Enhancement of hyperspectral imagery using spectrally weighted tensor anisotropic nonlinear diffusion for classification

Publication Date


Document Type

Conference Proceeding


Maider J. Marin-Mcgee, Miguel Velez-Reyes, "Enhancement of hyperspectral imagery using spectrally weighted tensor anisotropic nonlinear diffusion for classification", Proc. SPIE 8743, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XIX, 87431G (18 May 2013); doi: 10.1117/12.2017665; https://doi.org/10.1117/12.2017665


Tensor Anisotropic Nonlinear Diffusion (TAND) is a divergence PDE-based diffusion technique that is “guided” by an edge descriptor, such as the structure tensor, to stir the diffusion. The structure tensor for vector valued images such as HSI is most often defined as the average of the scalar structure tensors for each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened resulting in poor performance by processes that depend on the structure tensor. Iterative processes such as TAND, in particular, are vulnerable to this phenomenon. Recently a weighted structure tensor based on the heat operator has been proposed [1]. The weights are based on the heat operator. This tensor takes advantage of the fact that, in HSI, neighboring spectral bands are highly correlated, as are the bands of its gradient. By taking advantage of local spectral information, the proposed scheme gives higher weighting to local spectral features that could be related to edge information allowing the diffusion process to better enhance edges while smoothing out uniform regions facilitating the process of classification. This article present how classification results are affected by using TAND based on the heat weighted structure tensor as an image enhancement step in a classification system.