Surface Reconstruction in Gradient-Field Domain 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 dense 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 CS, which is particularly suited for reconstructions involving image/surface gradients. In DCS, a standard CS setting is augmented through incorporation of additional constraints arising from some intrinsic properties of potential vector fields. We demonstrate that using DCS results in reduction in the number of measurements as compared with the standard (dense) sampling, while producing estimates of higher accuracy and smaller variability as compared with CS-based estimates. The results of this study are further supported by a series of numerical experiments.