Optimal Surface Normal from Affine Transformation

Barath Daniel, Jozsef Molnar, Levente Hajder

2015

Abstract

This paper deals with surface normal estimation from calibrated stereo images. We show here how the affine transformation between two projections defines the surface normal of a 3D planar patch. We give a formula that describes the relationship of surface normals, camera projections, and affine transformations. This formula is general since it works for every kind of cameras. We propose novel methods for estimating the normal of a surface patch if the affine transformation is known between two perspective images. We show here that the normal vector can be optimally estimated if the projective depth of the patch is known. Other non-optimal methods are also introduced for the problem. The proposed methods are tested both on synthesized data and images of real-world 3D objects.

References

  1. B. Triggs and P. McLauchlan and R. I. Hartley and A. Fitzgibbon (2000). Bundle Adjustment - A Modern Synthesis. In Triggs, W., Zisserman, A., and Szeliski, R., editors, Vision Algorithms: Theory and Practice, LNCS, pages 298-375. Springer Verlag.
  2. Björck, A°. (1996). Numerical Methods for Least Squares Problems. Siam.
  3. Faugeras, O. and Lustman, F. (1988). Motion and structure from motion in a piecewise planar environment. Technical Report RR-0856, INRIA.
  4. Fischler, M. and Bolles, R. (1981). RANdom SAmpling Consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach., 24:358-367.
  5. Fodor, B., Kazó, C., Zsolt, J., and Hajder, L. (2014). Normal map recovery using bundle adjustment. IET Computer Vision, 8:66 - 75.
  6. Habbecke, M. and Kobbelt, L. (2006). Iterative multi-view plane fitting. In In VMV06, pages 73-80.
  7. Habbecke, M. and Kobbelt, L. (2007). A surface-growing approach to multi-view stereo reconstruction. In CVPR.
  8. Hartley, R. I. and Sturm, P. (1997). Triangulation. Computer Vision and Image Understanding: CVIU, 68(2):146- 157.
  9. Hartley, R. I. and Zisserman, A. (2003). Multiple View Geometry in Computer Vision. Cambridge University Press.
  10. Kreyszig, E. (1991). Differential geometry. Dover Publications.
  11. Liu, H. (2012). Deeper Understanding on Solution Ambiguity in Estimating 3D Motion Parameters by Homography Decomposition and its Improvement. PhD thesis, University of Fukui.
  12. Malis, E. and Vargas, M. (2007). Deeper understanding of the homography decomposition for vision-based control. Technical Report RR-6303, INRIA.
  13. Molnár, J., Huang, R., and Kato, Z. (2014). 3d reconstruction of planar surface patches: A direct solution. ACCV Big Data in 3D Vision Workshop.
  14. Tanacs, A., Majdik, A., Molnar, J., Rai, A., and Kato, Z. (2014). Establishing correspondences between planar image patches. In International Conference on Digital Image Computing: Techniques and Applications (DICTA).
  15. Woodham, R. J. (1978). Photometric stereo: A reflectance map technique for determining surface orientation from image intensity. In Image Understanding Systems and Industrial Applications, Proc. SPIE, volume 155, pages 136-143.
  16. Yu, G. and Morel, J.-M. (2011). ASIFT: An Algorithm for Fully Affine Invariant Comparison. Image Processing On Line, 2011.
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Paper Citation


in Harvard Style

Daniel B., Molnar J. and Hajder L. (2015). Optimal Surface Normal from Affine Transformation . In Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015) ISBN 978-989-758-091-8, pages 305-316. DOI: 10.5220/0005303703050316


in Bibtex Style

@conference{visapp15,
author={Barath Daniel and Jozsef Molnar and Levente Hajder},
title={Optimal Surface Normal from Affine Transformation},
booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)},
year={2015},
pages={305-316},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005303703050316},
isbn={978-989-758-091-8},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)
TI - Optimal Surface Normal from Affine Transformation
SN - 978-989-758-091-8
AU - Daniel B.
AU - Molnar J.
AU - Hajder L.
PY - 2015
SP - 305
EP - 316
DO - 10.5220/0005303703050316