Lattice Algebra Approach to Endmember Determination in Hyperspectral Imagery

Ritter, Gerhard X.; Urcid, Gonzalo

doi:10.1016/s1076-5670(10)60004-3

Cited by 12 publications

(12 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[10,16] is a fast procedure to obtain a set of affine independent vectors which are the vertices of a convex polytope covering the sample data. Applied to hyperspectral images, WM Algorithm produces a large set of candidate endmembers.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Endmember induction by lattice associative memories and multi-objective genetic algorithms

Graña

Veganzones

2012

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

Endmembers are the spectral signatures of the constituent materials of an scene captured with a hyperspectral sensor. Endmember induction algorithms (EIAs) try to extract the endmembers of the scene from the corresponding hyperspectral image. In this article, we benefit from recent theoretical results showing that a set of affine independent vectors can be extracted from the rows and columns of lattice autoassociative memories (LAAM). In the linear mixing model (LMM), endmembers are defined as the vertices of a convex polytope covering the data. Affine independence is a sufficient condition for a set of vectors to be the vertices of a convex polytope, and thus to be considered as endmembers. Our basic procedure is the WM algorithm extracting the endmembers from the dual LAAMs built to store the spectra of the hyperspectral image pixels. The set of endmembers induced by this algorithm defines a convex polytope covering the hyperspectral image data. However, the number of induced endmembers obtained by this procedure is too high for practical purposes, besides they are highly correlated. We apply a Multi-Objective Genetic Algorithm (MOGA) to the optimal selection of the image endmembers. Two fitness functions are used, the residual error of the unmixing process and the size of the set of endmembers. From the MOGA's Pareto front we decide the final set of endmembers by examining the decrease in residual error obtained by increasing the number of endmembers. We propose a faster MOGA where the error fitness function is replaced by a fitness function based on the correlation between endmembers. We compare our process with a state-of-the-art EIA on well known benchmark images.

show abstract

Section: Discussionmentioning

confidence: 99%

“…This number is too high for the actual distinct constituent materials in hyperspectral images. Besides, these endmembers are highly correlated and identification of useful endmembers with some physical interpretation is tricky [16].…”

Section: Introductionmentioning

confidence: 99%

Endmember induction by lattice associative memories and multi-objective genetic algorithms

Graña

Veganzones

2012

EURASIP J. Adv. Signal Process.

View full text Add to dashboard Cite

show abstract

“…Except for Theorem 4.5 that was proven in [34], the proofs of theorems and corollaries given in this section, including Eq. (15), appear in [36].…”

Section: The Shape Of Fðxþmentioning

confidence: 99%

“…The theoretical results embodied by the following theorems and corollaries are only stated since their proofs have been given in [36]. We shall use the notation W j and M j to denote the jth column of the matrices W XX and M XX , respectively.…”

Section: The Shape Of Fðxþmentioning

confidence: 99%