Robust Surface Reconstruction via Triple Sparsity

Reconstructing a surface/image from corrupted gradient fields is a crucial step in many imaging applications where a gradient field is subject to both noise and unlocalized outliers, resulting typically in a non-integrable field. We present in this paper a new optimization method for robust surface reconstruction. The proposed formulation is based on a triple sparsity prior: a sparse prior on the residual gradient field and a double sparse prior on the surface gradients. We develop an efficient alternate minimization strategy to solve the proposed optimization problem. The method is able to recover a good quality surface from severely corrupted gradients thanks to its ability to handle both noise and outliers. We demonstrate the performance of the proposed method on synthetic and real data. Experiments show that the proposed solution outperforms some existing methods in the three possible cases: noise only, outliers only and mixed noise/outliers.