4 research outputs found
Detecting Bias in Monte Carlo Renderers using Welchâs t-test
When checking the implementation of a new renderer, one usually compares the output to that of a reference implementation. However, such tests require a large number of samples to be reliable, and sometimes they are unable to reveal very subtle differences that are caused by bias, but overshadowed by random noise. We propose using Welchâs t-test, a statistical test that reliably finds small bias even at low sample counts. Welchâs t-test is an established method in statistics to determine if two sample sets have the same underlying mean, based on sample statistics. We adapt it to test whether two renderers converge to the same image, i.e., the same mean per pixel or pixel region. We also present two strategies for visualizing and analyzing the testâs results, assisting us in localizing especially problematic image regions and detecting biased implementations with high confidence at low sample counts both for the reference and tested implementation
Perceptual error optimization for Monte Carlo rendering
Realistic image synthesis involves computing high-dimensional light transport
integrals which in practice are numerically estimated using Monte Carlo
integration. The error of this estimation manifests itself in the image as
visually displeasing aliasing or noise. To ameliorate this, we develop a
theoretical framework for optimizing screen-space error distribution. Our model
is flexible and works for arbitrary target error power spectra. We focus on
perceptual error optimization by leveraging models of the human visual system's
(HVS) point spread function (PSF) from halftoning literature. This results in a
specific optimization problem whose solution distributes the error as visually
pleasing blue noise in image space. We develop a set of algorithms that provide
a trade-off between quality and speed, showing substantial improvements over
prior state of the art. We perform evaluations using both quantitative and
perceptual error metrics to support our analysis, and provide extensive
supplemental material to help evaluate the perceptual improvements achieved by
our methods
Quantifying the Error of Light Transport Algorithms
This paper proposes a new methodology for measuring the error of unbiased physically based rendering algorithms. The current state of the art includes mean squared error (MSE) based metrics and visual comparisons of equalâtime renderings of competing algorithms. Neither is satisfying as MSE does not describe behavior and can exhibit significant variance, and visual comparisons are inherently subjective. Our contribution is twoâfold: First, we propose to compute many short renderings instead of a single long run and use the short renderings to estimate MSE expectation and variance as well as perâpixel standard deviation. An algorithm that achieves good results in most runs, but with occasional outliers is essentially unreliable, which we wish to quantify numerically. We use perâpixel standard deviation to identify problematic lighting effects of rendering algorithms. The second contribution is the error spectrum ensemble (ESE), a tool for measuring the distribution of error over frequencies. The ESE serves two purposes: It reveals correlation between pixels and can be used to detect outliers, which offset the amount of error substantially.Academy of FinlandHorizon 20201111211