Dimensionality reduction (DR) using tensor structures in morphological scale-space decomposition (MSSD) for
HSI has been investigated in order to incorporate spatial information in DR.We present results of a comprehensive
investigation of two issues underlying DR in MSSD. Firstly, information contained in MSSD is reduced using
HOSVD but its nonconvex formulation implicates that in some cases a large number of local solutions can be
found. For all experiments, HOSVD always reach an unique global solution in the parameter region suitable to
practical applications. Secondly, scale parameters in MSSD are presented in relation to connected components
size and the influence of scale parameters in DR and subsequent classification is studied.
Stochastic watershed is a robust method to estimate the probability density function (pdf) of contours of a
multi-variate image using MonteCarlo simulations of watersheds from random markers. The aim of this paper is
to propose a stochastic watershed-based algorithm for segmenting hyperspectral images using a semi-supervised
approach. Starting from a training dataset consisting in a selection of representative pixel vectors of each spectral
class of the image, the algorithm calculate for each class a membership probability map (MPM). Then, the MPM
of class k is considered as a regionalized density function which is used to simulate the random markers for the
MonteCarlo estimation of the pdf of contours of the corresponding class k. This pdf favours the spatial regions
of the image spectrally close to the class k. After applying the same technique to each class, a series of pdf are
obtained for a single image. Finally, the pdf's can be segmented hierarchically either separately for each class or
after combination, as a single pdf function. In the results, besides the generic spatial-spectral segmentation of
hyperspectral images, the interest of the approach is also illustrated for target segmentation.
Manifold learning has been widely studied in pattern recognition, image processing, and machine learning. A large number of nonlinear manifold learning methods have been proposed attempting to preserve a different geometrical property of the underlying manifold. In contrast, its application to hyperspectral images is computationally difficult due to the calculation of distances among spectral values in high-dimensional spaces. This paper compares feature extraction algorithms using isomap, Laplacian Eigenmaps, and local linear embedding in real hyperspectral images. They are implemented using massively parallel general purpose Graphical Processor Units (GPUs) to speed up computation. Their performance in classification of hyperspectral images and speed up of their computation is presented. Results using real and synthetic hyperspectral scenarios are presented. Additionally, a formulation including spatial information in these manifold learning algorithms is presented.
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