2026-04-17T20:39:30Zhttps://recercat.cat/oai/request

oai:recercat.cat:10256/116562024-06-18T12:15:45Zcom_2072_452955com_2072_2054col_2072_453069

00925njm 22002777a 4500 dc García Hernandez, Rubén Jesús author Ureña, Carlos author Poch Garcia, Jordi author Sbert, Mateu author info:eu-repo/date/embargoEnd/2026-01-01 info:eu-repo/date/embargoEnd/2026-01-01 2014-10-01 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 http://hdl.handle.net/10256/11656 Kernel, Funcions de Kernel functions Infografia Computer graphics Funcional de densitat, Teoria del Density functionals Overestimation and underestimation biases in photon mapping with non-constant kernels