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

Manuel Graña,Miguel A Veganzones

doi:10.1186/1687-6180-2012-64

Manuel Graña, Miguel A Veganzones

Open Access

https://doi.org/10.1186/1687-6180-2012-64

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Abstract

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.

Highlights

The high spectral resolution provided by current hyperspectral imaging devices facilitates identification of fundamental materials that make up a remotely sensed scene [1,2]
5 Results We first provide the plots of the unmixing residual error versus the number of endmembers of the solutions found by the WM-Multi-Objective Genetic Algorithm (MOGA), WM-MOGACORR and N-FINDR based approach of [22]
The curve corresponding to the WM-MOGA is smooth because the MOGA searches for the Pareto front based on these criteria

Summary

Introduction

The high spectral resolution provided by current hyperspectral imaging devices facilitates identification of fundamental materials that make up a remotely sensed scene [1,2]. The linear mixing model (LMM) [1] assumes that the spectral signature of one pixel of the hyperspectral image is a linear combination of the endmember spectra corresponding to the aggregation of materials in the scene due to reduced sensor spatial resolution. Sub-pixel resolution analysis aims to the extraction of the fractional abundances of such endmembers inside the pixel. Endmember spectra define a convex polytopea in the high-dimensional space defined by the image pixel spectra. The fractional abundance of the endmembers at each pixel correspond to the convex coordinates relative to the convex polytope vertices. The set of endmembers can be defined on the basis of a priori knowledge about

Methods

Results

Conclusion