Estimation of Proportions in Mixed Pixels through Their Region Characterization

The estimation of proportions of classes in the mixed pixels of multichannel imagery data is considered in this paper. A significant portion of the imagery data consists of a mixture of the responses of two or more objects whenever the objects being viewed by a multispectral scanner are not large enough relative to the size of aresolution element. A region of mixed pixels can be characterized through the probability density function of proportions of classes in the mixed pixels. Using information from the spectral vectors of a given set of pixels from the mixed pixel region, expressions are developed for obtaining the maximum likelihood estimates of the parameters of probability densi ty functi ons of proporti ons. The proportions of classes in the mixed pixels can then be estimated. If the mixed pixels contain objects of two classes, the computation can be considerably reduced by transforming the spectral vectors using a transformation matrix that simultaneously diagonal i zes the covari ance matri ces of the two cl as ses. In addition to the spectral vectors, if the proportions of the classes of a set of mixed pixels from the region are given, then expressions are developed for obtaining the estimates of the parameters of the probability density function of the proportions of mixed pixels. Development of these expressions is based on the criterion of the minimum sum of squares of errors. Furthermore, experimental results from the processing of remotely sensed agricultural multispectral imagery data are presented.