Chebyshev Ambient Occlusion

Ambient Occlusion (AO) is a widely used shadowing technique in 3D rendering. One of the main disadvantages of using it is that it requires not only the surface depth but also the normal vector, which usually causes severe aliasing. This work introduces a novel AO algorithm by applying Chebyshev’s inequality. Instead of requiring the normal vector, we process the mean ( $\mu $ ) of the distribution of depth values from the screen space. We can efficiently calculate the variance ( $\sigma ^{2}$ ) over any kernel region. Using the Chebyshev AO, we can get the upper bound on the percentage of the shaded surface that is occluded. Our proposed method can usually provide a good approximation of true occlusion and can be used as an approximate value for AO rendering. As a post-processing rending, the time complexity of Chebyshev AO is $O\left ({2k}\right)$ which is simple to implement on current graphics devices and can be applied to the next generation of ray tracing technology.