We propose a new bilateral filtering algorithm with computational complexity invariant to filter kernel size, socalledO(1) or constant time in the literature. By showing that a bilateral filter can be decomposed into a number of constant time spatial filters, our method yields a new class of constant time bilateral filters that can have arbitrary spatial1and arbitrary range kernels. In contrast, the current available constant time algorithm requires the use of specific spatial or specific range kernels. Also, our algorithm lends itself to a parallel implementation leading to the first real-time O(1) algorithm that we know of. Meanwhile, our algorithm yields higher quality results since we are effectively quantizing the range function instead of quantizing both the range function and the input image. Empirical experiments show that our algorithm not only gives higherPSNR, but is about 10× faster than the state-of-the-art. It also has a small memory footprint, needed only 2% of the memory required by the state-of-the-art for obtaining the same quality as exact using 8-bit images. We also show that our algorithm can be easily extended for O(1) median filtering. Our bilateral filtering algorithm was tested in a number of applications, including HD video conferencing,video abstraction, highlight removal, and multi-focus imaging.

• Qingxiong Yang, Kar-Han Tan and N. Ahuja, Real-time O(1) Bilateral Filtering, IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2009.