Joint Reconstruction and Registration of a Deformable Planar Surface Observed by a 3D Sensor

We address the problem of reconstruction and registration of a deforming 3D surface observed by some 3D sensor giving a cloud of 3D points at each time instant. This problem is difficult since the basic data term does not provide enough constraints. We bring two main contributions. First, we examine a set of data and penalty terms that make the problem well-posed. The most important terms we introduce are the nonextensibility penalty and the attraction to boundary shape. Second, we show how the error function combining all these terms can be efficiently minimized with the Levenberg-Marquardt algorithm and sparse matrices. We report convincing results for challenging datasets coming from different kinds of 3D sensors. The algorithm is robust to missing and erroneous data points, and to spurious boundary detection.