Gradient-based surface reconstruction using compressed sensing

Surface reconstruction from measurements of spatial gradient is an important computer vision problem with applications in photometric stereo and shape-from-shading. In the case of morphologically complex surfaces observed in the presence of shadowing and transparency artifacts, a relatively large number of gradient measurements may be required for accurate surface reconstruction. Consequently, due to hardware limitations of image acquisition devices, situations are possible in which the available sampling density might not be sufficiently high to allow for recovery of essential surface details. In this paper, the above problem is resolved by means of derivative compressed sensing (DCS). DCS can be viewed as a modification of the classical compressed sensing (CS), which is particularly suited for reconstructions involving image/surface gradients. We demonstrate that using DCS results in substantial data savings as compared to the standard (dense) sampling, while producing estimates of higher accuracy and smaller variability, as compared to CS-base estimates. The results of this study are further supported by a series of numerical experiments.