This paper presents a new semisupervised segmentation algorithm, suited to high-dimensional data, of which remotely sensed hyperspectral image data sets are an example. The algorithm implements two main steps: 1) semisupervised learning of the posterior class distributions followed by 2) segmentation, which infers an image of class labels from a posterior distribution built on the learned class distributions and on a Markov random field. The posterior class distributions are modeled using multinomial logistic regression, where the regressors are learned using both labeled and, through a graph-based technique, unlabeled samples. Such unlabeled samples are actively selected based on the entropy of the corresponding class label. The prior on the image of labels is a multilevel logistic model, which enforces segmentation results in which neighboring labels belong to the same class. The maximum a posteriori segmentation is computed by the a-expansion min-cut-based integer optimization algorithm. Our experimental results, conducted using synthetic and real hyperspectral image data sets collected by the Airborne Visible/Infrared Imaging Spectrometer system of the National Aeronautics and Space Administration Jet Propulsion Laboratory over the regions of Indian Pines, IN, and Salinas Valley, CA, reveal that the proposed approach can provide classification accuracies that are similar or higher than those achieved by other supervised methods for the considered scenes. Our results also indicate that the use of a spatial prior can greatly improve the final results with respect to a case in which only the learned class densities are considered, confirming the importance of jointly considering spatial and spectral information in hyperspectral image segmentation.
