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International Conference on Natural Computation

ICNC 2006: Advances in Natural Computation pp 714–723Cite as

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

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4222))

Abstract

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.

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Author information

Authors and Affiliations

  1. Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Yi Liao & Rong-chun Zhao

Authors
  1. Yi Liao
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  2. Rong-chun Zhao
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Editor information

Editors and Affiliations

  1. Life Science Research Center, School of Electronic Engineering, Xidian University, 710071, Xi’an, Shaanxi, China

    Licheng Jiao

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, Block S1, Nanyang Avenue, 639798, Singapore

    Lipo Wang

  3. School of Electronic Engineering, Xidian Univ., P.O. Box, 710071, Xi’an, P.R. China

    Xinbo Gao

  4. College of Mathematics and Information Science, Hebei Normal University, 050016, Shijiazhuang, Hebei, P.R. China

    Jing Liu

  5. Multi-Agent Systems Lab,Department of Computer Science, University of Science and Technology of China, 230026, Hefei, China

    Feng Wu

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© 2006 Springer-Verlag Berlin Heidelberg

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Liao, Y., Zhao, Rc. (2006). A Novel Method for Solving the Shape from Shading (SFS) Problem. In: Jiao, L., Wang, L., Gao, X., Liu, J., Wu, F. (eds) Advances in Natural Computation. ICNC 2006. Lecture Notes in Computer Science, vol 4222. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11881223_90

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  • DOI: https://doi.org/10.1007/11881223_90

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-45907-1

  • Online ISBN: 978-3-540-45909-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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