We propose a family of positive-definite kernels between images, allowing to compute image similarity measures respectively in terms of color and of shape. The kernels consists in matching subtree-patterns called "tree-walks" of graphs extracted from the images, e.g. the segmentation graphs for color similarity and graphs of the discretized shapes or the point clouds in general for shape similarity. In both cases, we are able to design computationally efficient kernels which can be computed in polynomial-time in the size of the graphs, by leveraging specific properties of the graphs at hand such as planarity for adjacency graphs (segmentation graphs) or factorizability of the associated graphical model for point clouds. Our kernels can be used by any kernel-based learning method, and hence we present experimental results for supervised and semi-supervised classification as well as clustering of natural images and supervised classification of handwritten digits and Chinese characters from few training examples.