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We propose a least-squares formulation to the noisy hand-eye calibration problem using dual-quaternions, and introduce efficient algorithms to find the exact optimal solution, based on analytic properties of the problem, avoiding non-linear optimization. We further present simple analytic approximate solutions which provide remarkably good estimations compared to the exact solution. In addition, we show how to generalize our solution to account for a given extrinsic prior in the cost function. To the best of our knowledge our algorithm is the most efficient approach to optimally solve the hand-eye calibration problem.
We derive closed formulas for the condition number of a linear function of the total least squares solution. Given an over determined linear system Ax=b, we show that this condition number can be computed using the singular values and the right singu
This work provides a theoretical framework for the pose estimation problem using total least squares for vector observations from landmark features. First, the optimization framework is formulated for the pose estimation problem with observation vect
Penalization procedures often suffer from their dependence on multiplying factors, whose optimal values are either unknown or hard to estimate from the data. We propose a completely data-driven calibration algorithm for this parameter in the least-sq
Ophthalmic microsurgery is known to be a challenging operation, which requires very precise and dexterous manipulation. Image guided robot-assisted surgery (RAS) is a promising solution that brings significant improvements in outcomes and reduces the
We propose an efficient algorithm for solving group synchronization under high levels of corruption and noise, while we focus on rotation synchronization. We first describe our recent theoretically guaranteed message passing algorithm that estimates