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DX11 Need help implementing NDF-Filtering + LEAN mapping

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I manged so far to implement NVIDIA's NDF-Filtering at a basic level (the paper can be found here). Here is my code so far:

// project the half vector on the normal (?)
float3 hppWS = halfVector / dot(halfVector, geometricNormal)
float2 hpp = float2(dot(hppWS, wTangent), dot(hppWS, wBitangent));	

// compute the pixel footprint
float2x2 dhduv = float2x2(ddx(hpp), ddy(hpp));

// compute the rectangular area of the pixel footprint
float2 rectFp = min((abs(dhduv[0]) + abs(dhduv[1])) * 0.5, 0.3);

// map the area to ggx roughness 
float2 covMx = rectFp * rectFp * 2;
roughness = sqrt(roughness * roughness + covMx);

Now I want combine this with LEAN mapping as state in Chapter 5.5 of the NDF paper.

But I struggle to understand what theses sections actually means in Code: 


To combine this filtering method with our NDF filtering, we do
the following: We first interpret the first-order moments as a regular
shading normal coming from the normal map and perturb the shading
tangent frame with it.

I suppose the first-order moments are the B coefficent of the LEAN map, however things like

float3 hppWS = halfVector / dot(halfVector, float3(lean_B, 0));

doesn't bring up anything usefull.

Next theres:


We then compute a covariance matrix SIGMA
of the estimated Beckmann distribution (Eq. 5 in [OB10]) and interpret
this as another kernel filter image.png induced by variations of half
vectors caused by the normal map.

This simply means:

// M and B are the coefficents from the LEAN map
float2x2 sigma_mat = float2x2(
  M.x - B.x * B.x, M.z - B.x * B.y,
  M.z - B.x * B.y, M.y - B.y * B.y);

does it?



Finally, using the convolution formulation of NDF filtering from
Eq. 12, we perform a nested convolution


This is the part confuses me the most: how am I suppose to convolute two matrices? I know the concept of convolution in terms of functions, not matrices. Should I multiple them? That didn't make any usefully output.

I hope someone can help with this maybe too specific question, I'm really despaired to make this work and i've spend too many hours of trial & error...



Edited by schneckerstein

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