Image Invariants for Smooth Reflective Surfaces

  • swin C. Sankaranarayanan
  • Ashok Veeraraghavan
  • Oncel Tuzel
  • Amit Agrawal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6312)


Image invariants are those properties of the images of an object that remain unchanged with changes in camera parameters, illumination etc. In this paper, we derive an image invariant for smooth surfaces with mirror-like reflectance. Since, such surfaces do not have an appearance of their own but rather distort the appearance of the surrounding environment, the applicability of geometric invariants is limited. We show that for such smooth mirror-like surfaces, the image gradients exhibit degeneracy at the surface points that are parabolic. We leverage this result in order to derive a photometric invariant that is associated with parabolic curvature points. Further, we show that these invariant curves can be effectively extracted from just a few images of the object in uncontrolled, uncalibrated environments without the need for any a priori information about the surface shape. Since these parabolic curves are a geometric property of the surface, they can then be used as features for a variety of machine vision tasks. This is especially powerful, since there are very few vision algorithms that can handle such mirror-like surfaces. We show the potential of the proposed invariant using experiments on two related applications - object recognition and pose estimation for smooth mirror surfaces.


Iterative Close Point Image Gradient Parabolic Curvature Perspective Camera Parabolic Point 
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.
    Adato, Y., Vasilyev, Y., Ben-Shahar, O., Zickler, T.: Toward a Theory of Shape from Specular Flow. In: ICCV (October 2007)Google Scholar
  2. 2.
    Barrow, H.G., Tenenbaum, J.M., Bolles, R.C., Wolf, H.C.: Parametric correspondence and chamfer matching: two new techniques for image matching. In: Joint Conf. on Artificial Intelligence, pp. 659–663 (1977)Google Scholar
  3. 3.
    Besl, P., McKay, H.: A method for registration of 3-D shapes. TPAMI 14(2), 239–256 (1992)Google Scholar
  4. 4.
    Blake, A.: Specular stereo. In: Int. Joint Conf. on Artificial Intelligence, pp. 973–976 (1985)Google Scholar
  5. 5.
    Blake, A., Brelstaff, G.: Geometry from specularities. In: ICCV, pp. 394–403 (1988)Google Scholar
  6. 6.
    Bonfort, T., Sturm, P.: Voxel carving for specular surfaces. In: ICCV (October 2003)Google Scholar
  7. 7.
    Canas, G.D., Vasilyev, Y., Adato, Y., Zickler, T., Gortler, S., Ben-Shahar, O.: A Linear Formulation of Shape from Specular Flow. In: ICCV (September 2009)Google Scholar
  8. 8.
    Chang, J., Raskar, R., Agrawal, A.: 3D Pose Estimation and Segmentation using Specular Cues. In: CVPR (June 2009)Google Scholar
  9. 9.
    DelPozo, A., Savarese, S.: Detecting specular surfaces on natural images. In: CVPR (June 2007)Google Scholar
  10. 10.
    Ding, Y., Yu, J., Sturm, P.: Recovering specular surfaces using curved line images. In: CVPR (June 2009)Google Scholar
  11. 11.
    Fleming, R.W., Torralba, A., Adelson, E.H.: Specular reflections and the perception of shape. Journal of Vision 4(9), 798–820 (2004)CrossRefGoogle Scholar
  12. 12.
    Gremban, K., Ikeuchi, K.: Planning multiple observations for object recognition. IJCV 12(2), 137–172 (1994)CrossRefGoogle Scholar
  13. 13.
    Haralick, R., Joo, H., Lee, C., Zhuang, X., Vaidya, V., Kim, M.: Pose estimation from corresponding point data. IEEE Trans. on Systems, Man and Cybernetics 19(6), 1426–1446 (1989)CrossRefGoogle Scholar
  14. 14.
    Ihrke, I., Kutulakos, K.N., Lensch, H.P.A., Magnor, M., Heidrich, W., Ihrke, I., Stich, T., Gottschlich, H., Magnor, M., Seidel, H.P.: State of the Art in Transparent and Specular Object Reconstruction. In: IEEE Int. Conf. on Image Analysis and Processing, vol. 12, pp. 188–193 (2005)Google Scholar
  15. 15.
    Koenderink, J., Van Doorn, A.: Photometric invariants related to solid shape. Journal of Modern Optics 27(7), 981–996 (1980)CrossRefGoogle Scholar
  16. 16.
    Longuet-Higgins, M.S.: Reflection and refraction at a random moving surface. I. Pattern and paths of specular points. Journal of the Optical Society of America 50(9), 838 (1960)CrossRefMathSciNetGoogle Scholar
  17. 17.
    Mamassian, P., Kersten, D., Knill, D.: Categorical local-shape perception. Perception 25, 95–108 (1996)CrossRefGoogle Scholar
  18. 18.
    Miyazaki, D., Kagesawa, M., Ikeuchi, K.: Transparent surface modeling from a pair of polarization images. TPAMI 26(1), 73–82 (2004)Google Scholar
  19. 19.
    Savarese, S., Chen, M., Perona, P.: Local shape from mirror reflections. IJCV 64(1), 31–67 (2005)CrossRefGoogle Scholar
  20. 20.
    Savarese, S., Fei-Fei, L., Perona, P.: What do reflections tell us about the shape of a mirror? In: Applied Perception in Graphics and Visualization (August 2004)Google Scholar
  21. 21.
    Vasilyev, Y., Adato, Y., Zickler, T., Ben-Shahar, O.: Dense specular shape from multiple specular flows. In: CVPR (June 2008)Google Scholar
  22. 22.
    Waldon, S., Dyer, C.: Dynamic shading, motion parallax and qualitative shape. In: IEEE Workshop on Qualitative Vision. pp. 61–70 (1993)Google Scholar
  23. 23.
    Weidenbacher, U., Bayerl, P., Neumann, H., Fleming, R.: Sketching shiny surfaces: 3D shape extraction and depiction of specular surfaces. ACM Transactions on Applied Perception 3(3), 285 (2006)CrossRefGoogle Scholar
  24. 24.
    Yu, J., McMillan, L.: Modelling Reflections via Multiperspective Imaging. In: CVPR (June 2005)Google Scholar
  25. 25.
    Zisserman, A., Giblin, P., Blake, A.: The information available to a moving observer from specularities. Image and Vision Computing 7(1), 38–42 (1989)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • swin C. Sankaranarayanan
    • 1
  • Ashok Veeraraghavan
    • 2
  • Oncel Tuzel
    • 2
  • Amit Agrawal
    • 2
  1. 1.Rice UniversityHoustonUSA
  2. 2.Mitsubishi Electric Research LabsCambridgeUSA

Personalised recommendations