 This paper is based, in part, on a paper presented at the Tenth International Conference on Image Analysis and Process- ing, Venice, Italy, Sep. 27}29, 1999. This work was sponsored by the US Air Force Materiel Command under contract F33615- 97-1020. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the o$cial policies or endorsements, either ex- pressed or implied, of the Air Force Research Laboratory or the US Government. * Corresponding author. Tel.: #1-614-292-1325; fax: #1- 614-292-7596. E-mail address: randy@ee.eng.ohio-state.edu (R.L. Moses). Pattern Recognition 34 (2001) 1539}1553 Model-based Bayesian feature matching with application to synthetic aperture radar target recognition  Hung-Chih Chiang, Randolph L. Moses*, Lee C. Potter Department of Electrical Engineering, The Ohio State University, 2015 Neil Avenue, Columbus, OH 43210, USA Received 15 May 2000; accepted 15 May 2000 Abstract We present a Bayesian approach for model-based classi"cation from unordered, attributed feature sets. A set of features is estimated from measured data and is matched with a set predicted for each candidate hypothesis using a feature model. Both extracted and predicted feature sets have uncertainty, and some features may not be present in one set or the other. Computation of the match likelihoods requires a correspondence between estimated and predicted features, and two Bayesian correspondence methods are discussed. The proposed procedure is used to predict classi"ca- tion performance as a function of sensor parameters for a 10-vehicle target recognition problem using X-band synthetic aperture radar imagery.  2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved. Keywords: Hypothesis testing; Structural matching; Point correspondences; Performance Estimation; Synthetic aperture radar; Target recognition 1. Introduction A statistical decision approach is presented for model- based M-ary classi"cation using feature sets. The ap- proach provides a structured, implementable method for managing complexity of the hypothesis set and measure- ment uncertainty. Model-based pattern matching com- bines uncertainty in both the object class models and the sensor data to compute posterior probabilities of hypotheses. Further, the approach permits tractable performance estimation. 1.1. Managing complexity Classi"cation tasks often must confront the combined complexity of a high-dimensional observation space and a large set of multi-modal candidate hypotheses. Pattern recognition from measured imagery is charac- terized by a high-dimensional observation space. A typi- cal image may comprise a 256256 array of pixels, yielding an observation vector in R, where N"2. For both computational simplicity and performance robust- ness, feature extraction is used to reduce the data to lower dimension. Signi"cantly, physically motivated features can allow a tractable alternative to a 22 covariance matrix for description of measurement uncer- tainty. The features serve as statistics for the classi"cation problem. In addition, many pattern recognition problems are characterized by a complex hypothesis space. The hy- pothesis set consists of M classes, or objects. The com- plexity arises in that each object may be observed in a variety of poses, con"gurations and environments, thereby resulting in an intractable density function for the measurement conditioned on the object. The number of enumerated subclasses explodes exponentially; a 0031-3203/01/$20.00  2001 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved. PII: S 0 0 3 1 - 3 2 0 3 ( 0 0 ) 0 0 0 8 9 - 3