Fast bilateral filtering of vector-valued multiple images with decomposition of weights

We present a technique for fast bilateral filtering of vector-valued multiple images including color, flow field, moving pictures, and volumetric. Weights in the bilateral filter were approximately decomposed into orthogonal factors. This decomposition enabled us to execute high-dimensional integration sequentially in 1-dimensional spaces. Acceleration rates in our method grew with the dimensionality, We experimentally verified that the approximation error caused by the decomposition of the weights in the bilateral filter stayed sufficiently small for color and volumetric images.