A nonlinear unmixing method in the infrared domain

This paper presents the physical principle of a new (to our knowledge) unmixing method to retrieve optical properties (reflectance and emissivity) and surface temperatures over a heterogeneous and a folded landscape using hyperspectral and multiangular airborne images acquired with high spatial resolution. In fact, over such a complex scene, the linear mixing model of the reflectance commonly used in the reflective domain is no longer valid in the IR range for the two following reasons: multiple reflections due to the three-dimensional (3D) structure and the radiative phenomenon introduced by the temperature by way of the black body law. Thus, to solve this nonlinear unmixing problem, a new physical model of aggregation is used. Our model requires as inputs knowledge of the 3D scene structure and the spatial contribution of each material in the scene. Each elementary scene element is characterized by its optical properties, and its temperature, spectral, and multiangular acquisitions are required. This paper focuses only on the theoretical feasibility of such a method. In addition, an analysis is conducted evaluating the impact of the misregistration between the radiometric image and its digital terrain model, estimating a threshold of the relative importance of every elementary material to retrieve its corresponding optical properties and temperature. The results show that the 3D geometry must be accurately known (accuracy of 1 m for a spatial resolution of 20 m), and the relative contribution of material in the mixed area must be above 15% to retrieve its surface temperature with an accuracy better than 1 K. So, this method is applied on three different landscapes (heterogeneous flat surface, V shape, and urban canyon), and the results exhibit performances better than 1% for optical properties and 1 K for surface temperatures.