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12 August 2004 The extension of endmember extraction to multispectral scenes
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A multiple simplex endmember extraction method has been developed. Unlike convex methods that rely on a single simplex, the number of endmembers is not restricted by the number of linearly independent spectral channels. The endmembers are identified as the extreme points in the data set. The algorithm for finding the endmembers can simultaneously find endmember abundance maps. Multispectral and hyperspectral scenes can be complex and contain many materials under a variety of illumination and environmental conditions, but individual pixels typically contain only a few materials in a small subset of the illumination and environmental conditions which exist in the scene. This forms the physical basis for the approach that restricts the number of endmembers that combine to model a single pixel. No restriction is placed on the total number of endmembers, however. The algorithm for finding the endmembers and their abundances maps is sequential. Extreme points are identified based on the angle they make with the existing set. The point making the maximum angle with the existing set is chosen as the next endmember to add to enlarge the endmember set. The maximum number of endmembers that are allowed to be in a subset model for individual pixels is controlled by an input parameter. The subset selection algorithm is sequential and takes place simultaneously with the overall endmember extraction. The algorithm updates the abundances of previous endmembers and ensures that the abundances of previous and current endmembers remain positive or zero. The method offers advantages in multispectral data sets where the limited number of channels impairs material un-mixing by standard techniques. A description of the method is presented herein and applied to real and synthetic hyperspectral and multispectral data sets.
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John H. Gruninger, Anthony J. Ratkowski, and Michael L. Hoke "The extension of endmember extraction to multispectral scenes", Proc. SPIE 5425, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery X, (12 August 2004);

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