In a variety of applications (including automatic target recognition) image classification algorithms operate on compressed image data. This paper explores the design of optimal transform coders and scalar quantizers using Chernoff bounds on probability of misclassification as the measure of classification accuracy. This design improves classification performance but the mean square error (as well as the visual quality) of the coded image degrades. However, by appropriately combining classification accuracy and mean square error in the cost function, one can achieve good classification with low (visual) distortion, which is desirable in classification systems requiring visual authentication.