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.
Subsurface scattering (or SSS) is a mechanism of light transport in which light penetrates the surface of a translucent object, is scattered by interacting with the material, and exits the surface at a different point. Subsurface scattering is important in 3D computer graphics, being necessary for the realistic rendering of materials such as marble, skin and milk. However, SSS is also one of the most complex materials in the stateoftheart rendering. One reason for this is that the radiance at each point of the object depends on all the other points' radiance and the object's optical thickness, which makes the rendering equation of SSS material a complicated differential equation. So the computational cost of solving this equation is significant, let alone the varyingdensity property of the material.

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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