J Math Imaging Vis (2012) 42:163–175 DOI 10.1007/s10851-011-0276-0 On Endmember Identification in Hyperspectral Images Without Pure Pixels: A Comparison of Algorithms Javier Plaza · Eligius M.T. Hendrix · Inmaculada García · Gabriel Martín · Antonio Plaza Published online: 25 March 2011 © Springer Science+Business Media, LLC 2011 Abstract Hyperspectral imaging is an active area of re- search in Earth and planetary observation. One of the most important techniques for analyzing hyperspectral images is spectral unmixing, in which mixed pixels (resulting from in- sufficient spatial resolution of the imaging sensor) are de- composed into a collection of spectrally pure constituent spectra, called endmembers weighted by their correspondent fractions, or abundances. Over the last years, several algo- rithms have been developed for automatic endmember ex- traction. Many of them assume that the images contain at least one pure spectral signature for each distinct material. However, this assumption is usually not valid due to spa- tial resolution, mixing phenomena, and other considerations. A recent trend in the hyperspectral imaging community is to design endmember identification algorithms which do not assume the presence of pure pixels. Despite the prolifera- tion of this kind of algorithms, many of which are based on minimum enclosing simplex concepts, a rigorous quantita- J. Plaza ( ) · G. Martín · A. Plaza Hyperspectral Computing Laboratory, Dept. Technology of Computers and Communications, University of Extremadura, Avda. de la Universidad s/n, 10071 Caceres, Spain e-mail: jplaza@unex.es G. Martín e-mail: gamahefpi@unex.es A. Plaza e-mail: aplaza@unex.es E.M.T. Hendrix · I. García Department of Computer Architecture, University of Málaga, 29071 Málaga, Spain E.M.T. Hendrix e-mail: Eligius.Hendrix@wur.nl I. García e-mail: igarcia@ual.es tive and comparative assessment is not yet available. In this paper, we provide a comparative analysis of endmember ex- traction algorithms without the pure pixel assumption. In our experiments we use synthetic hyperspectral data sets (con- structed using fractals) and real hyperspectral scenes col- lected by NASA’s Jet Propulsion Laboratory. Keywords Hyperspectral imaging · Endmember extraction · Spectral unmixing · Minimum enclosing simplex 1 Introduction Hyperspectral imaging has been transformed from a sparse research tool into a commodity product available to a broad user community [1]. The wealth of spectral information available from advanced hyperspectral imaging instruments currently in operation has opened new perspectives in many application domains, such as monitoring of environmen- tal and urban processes or risk prevention and response, including—among others—tracking wildfires, detecting bi- ological threats, and monitoring oil spills and other types of chemical contamination. Advanced hyperspectral instru- ments such as NASA’sAirborne Visible Infra-Red Imaging Spectrometer (AVIRIS) [2] are now able to cover the wave- length region from 0.4 to 2.5 μm using more than 200 spec- tral channels, at nominal spectral resolution of 10 nm. In hyperspectral imaging, endmember extraction is the process of selecting a collection of pure signature spectra of the materials present in a remotely sensed hyperspectral scene. These pure signatures are then used to decompose the scene into a set of so-called abundance fractions by means of a spectral unmixing algorithm. Most techniques available