li, Ke
Format: Preprint
Published: 2023
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author Uy, Mikaela Angelina
Nakayama, Kiyohiro
Yang, Guandao
Thomas, Rahul Krishna
Guibas, Leonidas
Li, Ke
author_facet Uy, Mikaela Angelina
Nakayama, Kiyohiro
Yang, Guandao
Thomas, Rahul Krishna
Guibas, Leonidas
Li, Ke
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2310_20685
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle NeRF Revisited: Fixing Quadrature Instability in Volume Rendering
Uy, Mikaela Angelina
Nakayama, Kiyohiro
Yang, Guandao
Thomas, Rahul Krishna
Guibas, Leonidas
Li, Ke
Computer Vision and Pattern Recognition
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.
title NeRF Revisited: Fixing Quadrature Instability in Volume Rendering
topic Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2310.20685