Multivariate Association of Compositional Data Matrices with Applications in Comparing Hyperspectral Images

Cuadras, C.M.
Valero, S.
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It is well-known in image processing that, by varying the wavelength, any material reflects and absorbs in a different way the solar radiation. This is registered by hyperspectral sensors, which collect multivariate discrete images in a series of contiguous wavelength bands, providing the spectral curves, which can distinguish between materials. In order to partition a multivariate image in regions belonging to different materials, we need to compare these regions which are previously modelled by using compositional data matrices, where the entries in each row is a statistical discrete distribution of the radiance values (columns). These rows correspond to distinct but contiguos wavelengths. Thus the distribution in a row is very similar to the distribution in close rows. To measure this proximity, we use Hellinger distance between rows, which provides a distance matrix. Given two hyperspectral regions of an image providing two compositional data matrices, we obtain the corresponding distance matrices and, by using metric multidimensional scaling, we compute two sets of principal coordinates, which are related by a multivariate association measure based on canonical correlations. We ilustrate this approach comparing some multivariate regions of images captured by hyperspectral remote sensors ​
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