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Novel Methods for Estimating Surface Normals from Affine Transformations

  • Daniel Barath
  • Jozsef Molnar
  • Levente HajderEmail author
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 598)

Abstract

The aim of this paper is to describe different estimation techniques in order to deal with point-wise surface normal estimation from calibrated stereo configuration. We show here that the knowledge of the affine transformation between two projections is sufficient for computing the normal vector unequivocally. The formula which describes the relationship among the cameras, normal vectors and affine transformations is general, since it works for every kind of cameras, not only for the pin-hole one. However, as it is proved in this study, the normal estimation can optimally be solved for the perspective camera. Other non-optimal solutions are also proposed for the problem. The methods are tested both on synthesized data and real-world images. The source codes of the discussed algorithms are available on the web.

Keywords

Normal Vector Affine Transformation Stereo Image Projection Matrice Point Correspondence 
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.

References

  1. 1.
    Triggs, B., McLauchlan, P.F., Hartley, R.I., Fitzgibbon, A.W.: Bundle adjustment – a modern synthesis. In: Triggs, B., Zisserman, A., Szeliski, R. (eds.) ICCV-WS 1999. LNCS, vol. 1883, pp. 298–372. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Björck, Å.: Numerical Methods for Least Squares Problems. SIAM, Philadelphia (1996)CrossRefzbMATHGoogle Scholar
  3. 3.
    Faugeras, O., Lustman, F.: Motion and structure from motion in a piecewise planar environment. Technical Report RR-0856, INRIA (1988)Google Scholar
  4. 4.
    Fischler, M., Bolles, R.: Random Sampling Consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach. 24, 358–367 (1981)MathSciNetGoogle Scholar
  5. 5.
    Fodor, B., Kazó, C., Zsolt, J., Hajder, L.: Normal map recovery using bundle adjustment. IET Comput. Vis. 8, 66–75 (2014)CrossRefGoogle Scholar
  6. 6.
    Furukawa, Y., Ponce, J.: Accurate, dense, and robust multi-view stereopsis. IEEE Trans. Pattern Anal. Mach. Intell. 32(8), 1362–1376 (2010)CrossRefGoogle Scholar
  7. 7.
    Habbecke, M., Kobbelt, L.: Iterative multi-view plane fitting. In: VMV06, pp. 73–80 (2006)Google Scholar
  8. 8.
    Habbecke, M., Kobbelt, L.: A surface-growing approach to multi-view stereo reconstruction. In: CVPR (2007)Google Scholar
  9. 9.
    Hartley, R.I., Sturm, P.: Triangulation. Comput. Vis. Image Underst. CVIU 68(2), 146–157 (1997)CrossRefGoogle Scholar
  10. 10.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)zbMATHGoogle Scholar
  11. 11.
    Kreyszig, E.: Differential Geometry. Dover Publications, New York (1991)zbMATHGoogle Scholar
  12. 12.
    Liu, H.: Deeper Understanding on Solution Ambiguity in Estimating 3D Motion Parameters by Homography Decomposition and its Improvement. Ph.D. thesis, University of Fukui (2012)Google Scholar
  13. 13.
    Malis, E., Vargas, M.: Deeper understanding of the homography decomposition for vision-based control. Technical Report RR-6303, INRIA (2007)Google Scholar
  14. 14.
    Tanacs, A., Majdik, A., Molnar, J., Rai, A., Kato, Z.: Establishing correspondences between planar image patches. In: International Conference on Digital Image Computing: Techniques and Applications (DICTA) (2014)Google Scholar
  15. 15.
    Woodham, R.J.: Photometric stereo: A reflectance map technique for determining surface orientation from image intensity. In: Image Understanding Systems and Industrial Applications, Proceedings SPIE, vol. 155, pp. 136–143 (1978)Google Scholar
  16. 16.
    Yu, G., Morel, J.-M.: ASIFT: an algorithm for fully affine invariant comparison. Image Processing On Line, 2011 (2011)Google Scholar
  17. 17.
    Megyesi, Z., K’os, G., Chetverikov, D.: Dense 3d reconstruction from images by normal aided matching. Mach. Graph. Vis. 15, 3–28 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Distributed Events Analysis Research LaboratoryMTA SZTAKIBudapestHungary
  2. 2.Synthetic and Systems Biology UnitHungarian Academy of SciencesSzegedHungary
  3. 3.Eötvös Loránd UniversityBudapestHungary

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