We present a non-rigid alignment algorithm for aligning high-resolution range data in the presence of low-frequency deformations, such as those caused by scanner calibration error. Traditional iterative closest points (ICP) algorithms, which rely on rigid-body alignment, fail in these cases because the error appears as a non-rigid warp in the data. Our algorithm combines the robustness and efficiency of ICP with the expressiveness of thin-plate splines to align high-resolution scanned data accurately, such as scans from the Digital Michelangelo Project [The Digital Michelangelo Project: 3-D scanning of large statues]. This application is distinguished from previous uses of the thin-plate spline by the fact that the resolution and size of warping are several orders of magnitude smaller than the extent of the mesh, thus requiring especially precise feature correspondence.