Scale-Space Polygonalization of Target Silhouettes and Applications to Model-Based ATR

Economic descriptions of shapes and objects are essential for model based ATR. In addition to object silhouettes, geometric features such as corners and simplified representations such as polygonal approximations can be used to reduce shape description complexity. Here we analyze the polygonal approximation of object silhouette boundaries. Robust polygonalization for ATR requires the construction of polygonal approximations in various scales; namely polygons preserving features of the boundary with varying resolution. In this paper we introduce the notion of scalespace polygonalization. Scale-space polygonalization allows for the generation of polygonal approximations across a range of resolutions and achieve vertex localization which is uniform in scale. The notion of scale or resolution for a polygon involves the distances between its vertices and the magnitude of its vertex angles. Fine scale implies high resolution of the details of boundary contours while coarse scale implies only gross details of boundary contours with a consequent reduction of both computational and descriptive complexity. The polygonalization methods and algorithms presented here are novel in that we control the reduction of the contour complexity by adjusting resolution parameters which have a natural interpretation and achieve vertex localization which is uniform in scale and persistent in scale. These polygonalized boundaries can be used to generate a target fingerprint across a range of scales. Scale-space polygons are important for ATR because they provide a way to reduce the complexity of digitized planar curves consisting of polygons having hundreds of sides to polygons of about a dozen sides, while still capturing the essential features of the model silhouette. This is desirable because shorter polygonal descriptions yield faster correlations and matchings and reduce the overall computational complexity of the ATR problem. We show how scale-space polygonalization can be used to obtain efficient representations of targets, and fast matching algorithms. We also show how scale-space polygons can be used to obtain stable edges from noisy images. We demonstrate these results on examples involving synthetic FLIR data and CAD target models.