Calculation of Noise Components for Bidirectional Path Tracing with Photon Maps

Abstract

The classic Monte-Carlo ray tracing is a powerful method which allows to simulate virtually all effects in ray optics, but it may be inadmissibly slow for many cases, such as calculation of images seen by a lens or pin-hole camera. In this cases another stochastic method is more efficient such as the bi-directional ray Monte-Carlo tracing with photon maps (BDPM). The level of noise i.e. the r.m.s. (root mean square) of pixel luminance calculated in one iteration of the method, depends on various parameters of the method, such as the number of light and camera paths, radius of integration sphere etc. so it is desirable to be able to predict this dependence to choose optimal parameters of the method. It was shown that this r.m.s is a sum of 3 functions scaled by reverse number of camera and light rays. These functions themselves are independent of the number of rays, so knowing them one can predict the noise for any number of rays and thus find the optimal one. These functions are a sort of correlations and their calculation from ray tracing is not a trivial problem. In this paper we describe a practical method of calculation and demonstrate the usage of its results for the choice of ray number.