Query Regarding "Brain Surface Extractor" or BSE

Hey All,

I want to implement BSE algo in C.This algo is from the paper "Magnetic Resonance Image Tissue Classification Using
a Partial Volume Model" in 2001.
I have few doubts in this algo that is why finding difficulty to implement. Pls help me in this...
Doubt 1: In equation 1 it is clear by the definition of diffusion that
del I/ del t = div(c(p,t) grad I) but how it equal to c(p,t)Laplacian(I) + (grad c . grad I) ?
c(p,t) is diffusivity but its also not clear that what is single c ?

Doubt 2: What is g in equation 2 and how the value of Kd(diffusion constant) will be determined at the time of implementation?

These appear to be questions concerning a particular publication rather than concerning the implementation in C of an algorithm described in that publication, hence I shall move this thread to General Discussion.