For given color image with illumination color(white), the problem is to remove this illuminant color from the image. to do:
1st step: rotation RGB color space to SUV color space (Eq.6) in the paper.(So that "S" components determines the specular component)
2nd step: reparemeterizing each pixel point using spherical coordinates (Eq.10) (So that only \phi contains specular component and a little bit diffuse component. \theta and \rho only contains diffuse component)
3rd step: Eroding \phi value to distinguish specular component. Here We use erosion operator(Eq.13) and in Matlab we need to use "upwind scheme" to write.
4th step: Here we need to be careful with two points: First one: if the image includes shading, we need to put stopping function to (Eq.13) to keep the shading information while eroding the \phi function.
Here stopping function is \g (Eq.15). and this stopping function includes \rho (Because, only \rho value gives information about shading).
Second point: while eroding we need to be careful with textured images, so we use \theta (because theta includes texture information) and we obtain general equation Eq.21. Hence We can separate specular comp.
Download:- Paper.pdf