A region merging based algorithm for total variation denoising

In this paper, we propose a region merging based algorithm for total variation (TV) denoising. TV based on denoising is extremely effective for recovering "blocky", possibly discontinuous, functions from noisy data. It is necessary to solve a minimization problem, which results in a nonlinear integro-differential equation of elliptic type. An efficient numerical scheme for solving such an equation is essential. In this paper, the TV denoising energy function is simplified according to the piecewise characteristic which the denoised results reveal. Then the energy is decreased by "region merging" to get a local minimum, which is an estimate of the global minimum. Experimental examples for image denoising are illustrated to show the effectiveness of the method in not only denoising but also segmentation with computational complexity of O(n log n).