TY - CHAP A1 - Scheffler, Robert A1 - Mansouri Yarahmadi, Ashkan A1 - Breuß, Michael A1 - Köhler, Ekkehard ED - Pelillo, Marcello ED - Hancock, Edwin T1 - A Graph Theoretic Approach for Shape from Shading T2 - Energy minimization methods in computer vision and pattern recognition , 11th International Conference, EMMCVPR 2017, Venice, Italy, October 30 – November 1, 2017 N2 - 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 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. KW - Shape from shading KW - Ambiguity KW - Configuration graph KW - Cycle basis Y1 - 2018 SN - 978-3-319-78198-3 U6 - https://doi.org/10.1007/978-3-319-78199-0_22 SP - 328 EP - 341 PB - Springer CY - Cham ER -