Probabilistic Approach to Model Extraction from Training Data Michael D. DeVore a , Joseph A. O’Sullivan b , Sushil Anand c , Natalia A. Schmid d Electronic Systems and Signals Research Laboratory Department of Electrical Engineering, Washington University, St. Louis, MO 63130 ABSTRACT Many of the approaches to automatic target recognition (ATR) for synthetic aperture radar (SAR) images that have been proposed in the literature fall into one of two broad classes, those based on prediction of images from models (CAD or otherwise) of the targets and those based on templates describing typical received images which are often estimated from sample data. Systems utilizing model-based prediction typically synthesize an expected SAR image given some target class and pose and then search for the combination of class and pose which maximizes some match metric between the synthesized and observed images. This approach has the advantage of being robust with respect to target pose and articulation not previously encountered but does require detailed models of the targets of interest. On the other hand, template-based systems typically do not require detailed target models but instead store expected images for a range of targets and poses based on previous observations (training data) and then search for the template which most closely represents the observed image. We consider the design and use of probabilistic models for targets developed from training data which do not require CAD models of the targets but which can be used in a hypothesize-and-predict manner similar to other model-based approaches. The construction of such models requires the extraction from training data of functions which characterize the target radar cross section in terms of target class, pose, articulation, and other sources of variability. We demonstrate this approach using a conditionally Gaussian model for SAR image data and under that model develop the tools required to determine target models and to use those models to solve inference problems from an image of an unknown target. The conditionally Gaussian model is applied in a target-centered reference frame resulting in a probabilistic model on the surface of the target. The model is segmented based on the information content in regions of the target space. Modeling radar power variability and target positional uncertainty results in improved accuracy. Performance results are presented for both target classification and orientation estimation using the publicly available MSTAR dataset. Keywords: model-based recognition, conditionally Gaussian model, model extraction 1. INTRODUCTION A large number of approaches to automatic target recognition (ATR) from synthetic aperture radar (SAR) imagery have been reported in the literature and many of these can be divided into one of two broad classes. Approaches generally referred to as model-based often rely on physical models of the shape and composition of targets. These models are used to predict observable features in images of the target for arbitrary viewing conditions such as target pose relative to the radar platform. Recognition of an unknown target in an image consists of searching over the set of plausible poses and reporting the combination of target class and pose that most closely match the feature set actually observable in the image. The predict-extract-match-search methodology 10 of the Moving and Stationary Target Acquisition and Recognition (MSTAR) program is an example of this kind of approach. Such methods require detailed models of targets and a highly accurate characterization of electromagnetic phenomenology to support feature prediction. They have the advantage of being relatively robust with respect to viewing conditions, such as target pose or partial obscuration, not originally envisioned. Approaches generally referred to as template-based depend on the collection of statistics characterizing targets from sample images. The statistics are collected from sample observations (training data) for a wide variety of viewing conditions and are stored as part of the ATR implementation. An image of an unknown target is classified by finding the set of statistics that most accurately characterize the image and the corresponding target class and pose are reported. Examples of this kind of approach are found in Ross, et al. 7 and Owirka, et al. 6 Such methods do not require detailed models of targets, relying instead on training observations of actual data which is seen as an E-mail: a mdd2@cis.wustl.edu, b jao@ee.wustl.edu, c sushil@essrl.wustl.edu, d nar@essrl.wustl.edu Algorithms for Synthetic Aperture Radar Imagery VIII, Edmund G. Zelnio, Editor, Proceedings of SPIE Vol. 4382 (2001) © 2001 SPIE · 0277-786X/01/$15.00 358