Sampling Robustness in Gradient Analysis of Urban Material Mixtures

Many studies analyzing spaceborne hyperspectral images (HSIs) have so far struggled to deal with a lack of pure pixels due to complex mixtures of urban surface materials. Recently, an alternative concept of gradients in urban surface material composition has been proposed and successfully applied to map cities with spaceborne HSIs without the requirement for a previous determination of pure pixels. The gradient concept treats all pixels as mixed and aims to describe and quantify gradual transitions in the cover fractions of surface materials. This concept presents a promising approach to tackle urban mapping using spaceborne HSIs. However, since gradients are determined in a data-driven way, their transferability within urban areas needs to be investigated. For this purpose, we analyze the robustness of urban surface material gradients and their dependence across six systematic and three simple random sampling schemes. The results show high similarity between nine sampling schemes in the primary gradient feature space (Pspace) and individual gradient feature spaces (Ispaces). Comparing the Pspace with the Ispaces, the Mantel statistics show the resemblance of samples' distribution in the Pspace, and each Ispace is rather strong with high credibility, as the significance level is P < 0.01. Therefore, it can be concluded that the material gradients defined in the test area are independent of the specific sampling scheme. This study paves the way for subsequent analysis of the stability of urban surface material gradients and the interpretation of material gradients in other urban environments.