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The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data
Alberta Terrestrial Imaging Center, 401, 817 – 4th Avenue South, Lethbridge, Alberta Canada, T1J 0P3
Earth Observation Systems Laboratory, Department of Earth and Atmospheric Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2E3
* Author to whom correspondence should be addressed.
Received: 28 December 2007; Accepted: 19 February 2008 / Published: 22 February 2008
Abstract: Spectral mixing is a problem inherent to remote sensing data and results in fewimage pixel spectra representing "pure" targets. Linear spectral mixture analysis isdesigned to address this problem and it assumes that the pixel-to-pixel variability in ascene results from varying proportions of spectral endmembers. In this paper we present adifferent endmember-search algorithm called the Successive Projection Algorithm (SPA).SPA builds on convex geometry and orthogonal projection common to other endmembersearch algorithms by including a constraint on the spatial adjacency of endmembercandidate pixels. Consequently it can reduce the susceptibility to outlier pixels andgenerates realistic endmembers.This is demonstrated using two case studies (AVIRISCuprite cube and Probe-1 imagery for Baffin Island) where image endmembers can bevalidated with ground truth data. The SPA algorithm extracts endmembers fromhyperspectral data without having to reduce the data dimensionality. It uses the spectralangle (alike IEA) and the spatial adjacency of pixels in the image to constrain the selectionof candidate pixels representing an endmember. We designed SPA based on theobservation that many targets have spatial continuity (e.g. bedrock lithologies) in imageryand thus a spatial constraint would be beneficial in the endmember search. An additionalproduct of the SPA is data describing the change of the simplex volume ratio between successive iterations during the endmember extraction. It illustrates the influence of a newendmember on the data structure, and provides information on the convergence of thealgorithm. It can provide a general guideline to constrain the total number of endmembersin a search.
Keywords: hyperspectral; spectral unmixing; endmember; simplex
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Zhang, J.; Rivard, B.; Rogge, D.M. The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data. Sensors 2008, 8, 1321-1342.
Zhang J, Rivard B, Rogge DM. The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data. Sensors. 2008; 8(2):1321-1342.
Zhang, Jinkai; Rivard, Benoit; Rogge, D. M. 2008. "The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data." Sensors 8, no. 2: 1321-1342.