Semisupervised Hyperspectral Image Segmentation Using Multinomial Logistic Regression With Active Learning

This paper presents a new semi-supervised segmentation algorithm, suited to high dimensional data, of which remotely sensed hyperspectral image data sets are an example. The algorithm implements two main steps: (i) semi-supervised learning of the posterior class distributions, followed by (ii) segmentation, which infers an image of class labels from a posterior distribution built on the learned class distributions, and on a Markov random field (MRF). The posterior class distributions are modeled using multinomial logistic regression (MLR), 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 multi-level logistic (MLL) model, which enforces segmentation results in which neighboring labels belongs to the same class. The maximum a posteriori (MAP) segmentation is computed by the α-Expansion min-cut based integer optimization algorithm. Our experimental results, conducted using synthetic and real hyperspectral image data sets collected by the Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) system of NASA Jet Propulsion Laboratory over the regions of Indian Pines, Indiana, and Salinas Valley, California, reveal that the proposed approach can provide classification accuracies which 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.