Research on bilateral filtering algorithm based on trigonometric function

Bilateral filtering is a kind of filtering technology that can reduce noise of images and preserve edge of images effectively. The bilateral filtering algorithm proposed by Tomasi and Manduchi is quite time-consuming and it's time complexity is O(sigma(2)(s)), which is not conducive to the promotion of the algorithm. In view of this situation, this paper makes some improvement for the algorithm, which approaches Gaussian range function with raised cosines function and uses some characteristics of raised cosines function to decompose the range function into some superposition of functions and to implement the acceleration of the range function. Experiments show that the improved algorithm reduced time complexity into O(1), and implemented acceleration of the algorithm effectively. More than that, the improved algorithm has a better effect on reducing noise of images and preserving edge of images.