Multivariate diffusion and induced segmentation.
This paper explore the problem of unsupervised hierarchical segmentation for hyperspectral images using a multivariate version of the structure tensor  and morphological segmentation methods based on a pixel dissimilarity measures . This spatial structure tensor fusions the edge information along the spectral dimension of the gradient by using weights based on the heat kernel. The unsupervised morphological segmentation uses a graph-based model where the pixels are the nodes. A dissimilarity function based on the eccentricity of the local structure tensor at each node is proposed to define the weights of the edges. With a global threshold, applied to the distances between nodes an connectivity is defined. As increases its value, it can be proved that a hierarchy, i.e an ordered sequence of connected components is formed, producing a hierarchy of connective segmentations. Segmentation maps using the proposed tensor-based dissimilarity function, the Euclidean distance and the Spectral Angle Distance were performed and tested with the Endmember Extraction Problem. The comparison of the endmembers produced using the proposed segmentation with each of the above measures and the endmembers from the original image shows that the endmembers produced using the tensor-based dissimilarity function have the smallest averaged SAD than using the other measures.
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