Exact-NeRF: An Exploration of a Precise Volumetric Parameterization for Neural Radiance Fields

Isaac-Medina, B.K.S.; Willcocks, C.G.; Breckon, T.P.

Abstract

Neural Radiance Fields (NeRF) have attracted significant attention due to their ability to synthesize novel scene views with great accuracy. However, inherent to their underlying formulation, the sampling of points along a ray with zero width may result in ambiguous representations that lead to further rendering artifacts such as aliasing in the final scene. To address this issue, the recent variant mipNeRF proposes an Integrated Positional Encoding (IPE) based on a conical view frustum. Although this is expressed with an integral formulation, mip-NeRF instead approximates this integral as the expected value of a multivariate Gaussian distribution. This approximation is reliable for short frustums but degrades with highly elongated regions, which arises when dealing with distant scene objects under a larger depth of field. In this paper, we explore the use of an exact approach for calculating the IPE by using a pyramid-based integral formulation instead of an approximated conical-based one. We denote this formulation as Exact-NeRF and contribute the first approach to offer a precise analytical solution to the IPE within the NeRF domain. Our exploratory work illustrates that such an exact formulation (Exact-NeRF) matches the accuracy of mip-NeRF and furthermore provides a natural extension to more challenging scenarios without further modification, such as in the case of unbounded scenes. Our contribution aims to both address the hitherto unexplored issues of frustum approximation in earlier NeRF work and additionally provide insight into the potential future consideration of analytical solutions in future NeRF extensions.

Citation

Isaac-Medina, B., Willcocks, C., & Breckon, T. (2023, June). Exact-NeRF: An Exploration of a Precise Volumetric Parameterization for Neural Radiance Fields. Presented at IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023, Vancouver, BC

• Presentation Conference Type: Conference Paper (published)
• Conference Name: IEEE/CVF Conference on Computer Vision and Pattern Recognition 2023
• Start Date: Jun 18, 2023
• End Date: Jun 22, 2023
• Acceptance Date: Feb 27, 2023
• Publication Date: 2023-06
• Deposit Date: Apr 18, 2023
• Publicly Available Date: Jun 30, 2023
• Publisher: Institute of Electrical and Electronics Engineers
• Public URL: https://durham-repository.worktribe.com/output/1134358
• Publisher URL: https://ieeexplore.ieee.org/xpl/conhome/1000147/all-proceedings