We present a novel and effective skeletonization algorithm for binary and gray-scale images, based on the anisotropic heat diffusion analogy. We diffuse the image in the direction normal to the feature boundaries and also allow tangential diffusion (curvature decreasing diffusion) to contribute slightly. The proposed anisotropic diffusion provides a high quality medial function in the image: it removes noise and preserves prominent curvatures of the shape along the level-sets (skeleton features). The skeleton strength map, which provides the likelihood of a point to be part of the skeleton, is defined by the mean curvature measure. Finally, thin and binary skeleton is obtained by non-maxima suppression and hysteresis thresholding of the skeleton strength map. Our method outperforms the most related and the popular methods in skeleton extraction especially in noisy conditions. Results show that the proposed approach is better at handling noise in images and preserving the skeleton features at the centerline of the shape.