An end-member based ordering relation for the morphological description of hyperspectral images

Despite the popularity of mathematical morphology with remote sensing image analysis, its application to hyperspectral data remains problematic. The issue stems from the need to impose a complete lattice structure on the multi-dimensional pixel value space, that requires a vector ordering. In this article, we introduce such a supervised ordering relation, which conversely to its alternatives, has been designed to be image-specific and exploits the spectral purity of pixels. The practical interest of the resulting multivariate morphological operators is validated through classification experiments where it achieves state-of-the-art performance.