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International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition

EMMCVPR 2017: Energy Minimization Methods in Computer Vision and Pattern Recognition pp 328–341Cite as

A Graph Theoretic Approach for Shape from Shading

Part of the Lecture Notes in Computer Science book series (LNIP,volume 10746)

Abstract

Resolving ambiguities is a fundamental problem in shape from shading (SFS). The classic SFS approach allows to reconstruct the surface locally around singular points up to an ambiguity of convex, concave or saddle point type.

In this paper we follow a recent approach that seeks to resolve the local ambiguities in a global graph-based setting so that the complete surface reconstruction is consistent. To this end, we introduce a novel graph theoretic formulation for the underlying problem that allows to prove for the first time in the literature that the underlying surface orientation problem is \(\mathcal {NP}\)-complete. Moreover, we show that our novel framework allows to define an algorithmic framework that solves the disambiguation problem. It makes use of cycle bases for dealing with the graph construction and enables an easy embedding into an optimization method that amounts here to a linear program.

Keywords

  • Shape from shading
  • Ambiguity
  • Configuration graph
  • Cycle basis

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Author information

Authors and Affiliations

  1. Brandenburgische Technische Universität Cottbus-Senftenberg, Postfach 10 13 44, 03013, Cottbus, Germany

    Robert Scheffler, Ashkan Mansouri Yarahmadi, Michael Breuß & Ekkehard Köhler

Authors
  1. Robert Scheffler
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  2. Ashkan Mansouri Yarahmadi
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  3. Michael Breuß
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  4. Ekkehard Köhler
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Corresponding author

Correspondence to Robert Scheffler .

Editor information

Editors and Affiliations

  1. Ca’ Foscari University of Venice, Venice, Italy

    Marcello Pelillo

  2. University of York, York, United Kingdom

    Edwin Hancock

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Scheffler, R., Mansouri Yarahmadi, A., Breuß, M., Köhler, E. (2018). A Graph Theoretic Approach for Shape from Shading. In: Pelillo, M., Hancock, E. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2017. Lecture Notes in Computer Science(), vol 10746. Springer, Cham. https://doi.org/10.1007/978-3-319-78199-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-78199-0_22

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