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 shapes 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 to create a very fast ICP algorithm, gaining speed up to a factor 27 over a standard fast ICP algorithm.