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Overestimation and underestimation biases in photon mapping with non-constant kernels

This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the th nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the th nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate

This work has been supported by the research projects coded TIN2010-21089-C03-01 and IPT-2011-0885-430000 (Spanish Commission for Science and Technology), by Grant 2009SGR643 (Catalan Government), and by FEDER funding from the European Union

Institute of Electrical and Electronics Engineers (IEEE)

Manager: Ministerio de Ciencia e Innovación (Espanya)
Generalitat de Catalunya. Agència de Gestió d’Ajuts Universitaris i de Recerca
Author: García Hernandez, Rubén Jesús
Ureña, Carlos
Poch Garcia, Jordi
Sbert, Mateu
Abstract: This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the th nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the th nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate
This work has been supported by the research projects coded TIN2010-21089-C03-01 and IPT-2011-0885-430000 (Spanish Commission for Science and Technology), by Grant 2009SGR643 (Catalan Government), and by FEDER funding from the European Union
Document access: http://hdl.handle.net/2072/296926
Language: eng
Publisher: Institute of Electrical and Electronics Engineers (IEEE)
Rights: Tots els drets reservats
Subject: Kernel, Funcions de
Kernel functions
Infografia
Computer graphics
Funcional de densitat, Teoria del
Density functionals
Title: Overestimation and underestimation biases in photon mapping with non-constant kernels
Type: info:eu-repo/semantics/article
Repository: Recercat

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