Fast and robust 3D shape reconstruction from gradient data

The acquisition of the 3D shape of specular free-form surfaces is a challenging task. Recently developed sensors, based on deflectometry, are able to measure the local slope of the object surface with high precision. In order to reconstruct the object shape spatial integration is required. Recently, we presented a method employing radial basis functions (RBF) [1] which is able to accurately reconstruct local details as well as the global shape. However, for large data sets this method requires a domain decomposition technique which may introduce some error propagation. Further, this approach can be time consuming. Often the data is acquired on a regular grid. For this case, we developed a B-splines approximation method which overcomes the problems described above. This method yields an accuracy which is similar to the one obtained by the RBF approach: Surface details can be detected even if their order of magnitude is in the range of the noise of the measured data. The new method is faster and more robust against error propagation than the RBF method. [1] S. Lowitzsch, J. Kaminski, G. Häusler; Shape reconstruction of 3d-objects from noisy slope data, DGaO Proceedings, A22, 2005.