O(1) transposed bilateral filtering for optimization

This paper presents an essential algorithm for optimization-based image processing using the bilateral filter (BLF), called constant-time transposed BLF (O(1) TBLF). Some iterative solvers for optimization problems require a pair of filters defined as multiplying a filter matrix or its transpose to vectorized images. Since the BLF can be described as a matrix form, its paired filter also exists, called a TBLF in this paper. BLF-based optimization achieves high smoothing performance; whereas, it requires much high computational complexity due to iterating both BLF and TBLF many times. Hence, this paper designs an O(1) TBLF algorithm to accelerate the iterative process. Experiments show that our O(1) TBLF runs in low complexity regardless of its filter window size and works effectively for flash/no-flash image integration via BLF-based optimization.