Error and complexity of random walk Monte Carlo radiosity

In this paper, we study the error and complexity of the discrete random walk Monte Carlo technique for Radiosity, both the shooting and gathering methods. We show that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an 2(n log n) complexity. We give and compare three unbiased estimators for each method, and obtain closed forms and bounds for their variances. We also bound the expected value of the Mean Square Error (MSE). Some of the results obtained are also shown to be valid for the nondiscrete gathering case. We also give bounds for the variances and MSE for the infinite path length estimators; these bounds might be useful in the study of the biased estimators resulting of cutting off the infinite path.