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Common endmember extraction algorithms presume that the number of materials present is either known or may be predetermined by using spectral databases or other approaches. In this letter, we propose a new method called genetic orthogonal projection (GOP) for endmember extraction in imaging spectrometry. GOP is based on a fully unsupervised approach and uses convex geometric characteristics as well as a genetic algorithm. We compare GOP with existing endmember extraction algorithms and demonstrate that GOP partially outperforms them, without the need of a priori information.