R. Basri et D. Weinshall, DISTANCE METRIC BETWEEN 3D MODELS AND 2D IMAGES FOR RECOGNITION AND CLASSIFICATION, IEEE transactions on pattern analysis and machine intelligence, 18(4), 1996, pp. 465-470
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.