Convex Formulation for Multiband Image Classification With Superpixel-Based Spatial Regularization

Superpixels are a powerful device to characterize the spatial–contextual information in remotely sensed hyperspectral image (HSI) interpretation. However, the exploitation of superpixels in classification problems is not straightforward, often leading to unbearable NP-hard discrete integer optimization problems. In this paper, we attack this hurdle by leveraging on a convex relaxation of the original integer optimization problem, which opens the door to include oversegmented superpixel-based regularizers. Specifically, we develop a new method for generating oversegmented superpixels. Then, we introduce a family of convex regularizers in the form of graph total variation, which promotes the same labeling in each superpixel. Vectorial total variation is also included in order to promote piecewise smoothness and align discontinuities along the class boundaries. The solution of the obtained convex optimization problem is computed with the split-augmented Lagrangian shrinkage algorithm. Experiments on HSIs yield classification maps with precise boundaries and inner consistency inside oversegmented superpixels, leading to the state-of-the-art classification accuracies.