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The iterative closest point (ICP) algorithm is widely used for the registration of geometric data. One of its main drawbacks is its quadratic time complexity O(N2) with the shape number of points N, which implies long processing time, especially when using high resolution data. This paper proposes to accelerate the process by a coarse to fine multiresolution approach in which a solution at a coarse level is successively improved at a finer level of representation. Specifically, it investigates this multiresolution ICP approach when coupled with the tree search or the neighbor search closest point algorithms. A theoretical and practical analysis and a comparison of the considered algorithms are presented. Confirming the success of the multiresolution scheme, the results also show that this combination permits us to create a very fast ICP algorithm, gaining speed up to a factor of 27 over a standard fast ICP algorithm.