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Endmember extraction, which is an important technique for hyperspectral data interpretation, selects a collection of pure signature spectra of the different materials, called endmembers, which are present in a remotely sensed hyperspectral image scene. These pure signatures are then used in spectral unmixing algorithms to decompose the scene into abundance fractions, which indicate the proportion of each endmember's presence in a mixed pixel. In other words, abundances can be obtained by the given endmembers. Correspondingly, endmembers can be extracted based on an abundance constraint. In this paper, we first propose an endmember extraction framework based on an abundance constraint whose efficiency is related to the abundance calculation. The mainstream existing spatial-spectral algorithms can have a very high complexity and are sensitive to outliers, or the spatial information is considered followed by the spectral information. We therefore propose a strategy to consider the spectral information followed by the spatial information, using an abundance-constrained framework. The spatial strategy is also assumed to be immune to outliers. Experiments on both synthetic and real hyperspectral data sets indicate that: 1) the abundance constraint is effective for endmember extraction; and 2) the proposed spatial processing method used in the abundance-constrained endmember extraction framework can effectively avoid outliers.