A Linear Programming Approach to Surface Fitting

In this paper, we propose a robust surface reconstruction algorithm from the gradient field by minimizing the absolute error between the input and estimated gradient field from the reconstructed surface. The resulting L1 norm based cost function can then be efficiently solved via linear programming. Compared to conventional L2 estimation algorithms, the proposed approach is more robust to noise corruption and the influence of outliers, while still maintaining low computational cost and global optimality. Moreover, by using the results obtained by our algorithm as initializations for robust M-estimator based cost function, we can obtain much better estimates of surface depth than those initialized by the LS method. Experimental results evidence clear improvements of our proposed approach over the alternatives for the purpose of surface reconstruction.