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Adaptive Wavelet Densities for Monte Carlo Ray Tracing

Georg Pietrek, University of Dortmund, Informatik LS VII, Dortmund,
Germany

Ingmar Peter, University of Tuebingen, WSI/GRIS, Tuebingen, Germany

Monte Carlo integration is a well established technique to solve the
rendering equation. The efficiency of Monte Carlo integration strongly
depends on the probability density functions (pdfs) used to control the
stochastic process.

We will introduce a new method for representation and adaption of pdfs
for Monte Carlo importance sampling based on a

new mathematical approach for adaptive pdfs in basis representation.
During the normal Monte Carlo integration process an

approximation of the integrand is obtained that can be used to construct
refined pdfs that tend to achieve better results. Based on this strategy
we present a multi pass Monte Carlo algorithm using hierarchical function
bases as known from wavelet applications. This approach is used to optimise
the calculation of indirect illumination in a backward ray tracing application.
The results show that the use of adaptive pdfs improves the image quality
as well as the computational efficiency of the calculations.