Parallel Recursive Filtering of Infinite Input Extensions

摘要

Filters with slowly decaying impulse responses have many uses inrncomputer graphics. Recursive filters are often the fastest optionrnfor such cases. In this paper, we derive closed-form formulas forrncomputing the exact initial feedbacks needed for recursive filteringrninfinite input extensions. We provide formulas for the constantpaddingrn(e.g. clamp-to-edge), periodic (repeat) and even-periodicrn(mirror or reflect) extensions. These formulas were designed for easyrnintegration into modern block-parallel recursive filtering algorithms.rnOur new modified algorithms are state-of-the-art, filtering imagesrnfaster even than previous methods that ignore boundary conditions.