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.
Analyzing flow-like patterns in images for image understanding is an active research area but there have been much less
attention paid to the process of enhancement of those structures. The completion of interrupted lines or the enhancement
of flow-like structures is known as Coherence-Enhancement (CE). In this work, we are studying nonlinear anisotropic
diffusion filtering for coherence enhancement. Anisotropic diffusion is commonly used for edge enhancement by
inhibiting diffusion in the direction of highest spatial fluctuation. For CE, diffusion is promoted along the direction of
lowest spatial fluctuation in a neighborhood thereby taking into account how strongly the local gradient of the structures
in the image is biased towards that direction. Results of CE applied multispectral and hyperspectral images are
presented.
The hyperspectral image cube can be modeled as a three dimensional array. Tensors and the tools of multilinear algebra provide a natural framework to deal with this type of mathematical object. Singular value decomposition (SVD) and its variants have been used by the HSI community for denoising of hyperspectral imagery. Denoising of HSI using SVD is achieved by finding a low rank approximation of a matrix representation of the hyperspectral image cube. This paper investigates similar concepts in hyperspectral denoising by using a low multilinear rank approximation the given HSI
tensor representation. The Best Multilinear Rank Approximation (BMRA) of a given tensor A is to find a lower multilinear rank tensor B that is as close as possible to A in the Frobenius norm. Different numerical methods to compute the BMRA using Alternating Least Square (ALS) method and Newton's Methods over product of Grassmann manifolds are presented. The effect of the multilinear rank, the numerical method used to compute the BMRA, and
different parameter choices in those methods are studied. Results show that comparable results are achievable with both ALS and Newton type methods. Also, classification results using the filtered tensor are better than those obtained either with denoising using SVD or MNF.
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