An Improved Eikonal Method for Surface Normal Integration

  • Martin Bähr
  • Michael Breuß
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9358)


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.


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© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Applied Mathematics Group, BTU Cottbus-SenftenbergCottbusGermany

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