Quantifying the Convergence of Light-Transport Algorithms

Information

Abstract

This work aims at improving methods for measuring the error of unbiased, physically based light-transport algorithms. State-of-the-art papers show algorithmic improvements via error measures like Mean Square Error (MSE) or visual comparison of equal-time renderings. These methods are unreliable since outliers can cause MSE variance and visual comparison is inherently subjective. We introduce a simple proxy algorithm: pure algorithms produce one image corresponding to the computation budget N. The proxy, on the other hand, averages N independent images with a computation budget of 1. The proxy algorithm fulfils the preconditions for the Central Limit Theorem (CLT), and hence, we know that its convergence rate is (1/N). Since this same convergence rate applies for all methods executed using the proxy algorithm, comparisons using variance- or standard-deviation-per-pixel images are possible. These per-pixel error images can be routinely computed and allow comparing the render quality of different lighting effects. Additionally, the average of pixel variances is more robust against outliers compared to the traditional MSE or comparable metrics computed for the pure algorithm. We further propose the Error Spectrum Ensemble (ESE) as a new tool for evaluating lighttransport algorithms. It summarizes expected error and outliers over spatial frequencies. ESE is generated using the data from the proxy algorithm: N error images are computed using a reference, transformed into Fourier power spectra and compressed using radial averages. The descriptor is a summary of those radial averages. In the results, we show that standard-deviation images, short equal-time renderings, ESE and expected MSE are valuable tools for assessing light-transport algorithms.

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BibTeX

@mastersthesis{CELAREK-2017-QCL,
  title =      "Quantifying the Convergence of Light-Transport Algorithms",
  author =     "Adam Celarek",
  year =       "2017",
  abstract =   "This work aims at improving methods for measuring the error
               of unbiased, physically based light-transport algorithms.
               State-of-the-art papers show algorithmic improvements via
               error measures like Mean Square Error (MSE) or visual
               comparison of equal-time renderings. These methods are
               unreliable since outliers can cause MSE variance and visual
               comparison is inherently subjective. We introduce a simple
               proxy algorithm: pure algorithms produce one image
               corresponding to the computation budget N. The proxy, on the
               other hand, averages N independent images with a computation
               budget of 1. The proxy algorithm fulfils the preconditions
               for the Central Limit Theorem (CLT), and hence, we know that
               its convergence rate is (1/N). Since this same convergence
               rate applies for all methods executed using the proxy
               algorithm, comparisons using variance- or
               standard-deviation-per-pixel images are possible. These
               per-pixel error images can be routinely computed and allow
               comparing the render quality of different lighting effects.
               Additionally, the average of pixel variances is more robust
               against outliers compared to the traditional MSE or
               comparable metrics computed for the pure algorithm. We
               further propose the Error Spectrum Ensemble (ESE) as a new
               tool for evaluating lighttransport algorithms. It summarizes
               expected error and outliers over spatial frequencies. ESE is
               generated using the data from the proxy algorithm: N error
               images are computed using a reference, transformed into
               Fourier power spectra and compressed using radial averages.
               The descriptor is a summary of those radial averages. In the
               results, we show that standard-deviation images, short
               equal-time renderings, ESE and expected MSE are valuable
               tools for assessing light-transport algorithms.",
  month =      nov,
  address =    "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria",
  school =     "Institute of Computer Graphics and Algorithms, Vienna
               University of Technology ",
  keywords =   "error metric, global illumination",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2017/CELAREK-2017-QCL/",
}