IMPORTANCE-DRIVEN HIERARCHICAL STOCHASTIC RAY RADIOSITY Jan Pˇ rikryl † , Philippe Beakert ‡ , and Werner Purgathofer † † Institute of Computer Graphics, Vienna University of Technology Karlsplatz 13/186/2, A-1040 Wien, Austria e-mail: prikryl,wp @cg.tuwien.ac.at ‡ Department of Computer Science, Katholieke Universiteit Leuven Celestijnenlaan 200 A, B-3001 Leuven, Belgium e-mail: Philippe.Bekaert@cs.kuleuven.be ABSTRACT In this paper we present a hierarchical Monte-Carlo radiosity algorithm driven by the view importance. The algorithm makes to possible to concentrate the computational effort on solution in the immediate environ- ment of the observer, trading the low solution quality in invisible areas for better quality in areas that are visible for the observer. This is achieved by modifying the sampling probabilities of scene elements so that more samples are concentrated in the area of high importance and by extending the subdivision oracle func- tion so that the subdivision is coarser in areas of low importance. This paper extends the previous work by introducing a combination of hierarchical refinement and view importance driven method for Monte-Carlo radiosity. Keywords: Monte-Carlo, radiosity, hierarchy, hierarchical refinement, view importance, view potential 1 INTRODUCTION Radiosity algorithms generally attempt to compute ra- diosity to a uniform precision throughout the whole environment. This results in globally over-solved and locally under-solved radiosity solution for most scenes [Smits92]. If we allow low accuracy of the solution in those parts of the scene, that are not directly visible and that do not influence the visible parts too much, we can spend more computation effort on parts that are directly vis- ible. This way, we can save a lot of computational time when we are interested in illumination of only a part of a complex scene. The principle of the method is well known: During the course of radiosity system computation, we are computing the second quantity, called visual impor- tance. This quantity expresses the influence the ra- diosity of a particular mesh element has on the solu- tion in the visible part of the scene. In this paper we present a new radiosity method that combines the importance-driven Monte-Carlo radios- ity and the hierarchical refinement of scene mesh el- ements. This way, both the memory and the time ex- penses of computing a single view of the scene can be reduced. The paper is further organised as follows: in Section 2 we overview previous Monte-Carlo radiosity methods and importance-driven radiosity approaches. Hierar- chical refinement for radiosity is brieifly overviewed in Section 3. In Section 4 we derive the new method. Results and comparisons of our method are presented in Section 5. Finally, in Section 6 we summarise our experiences and draw some ideas for further research. 2 MONTE-CARLO RADIOSITY Monte-Carlo radiosity algorithms are — as well as their deterministic counterparts — based on algo- rithms used to compute radiative energy transport. Their advantage is that they quickly deliver solutions in that higher order interreflections are visible. Unfor- tunately, as with all Monte-Carlo methods, the vari- ance of the solution drops slowly and the results suffer from noise. Monte-Carlo radiosity solves the power form of the radiosity equation, given by P i W i ρ i M ∑ j 1 F ji P j (1)