Overestimation and Underestimation Biases in Photon Mapping with Non-Constant Kernels

Area of Science:

• Computer Graphics
• Computational Imaging
• Rendering Algorithms

Background:

• Photon mapping is crucial for realistic rendering.
• Existing filtering kernels in photon mapping can introduce significant overestimation bias.
• Accurate density estimation is vital for reducing rendering artifacts.

Purpose of the Study:

• To analyze the overestimation bias in commonly used filtering kernels for photon mapping density estimation.
• To develop new, consistent estimators for improved accuracy.
• To evaluate the performance of modified Gaussian, cone, and differential filters.

Main Methods:

• Utilized the joint distribution of order statistics to compute expected values of irradiance estimators.
• Analyzed the consistency of cone, Epanechnikov, Silverman, and Gaussian filters.
• Introduced a new normalization constant and modified photon selection for Gaussian and cone filters.

Main Results:

• The cone filter estimator is inconsistent unless the slope is one (triangular kernel).
• Epanechnikov and Silverman kernels were found to be consistent.
• The original Gaussian filter's normalization constant (α) causes a 46.9% radiance underestimation, slightly improved by using the kth nearest photon.
• New consistent estimators were derived for Gaussian and cone filters using a revised normalization constant and excluding the kth nearest photon's contribution.
• The differential filter also showed improvement with the new normalization constant.

Conclusions:

• Overestimation bias in filtering kernels is a significant issue in photon mapping.
• The proposed modifications to Gaussian and cone filters yield consistent estimators, enhancing rendering accuracy.
• These findings contribute to developing more robust and precise density estimation techniques in computer graphics.