A Novel Method for Solving the Shape from Shading (SFS) Problem

  • Yi Liao
  • Rong-chun Zhao
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4222)


We consider the generalized regularization problem of Shape-from- Shading. The traditional algorithms are to find the minimum point of the optimization problem where the regularization term is considered as the part of the objective function. However, the result of regularization may deviate from the true surface, due to the ill-posedness of the SFS problem. In this paper, we propose a novel method to solve this problem. The algorithm consists of two steps. In the first step, we recover the components of the surface in the range space of the transpose of the system matrix, from the observed image by using the Landweber iteration method, where the Pentland’s linear SFS model is adopted without any regularization. In the second step, we represent the regularization condition as an energy spline in the Fourier domain, and find the minimum value of the energy function with respect to the components of the surface in the null space of the system matrix. Quantitative and visual comparisons, using simulated data of a fractal and smooth surface, show that the proposed method significantly outperforms the Horn, Zheng-Chellappa, Tsai-Shah and Pentland linear methods for surface reconstruction.


Electrical Impedance Tomography Null Space Reconstructed Surface Regularization Term Fourier Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yi Liao
    • 1
  • Rong-chun Zhao
    • 1
  1. 1.Northwestern Polytechnical UniversityXi’anChina

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