Bilateral Filtering


The property of smoothing while preserving edges makes the bilateral filter a very popular image processing tool. However, its non-linear nature results in a computationally costly operation. Various works propose fast approximations to the bilateral filter. However, the  majority does not generalize to vector input as is the case with color images. In this paper, we propose a fast approximation to the bilateral filter for color images. The filter is based on two ideas. Firstly, the number of colors which occur in a single natural image is limited. We exploit this color sparseness to rewrite the initial non-linear bilateral filter as a number of linear filter operations. Secondly, we impose a statistical prior to the image values which are locally present within the filter window. We show that this statistical prior leads to a closed-form solution of the bilateral filter. Finally, we combine both ideas into a single fast and accurate bilateral filter for color images. Experimental results show that our bilateral filter based on the local prior yields an extremely fast bilateral filter approximation, but with limited accuracy, which has potential application in real-time video filtering. Our bilateral filter which combines color sparseness and local statistics yields a fast and accurate bilateral filter approximation and obtains state-of-the-art results.

M. G. Mozerov and J. van de Weijer, “Global color sparseness and a local statistics prior for fast bilateral filtering,” IEEE transactions on image processing, accepted 2015. (pdf)

CODE: both matlab and C-code is available here.