Fast Weighted Histograms for Bilateral Filtering and Nearest Neighbor Searching

The locality sensitive histogram (LSH) injects spatial information into the local histogram in an efficient manner, and has been demonstrated to be very effective for visual tracking. In this paper, we explore the application of this efficient histogram in two important problems. We first extend the LSH to linear time bilateral filtering, and then propose a new type of histogram for efficiently computing edge-preserving nearest neighbor fields (NNFs). While the existing histogram-based bilateral filtering methods are the state of the art for efficient grayscale image processing, they are limited to box spatial filter kernels only. In our first application, we address this limitation by expressing the bilateral filter as a simple ratio of linear functions of the LSH, which is able to extend the box spatial kernel to an exponential kernel. The computational complexity of the proposed bilateral filter is linear in the number of image pixels. In our second application, we derive a new bilateral weighted histogram (BWH) for NNF. The new histogram maintains the efficiency of LSH, which allows approximate NNF to be computed independent of patch size. In addition, BWH takes both spatial and color information into account, and thus provides higher accuracy for histogram-based matching, especially around color edges.