A Semi-Supervised Reduced-Space Method for Hyperspectral Imaging Segmentation

The development of the hyperspectral remote sensor technology allows the acquisition of images with a very detailed spectral information for each pixel. Because of this, hyperspectral images (HSI) potentially possess larger capabilities in solving many scientific and practical problems in agriculture, biomedical, ecological, geological, hydrological studies. However, their analysis requires developing specialized and fast algorithms for data processing, due the high dimensionality of the data. In this work, we propose a new semi-supervised method for multilabel segmentation of HSI that combines a suitable linear discriminant analysis, a similarity index to compare different spectra, and a random walk based model with a direct label assignment. The user-marked regions are used for the projection of the original high-dimensional feature space to a lower dimensional space, such that the class separation is maximized. This allows to retain in an automatic way the most informative features, lightening the successive computational burden. The part of the random walk is related to a combinatorial Dirichlet problem involving a weighted graph, where the nodes are the projected pixel of the original HSI, and the positive weights depend on the distances between these nodes. We then assign to each pixel of the original image a probability quantifying the likelihood that the pixel (node) belongs to some subregion. The computation of the spectral distance involves both the coordinates in a features space of a pixel and of its neighbors. The final segmentation process is therefore reduced to a suitable optimization problem coupling the probabilities from the random walker computation, and the similarity with respect the initially labeled pixels. We discuss the properties of the new method with experimental results carried on benchmark images.