Recovering Three-Dimensional Surfaces with Multi-images Shape-From-Shading Method

  • Lei Yang
  • Ning Zhang
Part of the Communications in Computer and Information Science book series (CCIS, volume 323)


Three-dimensional (3-D) shape reconstruction is one of the fundamental problems in the field of computer version. Most existing shape-from-shading (SFS) methods are based on signal image and orthogonal projection. But the reflectance map equation is a nonlinear partial differential equation about two random variables. So the SFS is an ill-posed problem. Further more, orthogonal projection used to simulate the imaging processes of camera is not very accurate. This paper proposes a new SFS method under perspective projection with multi-images. Three images with different lighting source directions are captured by camera firstly. Following three reflectance map equations which are described by Lambertain model are established. Then the gradient vectors of the 3-D surface are calculated by solving the reflectance map equations. The gray constraint and gradient component constraint conditions are used to construct target function, and the corresponding Eulor-Poision equations are derived. Simultaneously, discrete difference is used to approximate differential operation. New iterative 3-D shape reconstruction algorithm is proposed by the discrete difference equation. Three pixel values are used to solve certain gradient value in our method. So the ill-posed problem in traditional SFS which solves a single reflectance map equation can be avoided. At last, experimental results of 3-D reconstruction show that the proposed method is effective.


SFS method perspective projection multi-images point lighting source reflectance map equation 


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  1. 1.
    Horn, B.K.P.: Height and gradient from shading. Int. J. Computer Vision 5(1), 37–75 (1990)CrossRefGoogle Scholar
  2. 2.
    Woodham, R.J.: Photometric Method for Determining Surface Orientation from Multiple Images. Optical Engineering 19(1), 139–144 (1980)CrossRefGoogle Scholar
  3. 3.
    Horn, B.K.P., Brooks, M.J.: The variational approach to shape from shading. Computer Vision Graphics Image Process. 33(2), 174–208 (1986)zbMATHCrossRefGoogle Scholar
  4. 4.
    Lee, K.M., Kuocc, J.: Shape from shading with a linear triangular element surface model. IEEE Trans. Pattern Analysis and Machine Intelligence 15(8), 815–822 (1993)CrossRefGoogle Scholar
  5. 5.
    Cho, S.Y., Chow, T.W.S.: A new color 3D SFS methodology using neural-based color reflectance models and iterative recursive method. Neural Computation 14(11), 2751–2789 (2002)zbMATHCrossRefGoogle Scholar
  6. 6.
    Ron, K., James, A.S.: Optical Algorithm for shape from shading and path planning. Journal of Mathematical Imaging and Vision 14(3), 237–244 (2001)zbMATHMathSciNetCrossRefGoogle Scholar
  7. 7.
    Prados, E., Camilli, F., Faugeras, O.: A unifying and rigorous shape from shading method adapted to realistic data and applications. J. Math. Imaging 25(3), 307–328 (2006)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Woodham, R.J.: Gradient and Curvature from the Photometric Stereo Method, Including Local Confidence Estimation. J. Optical Soc. Am. 11(11), 3050–3068 (1994)CrossRefGoogle Scholar
  9. 9.
    Su, Q., Si, C.: Study on New Algorithm of Shape Reconstruction Based on Multi-images. Aeronautical Computing Technique 4(37), 17–19 (2007)Google Scholar
  10. 10.
    Yang, L., Han, J.Q.: 3-D shape reconstruction of medical images using perspective projection. International Journal of Computer Vision 63(1), 21–43 (2005)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Prados, E., Faugeras, O.: A generic and provably convergent shape-from-shading method for orthographic and pinhole cameras. Int. J. Comput. Vis. 65(1), 97–125 (2005)CrossRefGoogle Scholar
  12. 12.
    Breuss, M., Cristiani, E., Durou, J.D., Falcone, M., Oliver, V.: Numerical algorithms for perspective shape from shading. Kybernetika 46(2), 207–225 (2010)zbMATHMathSciNetGoogle Scholar
  13. 13.
    Zhang, R., Tsai, P.S., Cryer, J.E., Shah, M.: Shape from shading: a survey. IEEE Trans. PAMI 21(8), 690–706 (1999)CrossRefGoogle Scholar
  14. 14.
    Yang, L., Ma, S., Tian, B.: New Shape-from-Shading Method with Near-Scene Point Lighting Source Condition. In: Wang, Y., Li, T. (eds.) Foundations of Intelligent Systems. AISC, vol. 122, pp. 653–664. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lei Yang
    • 1
  • Ning Zhang
    • 1
  1. 1.School of Mechatronic Engineering & Automation, Shanghai Key Laboratory of Power Station Automation TechnologyShanghai UniversityShanghaiChina

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