Unmixing urban hyperspectral imagery using probability distributions to represent endmember variability

Urban composition can be analyzed through spectral unmixing of images from airborne imaging spectrometers. Unmixing given a spectral library can be accomplished by set-based methods or distribution-based methods. For computational efficiency and optimal accuracy, set-based methods employ a library reduction procedure when applied to large spectral libraries. On the other hand, distribution-based methods model the library by only a few parameters, hence innately accept large libraries. A natural question arises that can distribution-based methods with the original large spectral library achieve comparable performance to set-based methods in urban imagery. In this study, we aim to investigate the unmixing capability of several distribution-based methods, Gaussian mixture model (GMM), normal compositional model (NCM), and Beta compositional model (BCM) by comparing them to set-based methods MESMA and alternate angle minimization (AAM). The data for validation were collected by the AVIRIS sensor over the Santa Barbara region: two 16 m spatial resolution and two 4 m spatial resolution images. 64 validated regions of interest (ROI) (180 m by 180 m) were used to assess estimate accuracy. Ground truth was obtained using 1 m images leading to the following 6 classes: turfgrass, non-photosynthetic vegetation (NPV), paved, roof, soil, and tree. Spectral libraries were built by manually identifying and extracting pure spectra from both resolution images, resulting in 3287 spectra at 16 m and 15,426 spectra at 4 m. The libraries were further reduced to 61 spectra at 16 m and 95 spectra at 4 m for set-based methods. The results show that in terms of mean absolute error (MAE), GMM performed best among the distribution-based methods while MESMA performed best among the set-based methods. For 16 m data, there is no significant difference between GMM and MESMA (MAE = 0.069 vs. MAE = 0.074, p = 0.25). For 4 m data, though GMM is not as accurate as MESMA (MAE = 0.056 vs. MAE = 0.046, p = 7e - 5), it is better than AAM (MAE = 0.056 vs. MAE = 0.065, p = 0.02) which is a re-implementation of MESMA. Further evidence on a reconstructed synthetic dataset implies possible overfitting of the reduced library to the images for MESMA. These findings suggest that the distribution-based method GMM could achieve comparable unmixing accuracy to set-based methods without the need of library reduction, it may also be more stable across datasets, and the current 2-step workflow could be replaced by a single model in applying a universal spectral library.