Online computation of exterior orientation with application to hand-eye calibration

Computation of the relative position and orientation between a camera and an observed object from a single image is a central problem in computer vision. Although many solution methods have been proposed, several problems remain. Analytical methods do not take into account the issue of noise. Nonlinear least-squares methods depend critically on good initialization. Linear least-squares methods tend to be very sensitive to noise and outliers. These shortcomings limit their use in modern computer vision applications. In this article, we formulate a new least squares objective function that leads to a good initialization scheme based on weak-perspective projection, as well as a robust and efficient descent algorithm using absolute orientation. The new method combines model-based parameter search and data-driven backprojection which, unlike most existing methods, minimizes 3-D object space error rather than 2-D image error. Extensive experiments on simulated data indicate that the new method outperforms commonly used least squares methods under most conditions. Its performance as a kernel in the inner loop of a robust M-estimate algorithm for outlier rejections is also studied. We demonstrate the use of this method in the context of hand-eye calibration.