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Reconstruction of 3D Scenes by Camera Self-Calibration and Using Genetic Algorithms

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3D Research

Abstract

In this paper, we address a problem of reconstruction of three-dimensional scenes from images taken by cameras, with varying parameters, from different views. This method is based on the projection of 3D points in the image planes. The relationships between the matches and the camera parameters are used to formulate a nonlinear equation system. This system is transformed into an objective function, which is minimized by a genetic algorithm to estimate the intrinsic and extrinsic camera parameters. Finally, the coordinates of 3D points of the scene are obtained by solving a linear equation system. The experiments on synthetic and real data show the quality of this work and the good obtained results.

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References

  1. Beyer, H., A. (1992). Accurate calibration of CCD cameras. In Proceedings of the Conference on Computer Vision and Pattern Recognition. 96–101.

  2. Bouda, B., Masmoudi, L., H., Aboutajdine, D. (2006). A new grey level corner detection based on electrostatic model. In ICGST-GVIP, 21–26.

  3. Brown, D. C. (1996). Decentering distortion of lenses. Photogrammetric Engineering, 32(3), 444–462.

    Google Scholar 

  4. Brown, D. C. (1971). Close-range camera calibration. Photogrammetric Engineering, 37(8), 855–866.

    Google Scholar 

  5. Cao, X., Xiao, J., Foroosh, H., & Shah, M. (2006). Self-calibration from turn-table sequences in presence of zoom and focus. Computer Vision Image Understanding, 103(2), 227–237.

    Article  Google Scholar 

  6. Chambon, S., & Crouzil, A. (2011). Similarity measures for image matching despite occlusions in stereo vision. Pattern Recognition, 44(9), 2063–2075.

    Article  Google Scholar 

  7. Colombo, C., Bimbo, A. D., & Pernici, F. (2005). Metric 3D reconstruction and texture Acquisition of surfaces of revolution from a single uncalibrated view. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27, 99–114.

    Article  Google Scholar 

  8. Davis, L. (1991). Handbook of genetic algorithms. New York: Van Nostrand Reinhold.

    Google Scholar 

  9. El akkad, N., Merras, M., Saaidi, A., & Satori, K. (2013). Camera self-calibration with varying parameters from two views. Wseas Transactions on Information Science and Application, 10(11), 356–367.

    Google Scholar 

  10. El akkad, N., Merras, M., Saaidi, A., & Satori, K. (2014). Camera self-calibration with varying intrinsic parameters by an unknown three-dimensional scene. The Visual Computer, 30(5), 519–530.

    Article  Google Scholar 

  11. El akkad, N., Saaidi, A., Satori, K. (2012). Self-calibration based on a circle of the cameras having the varying intrinsic parameters. In Proceedings of IEEE International Conference on Multimedia Computing and Systems, pp. 161–166.

  12. Fischler, M. A., & Bolles, R. C. (1981). Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Graphics and Image Processing, 24, 381–395.

    MathSciNet  Google Scholar 

  13. Fusiello, A. (2000). Uncalibrated Euclidean reconstruction. A review. Image and Vision Computing, 18(200), 555–563.

    Article  Google Scholar 

  14. Gao, Y., Radha, H. (2004). A multistage camera self-calibration algorithm. In Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. s537–540.

  15. Goldberg, D. E. (1989). Genetic algorithms in search. Optimization and machine learning (pp. 1–432). Boston: Addison-Wesley.

    Google Scholar 

  16. Gremban, K. D., Thorpe, C. E. and Kanad, T. (1988). Geometric camera calibration using systems of linear equations. In Image Understanding Workshop, pp. 820–825.

  17. Gurdjos, P., Sturm, P. (2003). Methods and geometry for plane-based self-calibration. In Proceedings CVPR, 491–496.

  18. Harris, C., Stephens, M. (1988). A combined corner and edge detector. In Proceedings of the Fourth Alvey Vision Conference, pp. s147–151.

  19. Hartley, R. I.: Self-calibration from multiple views with a rotating camera. (1994). In Proceedings of European Conference on Computer Vision, LNCS 800/801. Springer-Verlag, pp. 471–478.

  20. Holland, J. H. Adaptation in Natural and Artificial Systems. Cambridge, MA: MIT Press. Second edition (1992) University of Michigan Press. First edition, University of Michigan Press (1975).

  21. Huanga, C. R., Chenb, C. S., & Chunga, P. C. (2004). An improved algorithm for two-image camera self-calibration and Euclidean structure recovery using absolute quadric. Pattern Recognition, 37(8), 1713–1722.

    Article  Google Scholar 

  22. Jiang, Z., Liu, S. (2011). The self-calibration of varying internal camera parameters based on image of dual absolute quadric transformation. In Information and Automation, Communications in Computer and Information Science. Springer, Berlin, Vol. 86, 452–461.

  23. Jiang, Z., & Liu, S. (2012). Self-calibration of varying internal camera parameters algorithm based on quasi-affine reconstruction. Journal of Computers, 7(3), 774–778.

    Article  Google Scholar 

  24. Knight, J., Zisserman, A., Reid, I. (2003). Linear auto-calibration for ground plane motion. In Proceedings of IEEE Conference on Computer Vision and Pattern Recognition.

  25. Kolev, K., Brox, T., & Cremers, D. (2012). Fast joint estimation of silhouettes and dense 3D geometry from multiple images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34, 1–13.

    Article  Google Scholar 

  26. Lei, C., Wu, F., Hu, Z., Tsui, H. T. (2002). A new approach to solving kruppa equations for camera self-calibration. International conference on Pattern Recognition, Québec City.

  27. Lhuillier, M., & Quan, L. (2002). Match propagation for image-based modeling and rendering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 1140–1146.

    Article  Google Scholar 

  28. Liu, P., Shi, J., Zhou, J., Jiang, L. (2003). Camera self-calibration using the geometric structure in real scenes. In Proceedings of the Computer Graphics International, 262–265.

  29. Lowe, D. G. (2004). Distinctive image features from scale-invariant key-points. International Journal of Computer Vision, 60, 91–110.

    Article  Google Scholar 

  30. Manolis, I.,A.,L., Deriche, R. (2000). Camera self-calibration using the Kruppa equations and the SVD of the fundamental matrix: The case of varying intrinsic parameters. Technical report 3911, INRIA.

  31. Mattoccia, S., Tombari, F., & Di Stefano, L. (2008). Fast full-search equivalent template matching by enhanced bounded correlation. IEEE Transactions on Image Processing, 17(4), 528–538.

    Article  MathSciNet  Google Scholar 

  32. Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs. Berlin: Springer-Verlag.

    Book  MATH  Google Scholar 

  33. Mohr, R., & Triggs, B. (1996). Projective geometry for image analysis. International Symposium on Photogrammetry & Remote Sensing.

  34. Mohr, R., Quan, L., & Veillon, F. (1995). Relative 3D reconstruction using multiple uncalibrated images. International Journal of Robotics Research, 14, 619–632.

    Article  Google Scholar 

  35. JJ, Moré. (1977). The Levenberg–Marquardt algorithm: Implementation and theory. In G. A. Watson (Ed.), Numerical Analysis. Lecture notes in mathematics (pp. 105–116). Berlin: Springer.

    Google Scholar 

  36. Mori, M., Kashino, K. (2010). Fast template matching based on normalized cross correlation using adaptive block partitioning and initial threshold estimation. In ss, 196–203.

  37. Peuchot, B. (1993). Camera virtual equivalent model: 0.01 pixel detectors. Computerized Medical Imaging and Graphics, 17(415), 289–294.

    Article  Google Scholar 

  38. Pollefeys, M., Koch, R., & Gool, L. V. (1999). Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. International Journal of Computer Vision, 32(1), 7–25.

    Article  Google Scholar 

  39. Saaidi, A., Halli, A., Tairi, H., & Satori, K. (2008). Self-calibration using a particular motion of camera. Wseas Transactions on Computer Research, 3(5), 295–299.

    Google Scholar 

  40. Shang, Y., Yue, Z., Chen, M., & Song, Q. (2012). A new method of camera self-calibration based on relative lengths. Information Technology Journal, 11(3), 376–379.

    Article  Google Scholar 

  41. Smith, S. M., & Brady, J. M. (1997). SUSAN—a new approach to low level image processing. International Journal of Computer Vision, 22(1), 45–78.

    Article  Google Scholar 

  42. Sturm, P. (2000). A case against Kruppa’s equations for camera self-calibration. IEEE Transactions on Pattern Analysis Machine Intelligence, 22, 1199–1204.

    Article  Google Scholar 

  43. Sturm, P. (2002). Critical motion sequences for the self-calibration of cameras and stereo systems with variable focal length. Image and Vision Computing, 20, 415–426.

    Article  Google Scholar 

  44. Triggs, B. (1998) Autocalibration from planar scenes. In: Proceedings of the 5th European Conference on Computer Vision, pp. 89–105.

  45. Wang, G., & Wu, Q. M. J. (2009). Perspective 3-d Euclidean reconstruction with varying camera parameters. IEEE Transactions on Circuits and Systems for Video Technology, 19(12), 1793–1803.

    Article  Google Scholar 

  46. Wei, G., Q. and Ma, S. D. (1991). Two plane camera calibration: a unified model. In Proceedings of the conference on Computer Vision and Pattern Recognition, pp. s133–138.

  47. Wright, A. (1991). Genetic algorithms for real parameter optimization (pp. 205–218). San Mateo: Morgan Kaufmann.

    Google Scholar 

  48. Zhang, W. (2005). A simple method for 3D reconstruction from two views. In: GVIP 05 Conference.

  49. Zhang, Z., Luong, Q., & Faugeras, O. (1996). Motion of an uncalibrated stereo rig: Self-calibration and metric reconstruction. IEEE Transactions on Robotics and Automation, 12, 103–113.

    Article  Google Scholar 

  50. Zhao, Y., & Lv, X. D. (2012). An approach for camera self-calibration using vanishing-line. Information Technology Journal, 112, 276–282.

    Article  Google Scholar 

  51. Civera, J., Davison, A., & Montiel, M. (2008). Inverse depth parametrization for monocular SLAM. IEEE Transactions on Robotics, 24(5), 932–945.

    Article  Google Scholar 

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Authors and Affiliations

  1. LIIAN, Department of Mathematics and Computer Science, Faculty of Science Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, B.P 1796, Atlas, Fez, Morocco

    Nabil El Akkad, Soulaiman El Hazzat & Khalid Satori

  2. LSI, Laboratory of Engineering Sciences, Polydisciplinary Faculty of Taza, Sidi Mohamed Ben Abdellah University, B.P 1223, Taza, Morocco

    Abderrahim Saaidi

Authors
  1. Nabil El Akkad
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  2. Soulaiman El Hazzat
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  3. Abderrahim Saaidi
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  4. Khalid Satori
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Correspondence to Nabil El Akkad.

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El Akkad, N., El Hazzat, S., Saaidi, A. et al. Reconstruction of 3D Scenes by Camera Self-Calibration and Using Genetic Algorithms. 3D Res 7, 6 (2016). https://doi.org/10.1007/s13319-016-0082-y

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  • DOI: https://doi.org/10.1007/s13319-016-0082-y

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