**Ferenc Csonka, László Szirmay-Kalos, Csaba Kelemen and György Antal
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Magyar tudósok krt. 2, H-1117, HUNGARY;
szirmay@iit.bme.hu
**

**Abstract:**

This paper presents a multi-phase algorithm to solve the global illumination problem. In the first phase dependent tests are applied, i.e. the random walks of different pixels are built from the same random numbers. The result of the first phase is used to identify homogeneous pixel groups in the image. The criterion of the formation of such groups is that averaging the color inside these groups should result in less error than handling the pixels independently. The second phase of the algorithm is a conventional random walk method that uses independent random samples in different pixels. The final result is calculated as the average of the results of the dependent tests and the low-pass filtered version of the independent tests. This low-pass filter averages the pixel values inside the homogenous groups. The algorithm takes advantage of the fact that the image can contain larger homogeneous regions that can be calculated from much less number of samples. Thus we can focus on those pixels where significant changes happen.

**Keywords:**

Monte-Carlo integration, random walks, dependent tests.