An Error Estimation Framework for Many‐Light Rendering

Abstract

Figure 1: Rendering results of (a) our method, relative error images of (b) our method and (c) Lightcuts [WFA * 05] in Sponza scene. Relative error threshold ε = 2% and confidence level α = 95% are specified. 92.96% pixels satisfy that the relative error is within 2% in our method, while only 43.67% pixels satisfy the condition in Lightcuts. In (d) Kitchen scene and (e) San Miguel scene, Cook-Torrance BRDFs and Ashikhmin-Shirely BRDFs are used, which cannot be used in Lightcuts. (f) and (g) show relative error images of (d) and (e), respectively. AbstractThe popularity of many-light rendering, which converts complex global illumination computations into a simple sum of the illumination from virtual point lights (VPLs), for predictive rendering has increased in recent years. A huge number of VPLs are usually required for predictive rendering at the cost of extensive computational time. While previous methods can achieve significant speedup by clustering VPLs, none of these previous methods can estimate the total errors due to clustering. This drawback imposes on users tedious trial and error processes to obtain rendered images with reliable accuracy. In this paper, we propose an error estimation framework for many-light rendering. Our method transforms VPL clustering into stratified sampling combined with confidence intervals, which enables the user to estimate the error due to clustering without the costly computing required to sum the illumination from all the VPLs. Our estimation framework is capable of handling arbitrary BRDFs and is accelerated by using visibility caching, both of which make our method more practical. The experimental results demonstrate that our method can estimate the error much more accurately than the previous clustering method.

Spherical Gaussian‐based Lightcuts for Glossy Interreflections

“…Nabata et al . [NIDN16] estimate the error due to clustering in a way of analyzing stratified sampling with confidence intervals. Stochastic Lightcuts 2019 uses stochastic sampling to eliminate sampling correlation of Lightcuts.…”

A method for estimating the errors in many-light rendering with supersampling

“…2, but the computational cost of obtaining this value is high. Therefore, our method estimates ΔÎ using the following equation [5]:…”

“…To select a pair of clusters to be subdivided, the standard deviation σ i for each pair (C L i , C G i ) is required. Although the sample variance s 2 i can be used to estimate σ i , the accuracy of this estimate is low, since our method estimatesÎ i with K = 2 samples, as does the previous method [5]. Instead of using the sample variance, our method calculates the standard deviation σ i for the i-th pair using the upper bounds of f and G, as follows:…”

“…To address this problem, Nabata et al [5] proposed a method to estimate errors in the pixel values due to VPL clustering. This method, however, estimates each pixel value using a single shading point and cannot be applied to visual effects such as anti-aliasing and depth-of-field (DOF), which require multiple shading points to estimate the pixel value.…”

“…MDLC estimates the upper bound for clustering error, but does not estimate the error in the pixel value (i.e., the sum of the errors due to clustering). We improve the estimation accuracy of the pixel value by combining a method for estimating errors [5] with MDLC [6]. Figure 3 shows an overview of our method, which estimates image pixel values by clustering VPLs and shading points.…”