We are addressing the problem of Euclidean reconstruction with an uncalibrated affine camera and the calibration of this camera. We investigate constraints under which the Euclidean shape and motion problem becomes linear. The theoretical study described in this paper leads us to impose some practical constraints that the camera is mounted onto a robot arm and that the robot is executing controlled motions whose parameters are known. The affine camera model considered here is just an approximation of the true projective mapping. Nevertheless, there is a large number of applications for which the camera is allowed to be at some distance from the scene and under these circumstances the affine model is a good approximation. The fact that we deal with an uncalibrated camera is an advantage over previous methods because we do not rely any more on the tedious task of camera calibration. The experimental results obtained show that the method described compares favourably with other similar methods.

We describe a method for solving the Euclidean reconstruction problem with a perspective camera model by incrementally performing Euclidean reconstruction with either a weak or a paraperspective camera model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated camera, this method converges in a few iterations, is computationally efficient, and solves for the sign (reversal) ambiguity. We give a detailed account of the method, analyze its convergence, and test it with both synthetic and real data.

D.F. Dementhon and L.S. Davis (1995) proposed a method for determining the pose of a 3D object with respect to a camera from 3D to 2D point correspondences. The method consists of iteratively improving the pose computed with a weak perspective camera model to converge at the limit, to a pose estimation computed with a perspective camera model. We show that the method of Dementhon and Davis can be extended to paraperspective. The iterative paraperspective pose algorithm that we describe in detail has interesting properties both in terms of speed and rate of convergence. Moreover, we introduce a simple way of taking into account the orthogonality constraint associated with the rotation matrix and we define the optimal experimental setup to be used in the presence of camera calibration errors.>

In this paper we describe a method for solving the Euclidean reconstruction problem with a perspective camera model by incrementally performing an Euclidean reconstruction with a weak perspective camera model. With respect to other methods that compute shape and motion from a sequence of images with a calibrated perspective camera, this method converges in a few iterations, is compositionally efficient, and does not suffer from the nonlinear nature of the problem. With respect to factorization and/or affine-invariant methods, this method solves for the sign (reversal) ambiguity in a very simple way and provides much more accurate reconstructions results.