A coupled total variation model with curvature driven for image colorization

In this paper, we study the problem of image colorization based on the propagation from given color pixels to the other grey-level pixels in grayscale images. We propose to use a coupled total variation model with curvature information of luminance channel to control the colorization process. There are two distinct advantages of the proposed model: (i) the involved optimization problem is convex and it is not sensitive to initial guess of colorization procedure; (ii) the proposed model makes use of curvature information to control the color diffusion process which is more effectively than that by using the gradient information. The existence of the minimizer of the proposed model can be shown, and the numerical solver based on convex programming techniques can be developed to solve the resulting model very efficiently. Experimental results are reported to demonstrate that the performance of the proposed model is better than those of the other color propagation models, especially when we deal with large regions of grayscale images for colorization.