Hyperspectral imaging is an active area of research in Earth and planetary observation. One of the most important techniques for analyzing hyperspectral images is spectral unmixing, in which mixed pixels (resulting from insufficient spatial resolution of the imaging sensor) are decomposed into a collection of spectrally pure constituent spectra, called endmembers weighted by their correspondent fractions, or abundances. Over the last years, several algorithms have been developed for automatic endmember extraction. 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 spatial 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 proliferation of this kind of algorithms, many of which are based on minimum enclosing simplex concepts, a rigorous quantitative and comparative assessment is not yet available. In this paper, we provide a comparative analysis of endmember extraction algorithms without the pure pixel assumption. In our experiments we use synthetic hyperspectral data sets (constructed using fractals) and real hyperspectral scenes collected by NASA’s Jet Propulsion Laboratory.