This paper provides a new method to colorize gray-scale images. While the reverse operation is only a matter of standard, the colorization process is an ill-posed problem that requires some priors. In the literature two classes of approach exist. The first class includes manual methods that needs the user to manually add colors on the image to colorize. The second class includes exemplar-based approaches where a color image, with a similar semantic content, is provided as input to the method.These two types of priors have their own advantages and drawbacks. In this paper, a new variational framework for exemplar-based colorization is proposed. A non-local approach is used to find relevant color in the source image in order to suggest colors on the gray-scale image. The spatial coherency of the result as well as the final color selection is provided by a non-convex variational framework based on a total variation. An efficient primal-dual algorithm is provided and a proof of its convergence is proposed. In this work, we also extend the proposed exemplar-based approach to combine both exemplar-based and manual methods. It provides a single framework that unifies advantages of both approaches. Finally, experiments and comparisons with state-of-the-art methods illustrate the efficiency of our method.