We investigate the rigid registration of a set of points onto a surface for computer-guided oral implants surgery. We first formulate the Iterative Closest Point (ICP) algorithm as a Maximum Likelihood (ML) estimation of the transformation and the matches. Then, considering matches as a hidden random variable, we show that the ML estimation of the transformation alone leads to a criterion efficiently solved using an Expectation-Maximisation (EM) algorithm. The experimental section provides evidences that this new algorithm is more robust and accurate than ICP and reaches a global accuracy of 0.2 mm with computation times compatible with a peroperative system.
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