Smooth Surface Reconstruction from Sparse Data: Comparison of Svsf and 3dhm Algorithms

We present in this paper an algorithm for surface reconstruction using thin plate splines on scattered patches or points on smooth surfaces. The algorithm is an improved version of Szeliski’s Variational Spline Fitting algorithm (SVSF). In particular, we introduce a different derivation of the discrete equations for the energy corresponding to the thin plat model. The results obtained on simulated data show that our proposed algorithm converges faster than the original algorithm. To complete this study, we also discuss the choice of the algorithm’s parameters in details using a cross validation technique. Finally, we compare our results to those obtained using a 3D Harmonic modelling (3DHM) Fourier-based algorithm (previously developed by the authors). We show that the proposed algorithm gives the best performance under a small sample size condition. However, when considering surfaces with a small percentage of the missing points, the 3DHM algorithm outperforms the other two spline-based algorithms.