A structure tensor for hyperspectral images

In this article, a structure tensor for hyperspectral images (HSI) is proposed. A weighted zero mean smoothed gradient to calculate the initial matrix field is used. The weights are constructed from the zero mean data by comparison with a normalized absolute value of the median. The problem with the classical definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result many non-edge pixels are reinforced producing false edges. Therefore, other processes that depend on the structure tensor will be misguided. The proposed weights are selected from pixel´s spectral values that are greater than and closely around the absolute value of the median, reinforcing only the better candidates in the spectra to be edges in their respective spectral interval, therefore making the structure tensor a better edge discriminator. Comparisons of this method with the standard definition of the structure tensor and results of using the proposed method for nonlinear tensor anisotropic diffusion are presented.