The Maximum Likelihood Estimation of Signature Transformation (MLEST) Algorithm

The original concept of the Large Area Crop Inventory Experiment (LACIE) called for the extensive use of signature extension (i.e., the ability to use statistics learned from a given LACIE training segment to classify data from one or more LACIE recognition segments located in the same general crop growing region). The signature extension effort was generally unsuccessful because of the existence of significant differences between the training and recognition segment wheat/nonwheat signatures. These differences are caused primarily by atmospheric factors such as differences in Sun elevation and haze levels over the training and recognition segments and by target-related factors such as differences in soil moisture levels and soil colors between the training and recognition segments. It is well known that the atmospheric effects mentioned above can be modeled by a positive definite diagonal affine transformation operating on the training segment signatures. However, no suitable model exists for the target-related factors. This has led to the partitioning-signature-correction approach to signature extension (i.e., the grouping of training and recognition segment pairs in order to minimize the effect of target related factors, followed by the estimation of affine transformations for the partitioned pairs). Various techniques haw been proposed recently to estimate the optimal affine transformation with which to transform the training segment statistics before classifying the recognition segment. These techniques fall into two broad categories: The first consists of techniques that use physical models for haze level and Sun angle effects to estimate the affine transformation; the second consists of techniques that attempt to match clusters from the training segment with corresponding recognition segment clusters. The matched pairs of clusters are then used to obtain an optimal affine transformation. The Maximum Likelihood Estimation of Signature Transformation (MLEST) algorithm is a method of obtaining maximum likelihood estimates (HLE) of the affine transformation. The technique allows the computation of HLE estimates for the recognition segment wheat/nonwheat a priori probabilities; further, the technique can easily be extended to allow the estimation of completely general nondiagonal affine transformations which possibly could model both atmospheric and target-related effects