Fast two-phase image segmentation based on diffusion equations and gray level sets

In this paper we propose a new scheme for image segmentation composed of two stages: in the first phase, we smooth the original image by some filters associated with noise types, such as Gaussian filters for Gaussian white noise and so on. Indeed, we propose a novel diffusion equations scheme derived from a non-convex functional for Gaussian noise removal in this paper. In the second phase, we apply a variational method for segmentation in the smoothed image domain obtained in the first phase, where we directly calculate the minimizer on the discrete gray level sets. In contrast to other image segmentation methods, there is no need for us to re-initialize parameters, which deduces the complexity of our algorithm to O(N) (N is the number of pixels) and provides significant efficiency improvement when dealing with large-scale images. The obtained numerical results of segmentation on synthetic images and real world images both clearly outperform the main alternative methods especially for images contaminated by noise.