13 May 2010 Iterative convex hull volume estimation in hyperspectral imagery for change detection
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Abstract
Historically in change detection, statistically based methods have been used. However, as the spatial resolution of spectral images improves, the data no longer maintain a Gaussian distribution, and some assumptions about the data - and subsequently all algorithms based upon those statistical assumptions - fail. Here we present the Simplex Volume Estimation algorithm (SVE), which avoids these potential hindrances by taking a geometrical approach. In particular, we employ the linear mixture model to approximate the convex hull enclosing the data through identification of the simplex vertices (known as endmembers). SVE begins by processing an image and tiling it into squares. Next, SVE iterates through the tiles and for each set of pixels it identifies the number of corners (as vectors) that define the simplex of that set of data. For each tile, it then iterates through the increasing dimensionality, or number of endmembers, while every time calculating the volume of the simplex that is defined by that number of endmembers. When the volume is calculated in a dimension that is higher than that of the inherent dimensionality of the data, the volume will theoretically drop to zero. This value is indicative of the inherent dimensionality of the data as represented by the convex hull. Further, the volume of the simplex will fluctuate when a new material is introduced to the dataset, indicating a change in the image. The algorithm then analyzes the volume function associated with each tile and assigns the tile a metric value based on that function. The values of these metrics will be compared by using hyperspectral imagery collected from different platforms over experimental setups with known changes between flights. Results from these tests will be presented along with a path forward for future research.
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Amanda K. Ziemann, Amanda K. Ziemann, David W. Messinger, David W. Messinger, William F. Basener, William F. Basener, } "Iterative convex hull volume estimation in hyperspectral imagery for change detection", Proc. SPIE 7695, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVI, 76951I (13 May 2010); doi: 10.1117/12.850122; https://doi.org/10.1117/12.850122
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