Linear Spectral Mixing Model: Theoretical Concepts, Algorithms and Applications in Studies in the Legal Amazon

Abstract

This paper presents a review of the Linear Spectral Mixing Model and its applications in the Legal Amazon. Studies on spectral mixture began in the 1970s, motivated by the problem of area estimation obtained by automatic interpretation. The pixel was classified or not based on the maximum probability of this pixel to belong to a given class, then overestimating or underestimating this class according to the decision made. Thus, interest in the study of the spectral mixture within the pixel arose. The response of each pixel can be considered as a linear combination of the spectral responses of each component that is within the pixel. Thus, knowing the spectral responses of the components, we can obtain the proportions of these components (fraction images). This paper presents the theoretical concepts that motivated the development of this model, and the algorithms (Constrained Least Squares, Weighted Least Squares, Principal Components) developed in the 1980s are described. With the availability of these algorithms in the digital image processing softwares in the 1990s, the number of studies using this technique increased in Brazil and worldwide. The fraction images were used to automate the PRODES Project (Monitoring deforestation of the Brazilian Amazon Forest by Satellite) which was the first systematic operational project of orbital Remote Sensing. Following the use of fraction images in studies conducted in the Brazilian Amazon are presented. In addition, a perspective of use of fraction images for global studies is presented. In conclusion, the Linear Spectral Mixture Model has contributed to the development of several research and applications of Remote Sensing due to its data reduction characteristics and by highlighting the targets of interest in the images.