Segmentation of retinal vessels from retinal fundus images is the key step in the automatic retinal image analysis. In this paper, we propose a new unsupervised automatic method to segment the retinal vessels from retinal fundus images. Contrast enhancement and illumination correction are carried out through a series of image processing steps followed by adaptive histogram equalization and anisotropic diffusion filtering. This image is then converted to a gray scale using weighted scaling. The vessel edges are enhanced by boosting the detail curvelet coefficients. Optic disk pixels are removed before applying fuzzy C-mean classification to avoid the misclassification. Morphological operations and connected component analysis are applied to obtain the segmented retinal vessels. The performance of the proposed method is evaluated using DRIVE database to be able to compare with other state-of-art supervised and unsupervised methods. The overall segmentation accuracy of the proposed method is 95.18% which outperforms the other algorithms.