Robust surface reconstruction from gradient fields

Surface reconstruction from gradient fields is a fundamental problem to shape from shading and photometric stereo. Proposed is a surface reconstruction method that is robust to both noise and outliers. The reconstruction problem is formulated to linear decoding in compressed sensing, by assuming the outliers are sparsely distributed. A Laplacian term is additionally employed to increase information in the construction matrix and suppress noise and/or outliers. Experimental results validate that the proposed method significantly outperforms the state of the art, and can produce satisfactory reconstruction even in the very extreme situation of 60% outliers.