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Iterative closest point (ICP) algorithm has been widely used for registering the geometry, shape and color of the 3-D meshes. However, ICP requires a long computation time to find the corresponding closest points between the model points and the data points. To overcome this problem, we propose a fast ICP algorithm that consists of two acceleration techniques: hierarchical model point selection (HMPS) and logarithmic data point search (LDPS). HMPS accelerates the search by reducing the search region of the data points corresponding to a model point effectively: it selects the model points in a coarse-to-fine manner and employs the four neighboring closest data points in the upper layer to make the search region for finding the closest data point corresponding to a model point in the lower layer. LDPS accelerates the search by visiting the data points within the search region using 2-D logarithm search. The HMPS method and the LDPS method can be operating separately or together. To evaluate the speed of the proposed ICP, we apply it to the 3-D human body motion tracking. The proposed fast ICP is about 3.17 times faster than the existing ICP such as the K-D tree.