Original Post
Hi, I have Variance Shadow Maps running for a while now and I have now some time to improve them. The old thread was retired: http://www.gamedev.net/community/forums/topic.asp?topic_id=374989&PageSize=25&WhichPage=5 So I had to open up a new one. I want to look into light bleeding artefacts. What I did first is go through the equations and see that I understand everything. I need to write a short documentation on how it works. Here is what I have: ----------------- The value in x is the depth value that is calculated based on the distance of the light to the vertex. The value in x -also called Moment 1- is stored in the x channel of the two-channel render target in the first render pass. E(x) holds the result from filtering x. The value x^2 (Moment 2) is stored in the y channel in the first rendering pass. E(x^2) holds the result of filtering x^2. Equation for mean μ value: μ = E(x) = M1 The mean μ value and E(x) keeps the result of filtering the x channel of the texture that holds the x = depth values. Equation to calculate variance: σ^2 = E(x^2) - E(x)^2 = M2 - M1^2 x^2 is the depth value multiplied with itself and stored in the y channel of the render target. E(x^2) holds the result of filtering this value. Chebyshev's inequality (one-tailed version): P(x >= t)<=pmax(t) = σ^2 / (σ^2 + (t - μ)^2 The variable t holds current fragment depth. ----------------- The interesting part is that all implementations I see seem to exchange the t - u part in the source code. It comes down to the following two lines:
//
float m_d = (moments.x - RescaledDistToLight);
// Chebyshev's inequality
float p = variance / (variance + m_d * m_d);