An efficient computational methodology for shape acquisition, processing and representation is developed. It includes 3D computer vision by applying triangulation and stereo-photogrammetry for high-accuracy 3D shape acquisition. Resulting huge 3D point clouds are successively parameterized into mathematical surfaces to provide for compact data-set representation, yet capturing local details sufficiently. B-spline surfaces are employed as parametric entities in fitting to point clouds resulting from optical 3D scanning. Beyond the linear best-fitting algorithm with control points as fitting variables, an enhanced non-linear procedure is developed. The set of best fitting variables in minimizing the approximation error norm between the parametric surface and the 3D cloud includes the control points coordinates. However, they are augmented by the set of position parameter values which identify the respectively closest matching points on the surface for the points in the cloud. The developed algorithm is demonstrated to be efficient on demanding test cases which encompass sharp edges and slope discontinuities originating from physical damage of the 3D objects or shape complexity. 
3D shape acquisition and integral compact representation using optical scanning and enhanced shape parameterization