The relationship between shape under similarity transformations and shape under affine transformations

Recent progress in shape theory, including the development of object/image equations for shape matching and shape space metrics (especially object/image metrics), is now being exploited to develop new algorithms for target recognition. This theory makes use of advanced mathematical techniques from algebraic and differential geometry to construct generalized shape spaces for various projection and sensor models, and then uses that construction to find natural metrics that express the distance (difference) between two configurations of object features, two configurations of image features, or an object and an image pair. Such metrics produce the most robust tests for target identification; at least as far as target geometry is concerned. Moreover, they also provide the basis for efficient hashing schemes to do target identification quickly and provide a rigorous foundation for error analysis in ATR.