Novel Ways to Estimate Homography from Local Affine Transformations

Daniel Barath, Levente Hajder

Abstract

State-of-the-art 3D reconstruction methods usually apply point correspondences in order to compute the 3D geometry of objects represented by dense point clouds. However, objects with relatively large and flat surfaces can be most accurately reconstructed if the homographies between the corresponding patches are known. Here we show how the homography between patches on a stereo image pair can be estimated. We discuss that these proposed estimators are more accurate than the widely used point correspondence-based techniques because the latter ones only consider the last column (the translation) of the affine transformations, whereas the new algorithms use all the affine parameters. Moreover, we prove that affine-invariance is equivalent to perspective-invariance in the case of known epipolar geometry. Three homography estimators are proposed. The first one calculates the homography if at least two point correspondences and the related affine transformations are known. The second one computes the homography from only one point pair, if the epipolar geometry is estimated beforehand. These methods are solved by linearization of the original equations, and the refinements can be carried out by numerical optimization. Finally, a hybrid homography estimator is proposed that uses both point correspondences and photo-consistency between the patches. The presented methods have been quantitatively validated on synthesized tests. We also show that the proposed methods are applicable to real-world images as well, and they perform better than the state-of-the-art point correspondence-based techniques.

References

  1. Agarwal, A., Jawahar, C., and Narayanan, P. (2005). A Survey of Planar Homography Estimation Techniques. Technical report, IIT-Hyderabad.
  2. Agarwal, S., Furukawa, Y., Snavely, N., Simon, I., Curless, B., Seitz, S. M., and Szeliski, R. (2011). Building rome in a day. Commun. ACM, 54(10):105-112.
  3. B., D. (1934). Sur la sphere vide. Izvestia Akademii Nauk SSSR, Otdelenie Matematicheskikh i Estestvennykh Nauk, 7:793-800.
  4. Barath, D., Molnar, J., and Hajder, L. (2015). Optimal Surface Normal from Affine Transformation. InVISAPP 2015, pages 305-316.
  5. Björck, A°. (1996). Numerical Methods for Least Squares Problems. Siam.
  6. Bódis-Szomorú, A., Riemenschneider, H., and Gool, L. V. (2014). Fast, approximate piecewise-planar modeling based on sparse structure-from-motion and superpixels. In IEEE Conference on Computer Vision and Pattern Recognition.
  7. Faugeras, O. and Lustman, F. (1988). Motion and structure from motion in a piecewise planar environment. Technical Report RR-0856, INRIA.
  8. Faugeras, O. D. and Papadopoulo, T. (1998). A Nonlinear Method for Estimating the Projective Geometry of Three Views. In ICCV, pages 477-484.
  9. 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.
  10. Furukawa, Y. and Ponce, J. (2010). Accurate, dense, and robust multi-view stereopsis. IEEE Trans. on Pattern Analysis and Machine Intelligence, 32(8):1362-1376.
  11. Habbecke, M. and Kobbelt, L. (2006). Iterative multi-view plane fitting. InProceeding of Vision, Modelling, and Visualization, pages 73-80.
  12. Hartley, R. I. and Sturm, P. (1997). Triangulation. Computer Vision and Image Understanding: CVIU, 68(2):146- 157.
  13. Hartley, R. I. and Zisserman, A. (2003). Multiple View Geometry in Computer Vision. Cambridge University Press.
  14. He, L. (2012). Deeper Understanding on Solution Ambiguity in Estimating 3D Motion Parameters by Homography Decomposition and its Improvement. PhD thesis, University of Fukui.
  15. Kanatani, K. (1998). Optimal homography computation with a reliability measure. In Proceedings of IAPR Workshop on Machine Vision Applications, MVA, pages 426-429.
  16. Kannala, J., Salo, M., and Heikkil, J. (2006). Algorithms for computing a planar homography from conics in correspondence. In Proceedings of the British Machine Vision Conference.
  17. Kruger, S. and Calway, A. (1998). Image registration using multiresolution frequency domain correlation. In Proceedings of the British Machine Vision Conference.
  18. Kumar, M. P., Goyal, S., Kuthirummal, S., Jawahar, C. V., and Narayanan, P. J. (2004). Discrete contours in multiple views: approximation and recognition. Image and Vision Computing, 22(14):1229-1239.
  19. Lee, D.-T. and Schachter, B. J. (1980). Two algorithms for constructing a delaunay triangulation. International Journal of Computer & Information Sciences, 9(3):219-242.
  20. Malis, E. and Vargas, M. (2007). Deeper understanding of the homography decomposition for vision-based control. Technical Report RR-6303, INRIA.
  21. Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM J. Appl. Math., 11:431-441.
  22. Mikolajczyk, K. and Schmid, C. (2004). Scale & affine invariant interest point detectors. International Journal of Computer Vision, 60(1):63-86.
  23. Molnár, J. and Chetverikov, D. (2014). Quadratic transformation for planar mapping of implicit surfaces. Journal of Mathematical Imaging and Vision, 48:176-184.
  24. Molnár, J., Huang, R., and Kato, Z. (2014). 3d reconstruction of planar surface patches: A direct solution. ACCV Big Data in 3D Vision Workshop.
  25. Morel, J.-M. and Yu, G. (2009). ASIFT: A new framework for fully affine invariant image comparison. SIAM Journal on Imaging Sciences, 2(2):438-469.
  26. Mudigonda, P. K., Kumar, P., Jawahar, M. C. V., and Narayanan, P. J. (2004). Geometric structure computation from conics. In In ICVGIP, pages 9-14.
  27. Murino, V., Castellani, U., Etrari, A., and Fusiello, A. (2002). Registration of very time-distant aerial images. In Proceedings of the IEEE International Conference on Image Processing (ICIP), volume III, pages 989-992. IEEE Signal Processing Society.
  28. Musialski, P., Wonka, P., Aliaga, D. G., Wimmer, M., van Gool, L., and Purgathofer, W. (2012). A survey of urban reconstruction. In EUROGRAPHICS 2012 State of the Art Reports, pages 1-28.
  29. Pollefeys, M., Nistér, D., Frahm, J. M., Akbarzadeh, A., Mordohai, P., Clipp, B., Engels, C., Gallup, D., Kim, S. J., Merrell, P., Salmi, C., Sinha, S., Talton, B., Wang, L., Yang, Q., Stewénius, H., Yang, R., Welch, G., and Towles, H. (2008). Detailed real-time urban 3d reconstruction from video. Int. Journal Comput. Vision, 78(2-3):143-167.
  30. Tanács, A., Majdik, A., Hajder, L., Molnár, J., Sánta, Z., and Kato, Z. (2014). Collaborative mobile 3d reconstruction of urban scenes. In Computer Vision - ACCV 2014 Workshops - Singapore, Singapore, November 1- 2, 2014, Revised Selected Papers, Part III, pages 486- 501.
  31. Toldo, R. and Fusiello, A. (2010). Real-time incremental j-linkage for robust multiple structures estimation. In International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), volume 1, page 6.
  32. Vu, H.-H., Labatut, P., Pons, J.-P., and Keriven, R. (2012). High accuracy and visibility-consistent dense multiview stereo. IEEE Trans. Pattern Anal. Mach. Intell., 34(5):889-901.
  33. Z. Megyesi, G. and D.Chetverikov (2006). Dense 3d reconstruction from images by normal aided matching. Machine Graphics and Vision, 15:3-28.
  34. Zhang, Z. (2000). A flexible new technique for camera calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(11):1330-1334.
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Paper Citation


in Harvard Style

Barath D. and Hajder L. (2016). Novel Ways to Estimate Homography from Local Affine Transformations . In Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, pages 432-443. DOI: 10.5220/0005674904320443


in Bibtex Style

@conference{visapp16,
author={Daniel Barath and Levente Hajder},
title={Novel Ways to Estimate Homography from Local Affine Transformations},
booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)},
year={2016},
pages={432-443},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005674904320443},
isbn={978-989-758-175-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)
TI - Novel Ways to Estimate Homography from Local Affine Transformations
SN - 978-989-758-175-5
AU - Barath D.
AU - Hajder L.
PY - 2016
SP - 432
EP - 443
DO - 10.5220/0005674904320443