Fuzzy Assessment of Spectral Unmixing Algorithms

While a single spectrum is often used to present a pure class, it is more realistic to consider intra-class spectral variation and model a pure class using a group of its representative spectra. In line with this consideration, crisp unmixing accuracy assessment, where unmixing performance is assessed using a mean squared error of the estimated endmember fractions, can be misleading. In this paper, alterative spectral unmixing assessment methods are introduced to account for the uncertainty contained in the spectral measurements and during the ground truth data collection. Two fuzzy measures are developed to assess unmixing performance. One is fuzzy unmixing fraction error for a realistic assessment and the other is pixel level unmixing accuracy to provide a good quantitative understanding of the unmixing success rates spatially. To demonstrate and illustrate how they work, the two fuzzy measures are applied to evaluate the performance of several spectral unmixing methods including both single spectrum based and multiple spectra based algorithms. Crisp assessments and fuzzy results at various tolerance levels are presented and compared. Based on the realistic measures proposed, it is found the recent developed unmixing method with extended Support Vector Machines outperforms other algorithms tested.