Mathematics and Statistics Vol. 12(1), pp. 55 - 62
DOI: 10.13189/ms.2024.120108
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Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies

Carlos Lopez Garces , Nayeong Kong ^*
Department of Mathematics, Indiana University East, Richmond, IN 47374, USA

ABSTRACT

This paper investigates three distinct Monte Carlo estimators derived from the research of Sbert et al. These estimators are specifically tailored to the scattering equations using the Ward Bidirectional Reflectance Distribution Function (BRDF) integrated with a designed cosine-weighted environment map. In this paper, we have two goals. First, to bridge the gap between theoretical foundations and practical applicability to understand how these estimators can be seamlessly integrated as extensions to the acclaimed PBRT renderer. And the second is to measure their real-world performance. We aim to validate our methodology by comparing rendered images with varying convergence rates and deviations to the results of Sbert et al. This validation will ensure the robustness and reliability of our approaches. We analyze the analytical structure of these estimators to derive their precise form. We then implement the three estimators as extensions to the PBRT renderer, subjecting them to a numerical evaluation. We further evaluate the results of the estimator set and sampling strategy by utilizing another pair of incident radiance functions and BRDFs. The final step is to generate rendered images from the implementation to verify the results observed by Svart et el. and extend them with this new pair of functions.

KEYWORDS
Monte Carlo Estimators, Scattering Equation, Multiple Importance Sampling, Physically Based Rendering

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Carlos Lopez Garces , Nayeong Kong , "Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies," Mathematics and Statistics, Vol. 12, No. 1, pp. 55 - 62, 2024. DOI: 10.13189/ms.2024.120108.

(b). APA Format:
Carlos Lopez Garces , Nayeong Kong (2024). Derivation and Evaluation of Monte Carlo Estimators of the Scattering Equation Using the Ward BRDF and Different Sample Allocation Strategies. Mathematics and Statistics, 12(1), 55 - 62. DOI: 10.13189/ms.2024.120108.