Distance Metric between 3d Models and 2d Images for Recognition and Classiication

Similarity measurements between 3D objects and 2D images are useful for the tasks of object recognition and classi cation. We distinguish between two types of similarity metrics: metrics computed in image-space (image metrics) and metrics computed in transformationspace (transformation metrics). Existing methods typically use image metrics; namely, metrics that measure the di erence in the image between the observed image and the nearest view of the object. Example for such a measure is the Euclidean distance between feature points in the image and their corresponding points in the nearest view. (Computing this measure is equivalent to solving the exterior orientation calibration problem.) In this paper we introduce a di erent type of metrics: transformation metrics. These metrics penalize for the deformations applied to the object to produce the observed image. We present a transformation metric that optimally penalizes for \a ne deformations" under weak-perspective. A closed-form solution, together with the nearest view according to this metric, are derived. The metric is shown to be equivalent to the Euclidean image metric, in the sense that they bound each other from both above and below. For the Euclidean image metric we o er a sub-optimal closed-form solution and an iterative scheme to compute the exact solution. c Massachusetts Institute of Technology (1992) This report describes research done at the Massachusetts Institute of Technology within the Arti cial Intelligence Laboratory and the McDonnell-Pew Center for Cognitive Neuroscience. Support for the laboratory's arti cial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under O ce of Naval Research contract N00014-91-J-4038. Ronen Basri is supported by the McDonnell-Pew and the Rothchild postdoctoral fellowships. Daphna Weinshall is at IBM T.J. Watson Research Center, Hawthorne, NY.