Characterizing intimate mixtures of materials in hyperspectral imagery with albedo-based and kernel-based approaches

Linear mixtures of materials in a scene often occur because the pixel size of a sensor is relatively large and consequently they contain patches of different materials within them. This type of mixing can be thought of as areal mixing and modeled by a linear mixture model with certain constraints on the abundances. The solution to these models has received a lot of attention. However, there are more complex situations, such as scattering that occurs in mixtures of vegetation and soil, or intimate mixing of granular materials like soils. Such multiple scattering and microscopic mixtures within pixels have varying degrees of non-linearity. In such cases, a linear model is not sufficient. Furthermore, often enough, scenes may contain cases of both linear and non-linear mixing on a pixel-by-pixel basis. This study considers two approaches for use as generalized methods for un-mixing pixels in a scene that may be linear (areal mixed) or non-linear (intimately mixed). The first method is based on earlier studies that indicate non-linear mixtures in reflectance space are approximately linear in albedo space. The method converts reflectance to single-scattering albedo (SSA) according to Hapke theory assuming bidirectional scattering at nadir look angles and uses a constrained linear model on the computed albedo values. The second method is motivated by the same idea, but uses a kernel that seeks to capture the linear behavior of albedo in nonlinear mixtures of materials. The behavior of the kernel method can be highly dependent on the value of a parameter, gamma. Furthermore, both methods are dependent on the choice of endmembers, and also on RMSE (root mean square error) as a performance metric. This study compares the two approaches and pays particular attention to these dependencies. Both laboratory and aerial collections of hyperspectral imagery are used to validate the methods.