19 May 2016 Geometric convex cone volume analysis
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Abstract
Convexity is a major concept used to design and develop endmember finding algorithms (EFAs). For abundance unconstrained techniques, Pixel Purity Index (PPI) and Automatic Target Generation Process (ATGP) which use Orthogonal Projection (OP) as a criterion, are commonly used method. For abundance partially constrained techniques, Convex Cone Analysis is generally preferred which makes use of convex cones to impose Abundance Non-negativity Constraint (ANC). For abundance fully constrained N-FINDR and Simplex Growing Algorithm (SGA) are most popular methods which use simplex volume as a criterion to impose ANC and Abundance Sum-to-one Constraint (ASC). This paper analyze an issue encountered in volume calculation with a hyperplane introduced to illustrate an idea of bounded convex cone. Geometric Convex Cone Volume Analysis (GCCVA) projects the boundary vectors of a convex cone orthogonally on a hyperplane to reduce the effect of background signatures and a geometric volume approach is applied to address the issue arose from calculating volume and further improve the performance of convex cone-based EFAs.
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Hsiao-Chi Li, Hsiao-Chi Li, Chein-I Chang, Chein-I Chang, "Geometric convex cone volume analysis", Proc. SPIE 9874, Remotely Sensed Data Compression, Communications, and Processing XII, 987403 (19 May 2016); doi: 10.1117/12.2223883; https://doi.org/10.1117/12.2223883
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