Lessig, ChristianMatthias Zwicker and Pedro Sander2017-06-192017-06-192017978-3-03868-045-11727-3463https://doi.org/10.2312/sre.20171189https://diglib.eg.org:443/handle/10.2312/sre20171189Anti-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.Computing methodologies> Visibility10.2312/sre.201711891-9