This paper aims to couple the powerful prediction of the convolutional neural network (CNN) to the accuracy at pixel scale of the variational methods. In this work, the limitations of the CNN-based image colorization approaches are described. We then focus on a CNN which is able to compute a statistical distribution of the colors for each pixel of the image based on a learning stage on a large color image database. After describing its limitation, the variational method of [17] is briefly recalled. This method is able to select a color candidate among a given set while performing regularization of the result. By combining this approach with a CNN, we designed a fully automatic image colorization framework with an improved accuracy in comparison with CNN alone. Some numerical experiments demonstrate the increased accuracy reached by our method.