Surface-from-Gradients with Incomplete Data for Single View Modeling

Surface gradients are useful to surface reconstruction in single view modeling, shape-from-shading, and photometric stereo. Previous algorithms minimize a complex, nonlinear energy functional, or require dense surface gradients to perform integration to generate 3D locations, or require user-input heights to constrain the solution space, or produce severe distortion and smooth out surface details. Most single-view algorithms output a Monge patch (height-field), which may introduce further surface distortion along object silhouettes and surface orientation discontinuities. Our proposed algorithm operates on a single view of complete or incomplete data. The data can be gradients without 3D locations, or 3D locations without gradients. The output surface, which is not necessarily a height-field, preserves salient depth and orientation discontinuities. Experimental comparisons on both simple and complex data show that our method produces better surfaces with significantly less distortion and more details preserved. The implementation of our closed-form solution is very straightforward.