Target recognition algorithms trained using finite sets of target and confuser data result in classifiers limited by the training set. Algorithms trained under closed set assumptions do not account for the infinite universe of confusers found in practice. In contrast, classification algorithms developed under open set assumptions label inputs not present in the training data as unknown instead of assigning the most likely class. We present an approach to open set recognition that utilizes class posterior estimates to determine probability thresholds for classification. This is accomplished by first training a support vector machine (SVM) in a 1-vs-all configuration on a training dataset containing only target classes. A validation set containing only class data belonging to the training set is used to iteratively determine appropriate posterior probability thresholds for each target class. The testing dataset, which contains targets present in the training data as well as several confuser classes, is first classified by the 1-vs-all SVM. If the estimated posterior for an input falls below the threshold, the target is labeled as unknown. Otherwise, it is labeled with the class resulting from the SVM decision. We apply our method to automatic target recognition (ATR) of ladar range images and compare its performance to current open set and closed set recognition techniques.