The Hausdorff distance measures the extent to which each point of a "model" set lies near some point of an "image" set and vice versa. Thus, this distance can he used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper, we provide efkient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then, we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors such as those that occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an image.

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Applying model-based vision techniques to SAR data is particularly challenging because of the inherent difficulty in generating accurate predictions of an electromagnetic signature and the variation of observed signatures to small changes in sensing conditions, imaging geometry, and object characteristics.In order to cope with these difficulties we are developing a robust feature matching module to be part of the Moving and Stationary Target Acquisition and Recognition (MSTAR) model-based automatic target recognition (ATR) system. The goals of this matching module are: (1) generate correspondences between predicted features and features extracted from a SAR image, (2) evaluate the match based on the degree of uncertainty of the features and their degree of match, (3) refine the target position/orientation/articulation based on the feature correspondences, and (4) analyze residual mis-matches for cueing scene interpretations of un-explained image features. We are developing a probabilistic optimization matching approach based on a(l) Bayesian evaluation metric and (2) the dynamic solution ofthe best correspondences during the search of pose space. The system is designed to support a wide range of features (points, regions, and other composite features) in a wide range of situations, such as obscuration, attenuation, layover, and vanable target articulations and configurations. Initial test results in these types of situations are presented.