A new volume formula for a simplex and its application to endmember extraction for hyperspectral image analysis

Based on the geometric properties of a simplex, endmembers can be extracted automatically from a hyperspectral image. To avoid the shortcomings of the N-FINDR algorithm, which requires the dimensions of the data to be one less than the number of end members needed, a new volume formula for the simplex without the requirement of dimension reduction is presented here. We demonstrate that the N-FINDR algorithm is a special case of the new method. Moreover, whether the null vector is included as an endmember has an important effect on the final result of the endmember extraction. Finally, we compare the new method with previous methods for endmember extraction of hyperspectral data collected by the Advanced Visible and Infrared Imaging Spectrometer (AVIRIS) over Cuprite, Nevada.