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.