The random walk methods based on Monte Carlo or quasi-Monte Carlo techniques can be applied for efficient solving of the rendering equation.
A possible alternative of generating random walks is the one-directional distribution ray tracing, where rays can be emitted from the eye or the light sources. In this case, it is necessary to use the importance sampling technique to determine the reflection directions of particles unless the possibility of hitting a light source (or the eye) would be extremely low. On the other hand, BRDFs must be taken into account when the new direction is chosen.
Random paths starting from the eye can miss all the light sources, or photons emitted from a light source do not necessary reach the eye. To avoid this, bi-directional algorithms can be used, where particles are traced from both directions at the same time. The weak spot of bi-directional ray tracing is the connection of the eye path and light path, since deterministic shadow rays may hit an object located between the end points to be connected.
The goal of our future research is to develop a new two-pass method, where the first pass is photon emission from the light sources and the second one is generation of random walks starting from the eye. Reflection directions are selected using importance sampling according to the information acquired in the first pass and BRDFs of the surfaces. In the first pass importance maps are built for each patch, which are used for sampling a new direction in the second pass. In fact, these importance maps are approximated probability density functions, where the density of a reflection direction is the product of the BRDF value and the relative number of photons coming from the given directions.