This paper tackles the problem of color transfer between images using discrete optimal transportation. Methods that only match discrete image color palettes through bijective assignments [1], without considering the spatial pixel location such as [2,3], suffer from several limitations such as spatial inconsistencies or noise amplification, so that additional post-processing must be considered in practice [1,4]. To tackle these issues, we here propose a variational model that directly deals with the regularity of the transport map and the spatial consistency of the reconstruction. Our approach is based on the relaxed and regularized discrete optimal transport method of [5]. We extend this model in order to take into account the spatial distribution of colors within the image domain and only relax locally the bijective assignment constraint, when required by the data. We rely on a spatio-color clustering framework to ensure fast computation while preserving the quality of the color transfer. Finally, we present some experiments on real images that demonstrate the capacity of our model to adapt itself to the considered data. [1] Piti e, F., Kokaram, A.C., Dahyot, R.: Automated colour grading using colour distribution transfer. Computer Vision and Image Understanding 107 (2007) 123-137 [2] Papadakis, N., Provenzi, E., Caselles, V.: A variational model for histogram transfer of color images. IEEE Transactions on Image Processing 20 (2011) 1682-1695 [3] Rabin, J., Peyr e, G.: Wasserstein regularization of imaging problem. In: IEEE International Conderence on Image Processing (ICIP'11). (2011) 1541-1544 [4] Rabin, J., Delon, J. and Gousseau, Y.: Regularization of transportation maps for color and contrast transfer, In: IEEE International Conderence on Image Processing (ICIP'10). (2010) 1933-1936 [5] Ferradans, A., Papadakis, N., Rabin, J., Peyré, G. and Aujol, J-F. Regularized discrere optimal transport. In: International Conference on Scale Space and Variational Methods in Computer Vision (2013) 1-12