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Detecting Bias in Monte Carlo Renderers using Welch’s t-test

Alisa Jung, Johannes Hanika, Carsten Dachsbacher

Journal of Computer Graphics Techniques 2020

Detecting Bias in Monte Carlo Renderers using Welch’s t-test
Welch’s t-test in an empty, gray box, testing a biased bidirectional path tracer (b) against an unbiased forward path tracer reference implementation (a), both limited to paths with 3 vertices, with 10 samples per pixel each. The two center images show the difference (c) and tile-wise difference (d), which hardly reveal any bias. Welch’s t-test outputs a color map (e) revealing bias to the right, and a non-uniform histogram of p-values (f) as strong evidence that (a) and (b) will not converge to the same image with more samples.


When developing a new renderer we usually want a way to check if it was implemented cor- rectly. Conventionally this is done by comparing to the output of a reference implementation. However, such tests require a large number of samples to be reliable, and sometimes are un- able to reveal very subtle differences that are caused by bias but overshadowed by random noise. We propose using a statistical test, Welch’s t-test, which reliably finds small bias even at low sample counts. Welch’s 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 re- gion. We also present two strategies for visualizing and analyzing the test’s 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.


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