Abstract: Segmentation for noisy images is a difficult topic in image processing.To break through the restriction of Euclidean distance and segment the noisy image effectively, a new method based on a geodesic framework and EWCVT (edge-weighted centroidal Voronoi tessellation) energy model is presented in this paper.Firstly, we propose an approximate model of geodesic distance according to image gradient, which can decrease the computation complexity of the algorithm greatly.Then, we apply this geodesic distance to achieve anti noisy image segmentation by minimizing EWCVT energy.Experimental results show that the proposed method can carry out anti noisy segmentation effectively.