Statistical Volume Analysis: A New Endmember Extraction Method for Multi/Hyperspectral Imagery

Simplex volume is the most commonly used parameter for endmember extraction. However, when outliers exist in the image, the maximum-volume-criterion (MVC)-based methods tend to extract them as endmembers. Those outlier endmembers could be either physically meaningless or not representative enough for prevalent land covers. This is the biggest bottleneck preventing MVC-based methods from being extended from theoretical analysis to practical applications. This is mainly due to the limitation of the simplex volume formula itself, which is only determined by simplex vertices and completely ignoring the statistics of the data cloud. Usually, the simplex with vertices containing outliers has a larger volume than the one with vertices only containing true endmembers; thus, outliers are more favorably extracted as endmembers. Usually, the outliers are distributed in the direction of low information content. When extracted endmembers contain outliers, the overall information content (OIC) of the data cloud projected onto the endmember subspace will be definitely reduced. Motivated by this fact, we present the concept of statistical volume and develop a new endmember extraction method, which is named statistical volume analysis (SVA). The algorithm simultaneously utilizes the geometrical property of the simplex and the statistical characteristic of the projected data in the endmember subspace. Therefore, SVA not only can find a simplex with a large volume but also can get a large OIC of the projected data. Experiments with both simulated and real data show that SVA can compete with state-of-the-art methods in extracting endmembers of prevalent land covers. Moreover, it is capable of avoiding extracting outliers as endmembers.