A key challenge in reconstructing high-quality 3D scans and image mosaics is registration of data from different viewpoints. Existing global alignment algorithms are restricted to rigid-body transformations, and cannot adequately handle non-rigid warps in the data. Algorithms that can compensate for such warps between pairs of scans do not easily generalize to the multiview case. We present an algorithm for obtaining a globally-optimal alignment of multiple overlapping datasets in the presence of low-frequency non-rigid deformations, such as those caused by device nonlinearities or calibration error. The process first obtains sparse correspondences between views using a locally-weighted stability-guaranteeing variant of iterative closest points (ICP). Global positions for feature points are found using a relaxation method, and the scans are warped to their final positions using thin-plate splines. The technique is efficient, with only minimal overhead beyond comparable rigid-body global alignment techniques. We demonstrate that, relative to rigid-body registration, it improves the quality of alignment and better preserves detail in large 3D-scanned meshes, range images obtained using photometric stereo, and image sequences obtained with an uncalibrated camcorder.