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A method for classifying objects in sonar imagery is proposed. Motivated by the high-resolution achievable by modern imaging sonars, a novel template matching technique is developed that compares a target signature generated from a simple acoustic model with the actual image of an object being classified. The approach uses both the correlation with target echoes as well as projected acoustic shadow, and is tested on data obtained from a synthetic aperture sonar during experiments at sea. It is compared to two commonly used methods that are based on normalized cross-correlation, and results show that the proposed method outperforms the standard methods in terms of receiver-operating characteristic (ROC) curves as well as confusion matrices.