Fast bilateral filtering by adapting block size

Direct implementations of bilateral filtering show O(r²) computational complexity per pixel, where r is the filter window radius. Several lower complexity methods have been developed. State-of-the-art low complexity algorithm is an O(1) bilateral filtering, in which computational cost per pixel is nearly constant for large image size. Although the overall computational complexity does not go up with the window radius, it is linearly proportional to the number of quantization levels of bilateral filtering computed per pixel in the algorithm. In this paper, we show that overall runtime depends on two factors, computing time per pixel per level and average number of levels per pixel. We explain a fundamental trade-off between these two factors, which can be controlled by adjusting block size. We establish a model to estimate run time and search for the optimal block size. Using this model, we demonstrate an average speedup of 1.2-26.0x over the previous method for typical bilateral filtering parameters.