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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

© IEEE Transactions on Visualization and Computer Graphics, 2014, vol. 20, núm. 10, p. 1441-1450

Institute of Electrical and Electronics Engineers (IEEE)

Autor: García Hernandez, Rubén Jesús
Ureña, Carlos
Poch Garcia, Jordi
Sbert, Mateu
Data: 1 octubre 2014
Resum: 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
Format: application/pdf
ISSN: 1077-2626 (versió paper)
1941-0506 (versió electrònica)
Accés al document: http://hdl.handle.net/10256/11656
Llenguatge: eng
Editor: Institute of Electrical and Electronics Engineers (IEEE)
Col·lecció: MICINN/PN 2011-2013/TIN2010-21089-C03-01
AGAUR/2009-2014/2009 SGR-643
Reproducció digital del document publicat a: http://dx.doi.org/10.1109/TVCG.2014.2314665
Articles publicats (D-IMA)
És part de: © IEEE Transactions on Visualization and Computer Graphics, 2014, vol. 20, núm. 10, p. 1441-1450
Drets: Tots els drets reservats
Matèria: Kernel, Funcions de
Kernel functions
Infografia
Computer graphics
Funcional de densitat, Teoria del
Density functionals
Títol: Overestimation and underestimation biases in photon mapping with non-constant kernels
Tipus: info:eu-repo/semantics/article
Repositori: DUGiDocs

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