A Spectrally Weighted Structure Tensor for Hyperspectral Imagery

The structure tensor (ST) for vector valued images such as hyperspectral images (HSIs) is most often defined as the average of the scalar STs in each band. The problem with this definition for HSI is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result, nonedge pixels can be reinforced and edges can be weakened resulting in a poor performance by algorithms that depend on the ST. In this paper, a spectrally weighted ST for HSI is proposed. The weights are motivated by the fact that in HSI, neighboring spectral bands are highly correlated, as are the bands of its gradient. The proposed scheme gives higher weight where significant changes in the gradient between bands are detected. The spectrally weighted ST is used in tensor nonlinear anisotropic diffusion (TAND) for edge enhancing diffusion (EED). Comparisons with Weicker's uniform weighting show that the spectrally weighted ST better discriminates edges with EED. Experimental results using the airborne visible/infrared imaging spectrometer (AVIRIS) Indian Pines and Cuprite HSIs are presented.