The pixel purity index (PPI) and two-dimensional (2-D) scatter plots are two popular techniques for endmember extraction in remote sensing spectral mixture analysis, yet both suffer from one major drawback, that is, the selection of a final set of endmembers has to endure a cumbersome process of iterative visual inspection and human intervention, especially when a spectrally-complex urban scene is involved. Within the conceptual framework of a V-H-L-S (vegetation-high albedo-low albedo-soil) model, which is expanded from the classic V-I-S (vegetation-impervious surface-soil) model, a tetrahedron-based endmember selection approach combined with a multi-objective optimization genetic algorithm (MOGA) was designed to identify urban endmembers from multispectral imagery. The tetrahedron defining the enclosing volume of MNF-transformed pixels in a three-dimensional (3-D) space was algorithmically sought, so that the tetrahedral vertices can ideally match the four components of the adopted model. A case study with Landsat Enhanced Thematic Mapper Plus (ETM+) satellite imagery in Shanghai, China was conducted to verify the validity of the method. The method performance was compared with those of the traditional PPI and 2-D scatter plots approaches. The results indicated that the tetrahedron-based endmember selection approach performed better in both accuracy and ease of identification for urban surface endmembers owing to the 3-D visualization analysis and use of the MOGA.
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