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Comparative study of the Gaussian form of the Bhattacharyya metric for ATR performance evaluation

The Gaussian form of the Bhattacharyya distance measure is being used by some in the automatic target recognition (ATR) community to select features and to estimate an upper performance bound for ATR algorithms. One reason for the popularity of this measure is that it is readily computed. This paper shows through both empirical and analytic results the inadequacy of this metric. Empirical results are obtained by processing ADTS field data through both the Gaussian form of the Bhattacharyya distance and a nonparametric error estimation scheme. Analytic results are obtained by deriving the Gaussian form of the Bhattacharyya distance metric for distributions other than Gaussian. These results show that the Gaussian form of the Bhattacharyya distance cannot be trusted to provide a reliable upper performance bound. Additional empirical and analytic results show by using a nonparametric performance estimator that when the data is transformed to be more Gaussian the Bhattacharyya metric gives better performance estimates. The transformations discussed are the power transform and a mode seeker that decomposes the data into Gaussian modes. A conclusion is that tools can be and should be developed that improve the utility of the Bhattacharyya metric mainly since they provide useful information about the distribution of the data. The major conclusion is that even with these tools nonparametric error estimation techniques are superior. The nonparametric performance bounds are more reliable, and the proper use of the Bhattacharyya metric depends upon considerable knowledge of the data distributions.