Fast Gauss Bilateral Filtering

In spite of high computational complexity, the bilateral filter and its modifications and extensions have recently become very popular image and shape processing tools. In this paper, we propose a fast and accurate approximation of the bilateral filter. Our approach combines a dimension elevation trick with a Fast Gauss Transform. First we represent the bilateral filter as a convolution in a high dimensional space. Then the convolution is efficiently approximated by using space partitioning and Gaussian function expansions. Advantages of our approach include linear computational complexity, user-specified precision, and an ability to process high dimensional and non-uniformly sampled data. We demonstrate capabilities of the approach by considering its applications to the image and volume denoising and high-dynamic-range tone mapping problems.