If you have ever dealt with a global illumination algorithm based on path integral formulation, such as path tracing(PT), bidirectional path tracing(BDPT), or metropolis light transport(MLT) before, I am sure you are familiar with the notion of the probability of a light path. On the whole, the definition of probability density function(PDF) of a path seems quite direct. It is just the joint PDF in terms of surface area of all the vertices consist of the path, which can be computed by the directional probability of sampling the BRDF from the prevsious vertex times the geometry term, except for the first vertex in the camera path, where no previous BRDF directional PDF is available.

I am Shiqiu(Edward) Liu, currently working as a graphics engineer at NVIDIA. Prior to that I worked as a research assistant at the graphics lab at Georgia Tech, advised by Prof. Greg Turk on physics simulation, and graduated with a MS degree in Computer Science. I also used to work as an intern at Microsoft Research Asia (MSRA), and Tencent. I am a rendering enthusiast :) My Resume
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