Evaluation of corner extraction schemes using invariance methods

We describe a new method to evaluate corner extraction schemes using invariance methods. Since the locations of centers in an image depend both on the intrinsic parameters of the camera and the relative position and orientation of the object with respect to the camera, the exact positions of corners in an image are generally not known. To circumvent the need for this knowledge, we use sets of points (instead of individual points) extracted from images of polyhedral objects and projective invariants to calculate a manifold of constraints on the coordinates of the corners. We then estimate the variance of the detected corners from the distance of the coordinate vector to this manifold. This is independent of the camera parameters and the relative position and orientation between the camera and the object. Five different kinds of corner extraction schemes are investigated. The purpose of the paper is to show that invariance methods can effectively be used to make this comparison rather than to make a thorough comparison of different corner extraction schemes.