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The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data

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ABSTRACT

Spectral mixing is a problem inherent to remote sensing data and results in few image pixel spectra representing ″pure″ targets. Linear spectral mixture analysis is designed to address this problem and it assumes that the pixel-to-pixel variability in a scene results from varying proportions of spectral endmembers. In this paper we present a different endmember-search algorithm called the Successive Projection Algorithm (SPA). SPA builds on convex geometry and orthogonal projection common to other endmember search algorithms by including a constraint on the spatial adjacency of endmember candidate pixels. Consequently it can reduce the susceptibility to outlier pixels and generates realistic endmembers.This is demonstrated using two case studies (AVIRIS Cuprite cube and Probe-1 imagery for Baffin Island) where image endmembers can be validated with ground truth data. The SPA algorithm extracts endmembers from hyperspectral data without having to reduce the data dimensionality. It uses the spectral angle (alike IEA) and the spatial adjacency of pixels in the image to constrain the selection of candidate pixels representing an endmember. We designed SPA based on the observation that many targets have spatial continuity (e.g. bedrock lithologies) in imagery and thus a spatial constraint would be beneficial in the endmember search. An additional product 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 new endmember on the data structure, and provides information on the convergence of the algorithm. It can provide a general guideline to constrain the total number of endmembers in a search.

No MeSH data available.


Comparison between SPA endmember and PPI endmember(“true”endmember). The solid lines denotes PPI endmembers.
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f3-sensors-08-01321: Comparison between SPA endmember and PPI endmember(“true”endmember). The solid lines denotes PPI endmembers.

Mentions: We first examine the SPA endmembers in the context of the seven mineral PPI endmembers (zeolite, alunite, buddingtonite, calcite, kaolinite, silica and muscovite/illite) previously reported by Kruse and Huntington (1996)[2]. Out of 19 endmembers derived from the SPA, 16 are for minerals and 3 for shade/shadow (Table 1). A comparison of the 16 mineral endmembers and “true”endmembers (PPI_endmembers, Section 4.1.) is shown in Figure 3. Each SPA endmember was calculated from more than 2 pixels (2-9). For each of the seven minerals we found at least one SPA endmember with a good match in spectral shape to that of the field validated PPI endmembers. When SPA picks multiple endmembers for a given mineral these differ in spectral magnitude or in subtle variations in their spectral shape (Table 1 and Figure 3). For example, two SPA endmembers (SPA_12 and SPA_15) were selected for the mineral alunite_2 (Figure 3b). SPA and PPI_endmembers result from the average of multiple candidate pixels located at vertices of the simplex. However they differ in their list of candidate pixels as PPI does not take into account spatial information, and thus, the averaging process generates different solutions resulting in endmember spectra that are distinct in their detailed shape and amplitude. One endmember, SPA_9 (with an absorption feature at 2.27 μm, Figure 3j), could not be matched to a PPI mineral endmember and has yet to be properly labeled though the observed feature is consistent with the mineral jarosite discussed in Clark et al. (2003)[43].


The Successive Projection Algorithm (SPA), an Algorithm with a Spatial Constraint for the Automatic Search of Endmembers in Hyperspectral Data
Comparison between SPA endmember and PPI endmember(“true”endmember). The solid lines denotes PPI endmembers.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3927512&req=5

f3-sensors-08-01321: Comparison between SPA endmember and PPI endmember(“true”endmember). The solid lines denotes PPI endmembers.
Mentions: We first examine the SPA endmembers in the context of the seven mineral PPI endmembers (zeolite, alunite, buddingtonite, calcite, kaolinite, silica and muscovite/illite) previously reported by Kruse and Huntington (1996)[2]. Out of 19 endmembers derived from the SPA, 16 are for minerals and 3 for shade/shadow (Table 1). A comparison of the 16 mineral endmembers and “true”endmembers (PPI_endmembers, Section 4.1.) is shown in Figure 3. Each SPA endmember was calculated from more than 2 pixels (2-9). For each of the seven minerals we found at least one SPA endmember with a good match in spectral shape to that of the field validated PPI endmembers. When SPA picks multiple endmembers for a given mineral these differ in spectral magnitude or in subtle variations in their spectral shape (Table 1 and Figure 3). For example, two SPA endmembers (SPA_12 and SPA_15) were selected for the mineral alunite_2 (Figure 3b). SPA and PPI_endmembers result from the average of multiple candidate pixels located at vertices of the simplex. However they differ in their list of candidate pixels as PPI does not take into account spatial information, and thus, the averaging process generates different solutions resulting in endmember spectra that are distinct in their detailed shape and amplitude. One endmember, SPA_9 (with an absorption feature at 2.27 μm, Figure 3j), could not be matched to a PPI mineral endmember and has yet to be properly labeled though the observed feature is consistent with the mineral jarosite discussed in Clark et al. (2003)[43].

View Article: PubMed Central - PubMed

ABSTRACT

Spectral mixing is a problem inherent to remote sensing data and results in few image pixel spectra representing ″pure″ targets. Linear spectral mixture analysis is designed to address this problem and it assumes that the pixel-to-pixel variability in a scene results from varying proportions of spectral endmembers. In this paper we present a different endmember-search algorithm called the Successive Projection Algorithm (SPA). SPA builds on convex geometry and orthogonal projection common to other endmember search algorithms by including a constraint on the spatial adjacency of endmember candidate pixels. Consequently it can reduce the susceptibility to outlier pixels and generates realistic endmembers.This is demonstrated using two case studies (AVIRIS Cuprite cube and Probe-1 imagery for Baffin Island) where image endmembers can be validated with ground truth data. The SPA algorithm extracts endmembers from hyperspectral data without having to reduce the data dimensionality. It uses the spectral angle (alike IEA) and the spatial adjacency of pixels in the image to constrain the selection of candidate pixels representing an endmember. We designed SPA based on the observation that many targets have spatial continuity (e.g. bedrock lithologies) in imagery and thus a spatial constraint would be beneficial in the endmember search. An additional product 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 new endmember on the data structure, and provides information on the convergence of the algorithm. It can provide a general guideline to constrain the total number of endmembers in a search.

No MeSH data available.