Imagine an object such as a paper sheet being waved in front of some sensor. Reconstructing the time-varying 3D shape of the object finds direct applications in computer animation. The goal of this paper is to provide such a deformation capture system for surfaces. It uses temporal range data obtained by sensors such as those based on structured light or stereo. So as to deal with many different kinds of material, we do not make the usual assumption that the object surface has textural information. This rules out those techniques based on detecting and matching keypoints or directly minimizing color discrepancy. The proposed method is based on a planar mesh that is deformed so as to fit each of the range images. We show how to achieve this by minimizing a compound cost function combining several data and regularization terms, needed to make the overall system robust so that it can deal with low quality datasets. Carefully examining the parameter to residual relationship shows that this cost function can be minimized very efficiently by coupling nonlinear least squares methods with sparse matrix operators. Experimental results for challenging datasets coming from different kinds of range sensors are reported. The algorithm is reasonably fast and is shown to be robust to missing and erroneous data points. Copyright © 2008