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

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 mip-NeRF 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.

Research on 3D Visualization of Drone Scenes Based on Neural Radiance Fields

“…It employs a progressively refined NeRF with a hierarchical network structure that incrementally introduces new modules during training to capture details at varying observation distances. Exact-NeRF [36] improves the Exact Integral Positional Encoding (EIPE) using a pyramidal frustum integral formula, reducing edge blur and aliasing. LIRF [37] predicts local volumetric radiance fields using samples within truncated cones to render high-quality images of new viewpoints on a continuous scale.…”