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I'm trying to understand the separable subsurface scattering algorithm, but I'm a little confused on what the parameters mean from a notation and implementation standpoint, particularly for the artistic model (the paper includes two models). I'm also confused as to how the kernel should be placed in the equation.

The equation used is: $$M_e(x,y) = \int \int E(x',y')\frac{1}{||a_p||_1}a_p(x-x')a_p(y-y')dx'dy'$$

Later on the artistic model has a kernel equal to: $$a_m=wG(x,\sigma_{near})+(1-w)G(x,\sigma_{far})$$ $$A_m=a_m(x)a_m(y)$$

In the supplementary materials, there is an implementation clarification based on depth: $$a_m(\sqrt{d_{xy}^2+d_{z}^2}) \approx e^{\frac{-d_{z}^2}{2\sigma_{max}}}a_m(d_{xy})$$

Would this be the correct final form? $$M_e(x,y)=\int \int E(x',y')e^{\frac{-d_{z}^2}{2\sigma_{max}}}a_m(d_{xy})e^{\frac{-d_{z}^2}{2\sigma_{max}}}a_m(d_{xy})dx'dy'$$

where (some of these might not be correct interpretations):

  • $M_e$: output color
  • $E(x',y')$: color at sampling point (from color attachment)
  • $a_p$: kernel in one direction (not sure if this is somehow different than $a_m$)
  • $d_z$: linearized depth from depth buffer
  • $d_{xy}$: sampling points in the x and y direction (distance in x and y direction from the sampling point), not sure if this is in screen or world space
  • $w$: arbitrarily chosen weight between 0 and 1
  • $\sigma_{near}/\sigma_{far}$: diffuse profile for near/far Gaussian (3 color channels each), arbitrarily chosen
  • $\sigma_{max}$: $max(\sigma_{near}, \sigma_{far})$, this is keep the sampling from undersampling the larger Gaussian form my understanding
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