An Improved Eikonal Method for Surface Normal Integration

The integration of surface normals is a classic problem in computer vision. Recently, an approach to integration based on an equation of eikonal type has been proposed. A crucial component of this model is the data term in which the given data is complemented by a convex function describing a squared Euclidean distance. The resulting equation has been solved by a classic fast marching (FM) scheme. However, while that method is computationally efficient, the reconstruction error is considerable, especially in diagonal grid directions. In this paper, we present two improvements in order to deal with this problem. On the modeling side, we present a novel robust formulation of the data term. Moreover, we propose to use a semi-Lagrangian discretisation which improves the rotational invariance while it allows to keep the FM strategy. Our experiments confirm that our novel method gives a superior quality compared to the previous methods.