Semi-supervised image labelling using barycentric graph embeddings

Here, we turn our attention to barycentric embeddings and examine their utility for semi-supervised image labelling tasks. To this end, we view the pixels in the image as vertices in a graph and their pairwise affinities as weights of the edges between them. Abstracted in this manner, we can pose the semi-supervised labelling problem into a graph theoretic setting where the labels are assigned based upon the distance in the embedding space between the nodes corresponding to the unlabelled pixels and those whose labels are in hand. We do this using a barycentric embedding approach which naturally leads to a setting in which the embedding coordinates can be computed by solving a system of linear equations. Moreover, the method presented here can incorporate side information such as that delivered by colour priors used elsewhere in the literature for semi-supervised colour image labelling. We illustrate the utility of our method for colour image labelling and material classification on hyperspectal images. We also compare our results against other techniques elsewhere in literature.