In this paper, we consider the colorization problem of grayscale images in which some color scribbles are initially given. Our proposed method is based on the weighted color blending of the scribbles. Unlike previous works which utilize the shortest distance as the blending weights, we employ a new intrinsic distance measure based on the Random Walks with Restart (RWR), known as a very successful technique for defining the relevance between two nodes in a graph. In our work, we devise new modified data-driven RWR framework that can incorporate locally adaptive and data-driven restarting probabilities. In this new framework, the restarting probability of each pixel becomes dependent on its edgeness, generated by the canny detector. Since this data-driven RWR enforces color consistency in the areas bounded by the edges, it produces more reliable edge-preserving colorization results that are less sensitive to the size and position of each scribble. Moreover, if the additional information ...