Diffusion and Volume Maximization-Based Clustering of Highly Mixed Hyperspectral Images

Hyperspectral images of a scene or object are a rich data source, often encoding a hundred or more spectral bands of reflectance at each pixel. Despite being very high-dimensional, these images typically encode latent low-dimensional structure that can be exploited for material discrimination. However, due to an inherent trade-off between spectral and spatial resolution, many hyperspectral images are generated at a coarse spatial scale, and single pixels may correspond to spatial regions containing multiple materials. This article introduces the Diffusion and Volume maximization-based Image Clustering (D-VIC) algorithm for unsupervised material discrimination. D-VIC locates cluster modes - high-density, high-purity pixels in the hyperspectral image that are far in diffusion distance (a data-dependent distance metric) from other high-density, high-purity pixels - and assigns these pixels unique labels, as these points are meant to exemplify underlying material structure. Non-modal pixels are labeled according to their diffusion distance nearest neighbor of higher density and purity that is already labeled. By directly incorporating pixel purity into its modal and non-modal labeling, D-VIC upweights pixels that correspond to a spatial region containing just a single material, yielding more interpretable clusterings. D-VIC is shown to outperform baseline and comparable state-of-the-art methods in extensive numerical experiments on a range of hyperspectral images, implying that it is well-equipped for material discrimination and clustering of these data.