TV-L1 Optimization for B-Spline Surface Reconstruction with Sharp Features

The placement of knot vector and the determination of control points are two fundamental issues in B-spline surface reconstruction. This paper presents a variational approach to construct B-spline surfaces from a set of data points. The approach finds the optimal placement of knots and control points simultaneously while most previous methods determine the knots heuristically or in a separate step. Moreover, different from most previous methods using least squares metric, our approach adapts L_1-norm with total variation (TV) as regularization in the fitting procedure, which enables the approach to handle both Gaussian noise and outliers in the same manner and is able to automatically optimize the placement of knot vector to faithfully reconstruct the sharp features. A numerical solver based on the augmented Lagrangian method is also proposed in the paper to efficiently solve the TV-L_1 optimization. Experimental results demonstrate the effectiveness and efficiency of the proposed variational B-spline surface reconstruction.