Integrating surface normal vectors using fast marching method

Jeffrey Ho, Jongwoo Lim, Ming Hsuan Yang, David Kriegman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

23 Citations (Scopus)


Integration of surface normal vectors is a vital component in many shape reconstruction algorithms that require integrating surface normals to produce their final outputs, the depth values. In this paper, we introduce a fast and efficient method for computing the depth values from surface normal vectors. The method is based on solving the Eikonal equation using Fast Marching Method. We introduce two ideas. First, while it is not possible to solve for the depths Z directly using Fast Marching Method, we solve the Eikonal equation for a function W of the form W = Z + λf. With appropriately chosen values for λ, we can ensure that the Eikonal equation for W can be solved using Fast Marching Method. Second, we solve for W in two stages with two different λ values, first in a small neighborhood of the given initial point with large λ, and then for the rest of the domain with a smaller λ. This step is needed because of the finite machine precision and rounding-off errors. The proposed method is very easy to implement, and we demonstrate experimentally that, with insignificant loss in precision, our method is considerably faster than the usual optimization method that uses conjugate gradient to minimize an error function.

Original languageEnglish
Title of host publicationComputer Vision - ECCV 2006, 9th European Conference on Computer Vision, Proceedings
Number of pages12
Publication statusPublished - 2006
Event9th European Conference on Computer Vision, ECCV 2006 - Graz, Austria
Duration: 2006 May 72006 May 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume3953 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference9th European Conference on Computer Vision, ECCV 2006

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science


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