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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.
Highlights
Linear spectral mixture analysis (SMA) is based on the simple assumption that remotely sensed spectral measurements are mixed signatures that vary across the scene as the relative proportion of endmembers change
A number of algorithms have been developed over the past decade to automatically find image endmembers and these include the NFINDR [12], iterative error analysis (IEA) [13], vertex component analysis (VCA) [14], MaxD (Maximum Distance) [15], Sequential Maximum Angle Convex Cone (SMACC ) [16], iterated constrained endmembers (ICE)[17], simplex growing algorithm (SGA) [18], minimum volume constrained nonnegative factorization (MVC-nonnegative matrix factorization (NMF)) [19] and optical real-time adaptive spectral identification system (ORASIS) [20]
In this study we propose a more robust approach that uses the spectral angle and the spatial adjacency of pixels in the image to constrain the selection of candidate pixels representing an endmember
Summary
Linear spectral mixture analysis (SMA) is based on the simple assumption that remotely sensed spectral measurements are mixed signatures that vary across the scene as the relative proportion of endmembers change. A simplex is fit to the convex hull of the n-dimensional data cloud and the vertices of the simplex define the spectral properties of the endmembers Based on this concept, a number of algorithms have been developed over the past decade to automatically find image endmembers and these include the NFINDR [12], iterative error analysis (IEA) [13], vertex component analysis (VCA) [14], MaxD (Maximum Distance) [15], Sequential Maximum Angle Convex Cone (SMACC ) [16], iterated constrained endmembers (ICE)[17], simplex growing algorithm (SGA) [18], minimum volume constrained nonnegative factorization (MVC-NMF) [19] and optical real-time adaptive spectral identification system (ORASIS) [20].
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