Recovering Local Shape of a Mirror Surface from Reflection of a Regular Grid

  • Silvio Savarese
  • Min Chen
  • Pietro Perona
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)


We present a new technique to recover the shape of an unknown smooth specular surface from a single image. A calibrated camera faces a specular surface reflecting a calibrated scene (for instance a checkerboard or grid pattern). The mapping from the scene pattern to its reflected distorted image in the camera changes the local geometrical structure of the scene pattern. We show that if measurements of both local orientation and scale of the distorted scene in the image plane are available, this mapping can be inverted. Specifically, we prove that surface position and shape up to third order can be derived as a function of such local measurements when two orientations are available at the same point (e.g. a corner). Our results generalize previous work [1, 2] where the mirror surface geometry was recovered only up to first order from at least three intersecting lines. We validate our theoretical results with both numerical simulations and experiments with real surfaces.


Image Plane Mirror Surface Checkerboard Pattern Scene Point Specular Surface 
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.


  1. 1.
    Savarese, S., Perona, P.: Local Analysis for 3D Reconstruction of Specular Surfaces. In: IEEE Conf. on Computer Vision and Pattern Recognition, pp. II 738–745 (2001)Google Scholar
  2. 2.
    Savarese, S., Perona, P.: Local analysis for 3D reconstruction of specular surfaces - part ii. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2351, pp. 759–774. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Savarese, S., Chen, M., Perona, P.: Second Order Local Analysis for 3D Reconstruction of Specular Surfaces. 3DPVT, 356–360 (2002)Google Scholar
  4. 4.
    Binford, T.: Inferring surfaces from images. Artificial Intelligence 17, 205–244 (1981)CrossRefGoogle Scholar
  5. 5.
    Blake, A.: Specular stereo. IJCAI, 973–976 (1985)Google Scholar
  6. 6.
    Blake, A., Brelstaff, G.: Geometry from specularities. In: ICCV Proc. of Int Conf. of Computer Vision, pp. 394–403 (1988)Google Scholar
  7. 7.
    Chen, M., Arvo, J.: Theory and Application of Specular Path Perturbation. ACM Transactions on Graphics 19, 246–278 (2000)CrossRefGoogle Scholar
  8. 8.
    Cipolla, R., Giblin, P.: Visual motion of curves and surfaces. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  9. 9.
    Halsead, M., Barsky, A., Klein, S., Mandell, R.: Reconstructing curved surfaces from reflection patterns using spline surface fitting normals. SIGGRAPH (1996)Google Scholar
  10. 10.
    Healey, G., Binford, T.: Local shape from specularity. Computer Vision, Graphics, and Image Processing 42, 62–86 (1988)CrossRefGoogle Scholar
  11. 11.
    Ikeuchi, K.: Determining surface orientation of specular surfaces by using the photometric stereo method. IEEE PAMI 3, 661–669 (1981)Google Scholar
  12. 12.
    Koenderink, J., van Doorn, A.: Photometric invariants related to solid shape. Optica Apta 27, 981–996 (1980)Google Scholar
  13. 13.
    Oren, M., Nayar, S.K.: A theory of specular surface geometry. Trans. Int. Journal of Computer Vision, 105–124 (1997)Google Scholar
  14. 14.
    Zheng, J., Murata, A.: Acquiring a complete 3d model from specular motion under the illumination of circular-shaped light sources. IEEE PAMI 8 (2000)Google Scholar
  15. 15.
    Zisserman, A., Giblin, P., Blake, A.: The information available to a moving observer from specularities. Image and Video Computing 7, 38–42 (1989)CrossRefGoogle Scholar
  16. 16.
    Perard, D.: Automated visual inspection of specular surfaces with structuredlighting reflection techniques. PhD Thesis – VDI Verlag Nr. 869 (2001)Google Scholar
  17. 17.
    Tarini, M., Lensch, H., Goesele, M., Seidel, H.P.: Shape from Distortion 3D Range Scanning of Mirroring Objects. In: Proc. of SIGGRAPH, Sketches and Applications, p.248 (2002)Google Scholar
  18. 18.
    Bonfort, T., Sturm, P.: Voxel Carving for Specular Surfaces. In: Proceedings of the 9th IEEE International Conference on Computer Vision (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Silvio Savarese
    • 1
  • Min Chen
    • 2
  • Pietro Perona
    • 1
  1. 1.California Institute of TechnologyPasadenaUSA
  2. 2.Oracle ParkwayRedwood CityUSA

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