Weighted importance sampling in shooting algorithms

Abstract

This paper proposes the application of a variance reduction technique called weighted importance sampling in shooting type global illumination algorithms. The sampling applied by shooting type Monte-Carlo global illumination algorithms can mimic the power transfer, but not the BRDFs at the visible target of the transfer. Consequently, these algorithms are poor in rendering visible specular surfaces. In order to eliminate these drawbacks, the BRDFs at the visible targets are taken into account as an additional weighting of the sampling density. After discussing the basic concepts we demonstrate the proposed idea with two algorithms. The first one uses conventional rays, while the second one ray-bundles to transfer the light in the scene.

Early, Accurate and Fast Yield Estimation through Monte Carlo-Alternative Probabilistic Behavioral Analog System Simulations

“…The deviation from a Gaussian density for both of these examples has been confirmed in the experiments we have conducted. 2 Note that re-binning consumes the bulk of the runtime, whereas the implemented post processing algorithms consume only a fraction of this time for all the samples. Phase-locked loops, being analog components, are an important part of almost all large-scale digital and mixedsignal systems.…”

“…Yet, this requires more samples eventually. Gibbs sampling works for dimensions higher than 2, hence it is not applicable to the problem in this paper [17] [2].…”

“…Algorithm Implementing the F Operator: [1] While all samples of the target pdf computed [2] For each sample in X [3] Place an sample with height p i at x=f(w i ) Here, Y is the output parameter to be observed and X is the input parameter. The domain and the range of the F operator is an φ.…”

“…The re-bin operator can be implemented using the following algorithm: Algorithm Implementing the R Operator: [1] Find maximum and minimum values w i within propagated samples [2] Divide this range into M bins [3] For each bin [4] Place…”

“…Sample Skipping Algorithm: [1] For i=2 to number of FDPP samples-1, [2] If (Probability of i'th sample is 0 [3] & Probability of at least one of neighboring samples >>0) [4] Remove sample The complexity of this algorithm is O(N ), where N is the number of input samples.…”