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This paper presents a novel method for so-called hand-eye calibration. Using a calibration target is not possible for many applications of hand-eye calibration. In such situations Structure-from-Motion approach of hand-eye calibration is commonly used to recover the camera poses up to scaling. The presented method takes advantage of recent results in the $L_{\infty}$-norm optimization using Second-Order Cone Programming (SOCP) to recover the correct scale. Further, the correctly scaled displacement of the hand-eye transformation is recovered solely from the image correspondences and robot measurements, and is guaranteed to be globally optimal with respect to the $L_{\infty}$-norm. The method is experimentally validated using both synthetic and real world datasets.

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