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Proceedings Paper

Simplex volume analysis for finding endmembers in hyperspectral imagery
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Paper Abstract

Using maximal simplex volume as an optimal criterion for finding endmembers is a common approach and has been widely studied in the literature. Interestingly, very little work has been reported on how simplex volume is calculated. It turns out that the issue of calculating simplex volume is much more complicated and involved than what we may think. This paper investigates this issue from two different aspects, geometric structure and eigen-analysis. The geometric structure is derived from its simplex structure whose volume can be calculated by multiplying its base with its height. On the other hand, eigen-analysis takes advantage of the Cayley-Menger determinant to calculate the simplex volume. The major issue of this approach is that when the matrix is ill-rank where determinant is desired. To deal with this problem two methods are generally considered. One is to perform data dimensionality reduction to make the matrix to be of full rank. The drawback of this method is that the original volume has been shrunk and the found volume of a dimensionality-reduced simplex is not the real original simplex volume. Another is to use singular value decomposition (SVD) to find singular values for calculating simplex volume. The dilemma of this method is its instability in numerical calculations. This paper explores all of these three methods in simplex volume calculation. Experimental results show that geometric structure-based method yields the most reliable simplex volume.

Paper Details

Date Published: 21 May 2015
PDF: 8 pages
Proc. SPIE 9501, Satellite Data Compression, Communications, and Processing XI, 950107 (21 May 2015); doi: 10.1117/12.2176767
Show Author Affiliations
Hsiao-Chi Li, Univ. of Maryland, Baltimore County (United States)
Meiping Song, Dalian Maritime Univ. (China)
Chein-I Chang, Univ. of Maryland, Baltimore County (United States)

Published in SPIE Proceedings Vol. 9501:
Satellite Data Compression, Communications, and Processing XI
Bormin Huang; Chein-I Chang; Chulhee Lee; Yunsong Li; Qian Du, Editor(s)

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