Christian Lessig

Controlling and Sampling Visibility Information on the Image Plane

Christian Lessig

Eurographics Symposium on Rendering 2017, EI & I track

Triangle rasterized with a classical technique (left), our approach (middle two images), and a reference solution (right). As can be seen in the partially covered triangles, our approach yields anti-aliasing that is close to the reference with just four samples per pixel.

Anti-aliasing on the image plane is a classic problems in computer graphics. While mip-mapping provides an efficient means to pre-filter texture information, no comparable technique exists for visibility. We address visibility-induced aliasing by exploiting that the Fourier transform of a discontinuity decays slowly only in the normal direction. Pre-filtering is thus only necessary in this direction and, after a coordinate transformation, the corresponding one dimensional problem can be solved analytically or tabulated. The resulting pre-filtered signal can be reconstructed exactly from pointwise samples and we derive corresponding sampling theorems that are tailored to the pre-filtering as well as a set of irregular sampling locations. We demonstrate our methodology for the classical Shannon-Nyquist setting but also for shift-invariant spaces where exact reconstruction kernels with significantly faster decay than the sinc-function are available. Our experimental results demonstrate that our pre-filtering is highly effective and that going beyond the Shannon-Nyquist setting reduces aliasing error further.

C. Lessig, Controlling and Sampling Visibility Information on the Image Plane, in Eurographics Symposium on Rendering 2017, EI & I track, 2017.

EGSR talk

Supplementary material

Mathematica code

Mathematica code (cleaned up)