Convex formulation for hyperspectral image classification with superpixels

The superpixels provided by an unsupervised segmentation algorithm are sets of neighboring pixels homogeneous in some sense. Therefore it is very likely that, in a classification problem, most pixels in a superpixel belong to the same class, namely if the homogeneity criterion is compatible with the class statistics. Superpixels are, therefore, a powerful device to express spatial contextual information. However, the exploitation of superpixels in a principled way is not straightforward. Recent efforts attack this problem under a discrete optimization framework, by including regularization terms promoting consistence of the labels in the superpixels and computing approximate labelings with graph-cut algorithms. The well known hardness of integer optimization problems is a major limitation of this line of attack. In this paper, we introduce a new strategy, based on convex relaxation, to include the spatial information provided by superpixels in classification problems. The convex relaxation of an integer optimization problem opens a door to include extra information, such as spatial partitioning information given by over-segmented superpixels. The convex optimization problem thus obtained is solved by using SALSA algorithm. Experimental results with the ROSIS Pavia University dataset illustrate the effectiveness of the proposed framework.