Using Mixed Pixels for the Training of a Maximum Likelihood Classification

Most supervised image classification methods need pure pixels for training, which complicates training when pure pixels are scarce. In these cases, it can be difficult to obtain a sufficiently large number of representative training samples to accurately estimate the spectra of the classes. The direct use of ‘almost pure’ pixels is not advisable. These cause the estimated mean to be biased and the estimated variance to depend on the degree of occurrence of other classes, instead of on the natural variation in the spectrum of the class. The solution for the lack of pure training samples is to be found in the use of mixed pixels to estimate the spectra of pure classes. This article presents a method to estimate unbiased pure spectra out of mixed pixels using adjustment theory and probability model estimation. An advantage of such a fuzzy training method is that more pixels in the image can be used for training, which enables the use of heterogeneous areas for training or the random selection of training pixels. There are two conditions for this method. First, one needs to have estimates of the fractions of the classes in the mixed training samples. Secondly, the spectral values of the mixed pixels should be a linear combination of the spectra of the composing classes. * Corresponding author, currently employed at Geodesy Dept., Kadaster, Hofstraat 110, 7311 KZ Apeldoorn, the Netherlands.