Distance metric between 3D models and 2D images for recognition and classification

Similarity measurements between 3D objects and 2D images are useful for the tasks of object recognition and classification. Existing systems typically use image metrics; namely, metrics that measure the difference in the image between the observed image and the nearest view of the object (e.g., the Euclidean distance between corresponding points). In this paper we introduce a different 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 `affine 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 offer a sub-optimal closed-form solution and an iterative scheme to compute the exact solution.