AbstractA distance geometry-based representation of hyperspectral imagery In this talk, a representation for hyperspectral imagery is presented, in which hyperspectral image analysis problems are described in terms of distance geometry. Then, a manifold representation of the data set is generated by creation of a nearest-neighbor graph on which shortest paths are calculated yielding a geodesic distance matrix. As a use case, the problem of hyperspectral unmixing is presented in terms of distance geometry. This geometric representation allows to design some analytical methods that are extremely efficient compared to the classical methods based on optimization. Furthermore, the distance matrix can be used to apply the distance geometry-adapted algorithms on the non-linear data manifold. In this way, distance geometry-based (non)linear versions of dimensionality estimation, endmember extraction and abundance estimation methods will be presented. |