DISTANCE METRIC BETWEEN 3D MODELS AND 2D IMAGES FOR RECOGNITION AND CLASSIFICATION

Similarity measurements between 3D objects and 2D images are useful fo r the tasks of object recognition and classification. We distinguish b etween two types of similarity metrics: metrics computed in image-spac e (image metrics) and metrics computed in transformation-space (transf ormation metrics). Existing methods typically use image metrics; namel y, metrics that measure the difference in the image between the observ ed image and the nearest view of the object. Example for such a measur e is the Euclidean distance between feature points in the image and th eir corresponding points in the nearest view. (This measure can be com puted by solving the exterior orientation calibration problem.) In thi s paper we introduce a different type of metrics: transformation metri cs. These metrics penalize for the deformations applied to the object to produce the observed image. In particular, we define a transformati on metric that optimally penalizes for ''affine deformations'' under w eak-perspective. A closed-form solution, together with the nearest vie w according to this metric, are derived. The metric is shown to be equ ivalent to the Euclidean image metric, in the sense that they bound ea ch other from both above and below. It therefore provides an easy-to-u se closed-form approximation sor the commonly-used least-squares dista nce between models and images. We demonstrate an image understanding a pplication, where the true dimensions of a photographed battery charge r are estimated by minimizing the transformation metric.