Mapping impervious surface fractions using automated Fisher transformed unmixing

Spatial explicit monitoring of impervious surface fractions provides essential information for urban planning, urban disaster prevention and mitigation. Moderate spectral and spatial resolution satellite observation has become a tool to perform such monitoring across different spatial and temporal scales. Yet, one major challenge in urban remote sensing is the high spatial heterogeneity causing the presence of image pixels constituting a mixture of different land cover materials. Here we apply an automated unmixing procedure specifically designed to optimally account for the pronounced spectral variability (i.e. high within-class and low between-class variability) prevailing in urban settings. The approach is based on Fisher Discriminant Analysis (FDA), a data dimensionality reduction technique in which between-class variability is maximized and within-class variability is minimized while transforming spectra from the reflectance to the Fisher feature space. We integrated the FDA transformation in the widely-applied Multiple Endmember Spectral Mixture Analysis (MESMA) approach in an attempt to more effectively address the endmember variability problem. We made use of online spectral libraries to train the Fisher transformation parameters and steer the automated selection of image endmembers. Our Fisher transformed MESMA algorithm (F-MESMA) was tested on medium spatial resolution Landsat scenes and impervious fraction maps were generated for five major cities located in different regions of the world. The output of F-MESMA was compared to the output of state-of-the-art spectral mixture analysis approaches which were specifically designed to reduce endmember variability issues. We could demonstrate that compared to other spectral transformation approaches, the ratio of within- vs between-class variability of the endmembers was most strongly reduced after applying the Fisher transformation. As a direct consequence, across all five cities F-MESMA consistently provided the most accurate impervious surface fraction estimates (RMSE_F-MESMA = 0.13 vs. RMSE_alternative approaches = [0.16–0.17]).