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 achieving O (1) computational complexity using box spatial kernel. A recent study shows that this technique can be leveraged for O (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 many O (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.