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Colorization of gray-scale images relies on prior color information. Exemplar-based methods use a color image as source of such information. Then the colors of the source image are transferred to the gray-scale target image. In the literature, this transfer is mainly guided by texture descriptors. Face images usually contain few texture so that the common approaches frequently fail. In this work, we propose a new method taking the geometric structure of the images rather their texture into account such that it is more reliable for faces. Our approach is based on image morphing and relies on the YUV color space. First, a correspondence mapping between the luminance Y channel of the color source image and the gray-scale target image is computed. This mapping is based on the time discrete metamorphosis model suggested by Berkels, Effland and Rumpf. We provide a new finite difference approach for the numerical computation of the mapping. Then, the chrominance U,V channels of the source image are transferred via this correspondence map to the target image. A possible postprocessing step by a variational model is developed to further improve the results. To keep the contrast special attention is paid to make the postprocessing unbiased. Our numerical experiments show that our morphing based approach clearly outperforms state-of-the-art methods.