Abstract.
We propose a generalized equation to represent a continuum of sur- face reconstruction solutions of a given non-integrable gradient field. We show that common approaches such as Poisson solver and Frankot-Chellappa algo- rithm are special cases of this generalized equation. For a N × N pixel grid, the subspace of all integrable gradient fields is of dimension Our frame- work can be applied to derive a range of meaningful surface reconstructions from this high dimensional space. The key observation is that the range of solutions is related to the degree of anisotropy in applying weights to the gradients in the inte- gration process. While common approaches use isotropic weights, we show that by using a progression of spatially varying anisotropic weights, we can achieve significant improvement in reconstructions. We propose (a) α-surfaces using bi- nary weights, where the parameter α allows trade off between smoothness and robustness, (b) M-estimators and edge preserving regularization using continu- ous weights and (c) Diffusion using affine transformation of gradients. We pro- vide results on photometric stereo, compare with previous approaches and show that anisotropic treatment discounts noise while recovering salient features in reconstructions.