Optimal O(1) Bilateral Filter with Arbitrary Spatial and Range Kernels Using Sparse Approximation

A number of acceleration schemes for speeding up the time-consuming bilateral filter have been proposed in the literature. Among these techniques, the histogram-based bilateral filter trades the flexibility for achievingO(1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged forO(1) bilateral filter with arbitrary spatial and range kernels by linearly combining the results of multiple-box bilateral filters. However, this method requires many box bilateral filters to obtain sufficient accuracy when approximating the bilateral filter with a large spatial kernel. In this paper, we propose approximating arbitrary spatial kernel using a fixed number of boxes. It turns out that the multiple-box spatial kernel can be applied in manyO(1) acceleration schemes in addition to the histogram-based one. Experiments on the application to the histogram-based acceleration are presented in this paper. Results show that the proposed method has better accuracy in approximating the bilateral filter with Gaussian spatial kernel, compared with the previous histogram-based methods. Furthermore, the performance of the proposed histogram-based bilateral filter is robust with respect to the parameters of the filter kernel.