Suitability of the Normal Density Assumption for Processing Multispectral Scanner Data
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Multivariate normal probability density functions are usually used in classification decision (i.e., recognition) processes on multispectral scanner data. The mean and covariance matrix of the normal density function are usually estimated from a training data set. In this study, a comparison was made to determine whether or not improved classification results could be obtained by use of a different form to represent the probability density functions, namely, an empirical multivariate probability density histogram of decorrelated variables. First, tests were made of the normality of the individual subsets of data, and all were found to be non-normal at the 1% level of significance using a standard chi-square goodness-of-fit test. Operating characteristic curves then were generated to represent decisions made with each form between each given class and a uniformly distributed alternative class; a uniform distribution was chosen because the results are then least dependent on the choice of the alternative data set. It was found that the probabilities of misclassification using the two forms were approximately identical for almost every data set even though a large number of individual data points were classified differently. It was concluded that a decision rule based on the assumption of multivariate normal distributions of scanner signals performs sufficiently well, in comparison with a more accurate but more complicated rule, to warrant its continued use in recognition processing.
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