Hyperspectral Image Classification Based on Mathematical Morphology and Tensor Decomposition

Abstract Hyperspectral Image (HSI) classification refers to classifying hyperspectral data into features, where labels are given to pixels sharing the same features, distinguishing the present materials of the scene from one another. Naturally a HSI acquires spectral features of pixels, but spatial features based on neighborhood information are also important, which results in the problem of spectral-spatial classification. There are various ways to account to spatial information, one of which is through Mathematical Morphology, which is explored in this work. A HSI is a third-order data block, and building new spatial diversities may increase this order. In many cases, since pixel-wise classification requires a matrix of pixels and features, HSI data are reshaped as matrices which causes high dimensionality and ignores the multi-modal structure of the features. This work deals with HSI classification by modeling the data as tensors of high order. More precisely, multi-modal hyperspectral data is built and dealt with using tensor Canonical Polyadic (CP) decomposition. Experiments on real HSI show the effectiveness of the CP decomposition as a candidate for classification thanks to its properties of representing the pixel data in a matrix compact form with a low dimensional feature space while maintaining the multi-modality of the data.

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