Fast L1 smoothing splines with an application to Kinect depth data

Splines are a popular and attractive way of smoothing noisy data. Computing splines involves minimizing a functional which is a linear combination of a fitting term and a regularization term. The former is classically computed using a (sometimes weighted) L2 norm while the latter ensures smoothness. In this work we propose to replace the L2 norm in the fitting term with an L1 norm, leading to automatic robustness to outliers. To solve the resulting minimization problem we propose an extremely simple and efficient numerical scheme based on split-Bregman iteration and a DCT-based filter. The algorithm is applied to the problem of smoothing and impainting range data, where high-quality results are obtained in short processing times.