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Graph."],"published-print":{"date-parts":[[2012,8,5]]},"abstract":"<jats:p>We present a technique for performing high-dimensional filtering of images and videos in real time. Our approach produces high-quality results and accelerates filtering by computing the filter's response at a reduced set of sampling points, and using these for interpolation at all<jats:italic>N<\/jats:italic>input pixels. We show that for a proper choice of these sampling points, the total cost of the filtering operation is linear both in<jats:italic>N<\/jats:italic>and in the dimension<jats:italic>d<\/jats:italic>of the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, as well as for an algorithm to compute the sampling points. This provides a sound theoretical justification for our method and for its properties. The resulting filter is quite flexible, being capable of producing responses that approximate either standard Gaussian, bilateral, or non-local-means filters. Such flexibility also allows us to demonstrate the first hybrid Euclidean-geodesic filter that runs in a single pass. Our filter is faster and requires less memory than previous approaches, being able to process a 10-Megapixel full-color image at 50 fps on modern GPUs. 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