Fast Bilateral Filtering for Denoising Large 3D Images

A fast implementation of bilateral filtering is presented, which is based on an optimal expansion of the filter kernel into a sum of factorized terms. These terms are computed by minimizing the expansion error in the mean-square-error sense. This leads to a simple and elegant solution in terms of eigenvectors of a square matrix. In this way, the bilateral filter is applied through computing a few Gaussian convolutions, for which very efficient algorithms are readily available. Moreover, the expansion functions are optimized for the histogram of the input image, leading to improved accuracy. It is shown that this further optimization it made possible by removing the commonly deployed constrain of shiftability of the basis functions. Experimental validation is carried out in the context of digital rock imaging. Results on large 3D images of rock samples show the superiority of the proposed method with respect to other fast approximations of bilateral filtering.