If the resolution is low enough that disparate materials can jointly occupy a single pixel, the resulting spectral measurement, made by the sensor, will be the composite of the individual spectra. Under the linear mixing model (LMM), each observed spectrum in each pixel of a given image is assumed to result from the linear combination of the N endmember spectra present in the pixel. The reflectance spectrum of each endmember is weighted by the fractional area coverage of it in the pixel. However, if the components of interest in a pixel are in an intimate association, like sand grains of different composition in a beach deposit, light typically interacts with more than one component as it is multiply scattered, and the mixing between these different components are nonlinear. Such nonlinear effects have been recognized in spectra of: particulate mineral mixtures, aerosols and atmospheric particles, vegetation and canopy. In this case a non-linear mixing model (NLMM) should be applied. To summarize: Linear mixture model assumes that endmember substances are sitting side-by-side within the pixel; Nonlinear mixture model assumes that endmember components are randomly distributed throughout the pixel, causing multiple scattering effects. In the linear mixing case, the basic premise of mixture modelling is that within a given scene, the surface is dominated by a small number of distinct materials that have relatively constant spectral properties. These distinct substances (e.g., water, grass, mineral types), characterized by a well-defined spectral signature are called endmembers, and the fractions in which they appear in a mixed pixel are called fractional abundances. Then, finding the endmembers that can be used to ‘unmix’ other mixed pixels becomes a crucial issue. Identify fractional abundances of distinct substances from the spectral signal of a mixed pixel is one of the application in which hyperspectral images can provide an valuable support.
Explain the concept of composition of spectral signatures and apply the "linear mixing" models in some simple case
Completed