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
Beyer, H., A. (1992). Accurate calibration of CCD cameras. In Proceedings of the Conference on Computer Vision and Pattern Recognition. 96–101.
Bouda, B., Masmoudi, L., H., Aboutajdine, D. (2006). A new grey level corner detection based on electrostatic model. In ICGST-GVIP, 21–26.
Brown, D. C. (1996). Decentering distortion of lenses. Photogrammetric Engineering, 32(3), 444–462.
Brown, D. C. (1971). Close-range camera calibration. Photogrammetric Engineering, 37(8), 855–866.
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.
Chambon, S., & Crouzil, A. (2011). Similarity measures for image matching despite occlusions in stereo vision. Pattern Recognition, 44(9), 2063–2075.
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.
Davis, L. (1991). Handbook of genetic algorithms. New York: Van Nostrand Reinhold.
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.
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.
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.
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.
Fusiello, A. (2000). Uncalibrated Euclidean reconstruction. A review. Image and Vision Computing, 18(200), 555–563.
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.
Goldberg, D. E. (1989). Genetic algorithms in search. Optimization and machine learning (pp. 1–432). Boston: Addison-Wesley.
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.
Gurdjos, P., Sturm, P. (2003). Methods and geometry for plane-based self-calibration. In Proceedings CVPR, 491–496.
Harris, C., Stephens, M. (1988). A combined corner and edge detector. In Proceedings of the Fourth Alvey Vision Conference, pp. s147–151.
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.
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).
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.
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.
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.
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.
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.
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.
Lhuillier, M., & Quan, L. (2002). Match propagation for image-based modeling and rendering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 24, 1140–1146.
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.
Lowe, D. G. (2004). Distinctive image features from scale-invariant key-points. International Journal of Computer Vision, 60, 91–110.
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.
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.
Michalewicz, Z. (1996). Genetic algorithms + data structures = evolution programs. Berlin: Springer-Verlag.
Mohr, R., & Triggs, B. (1996). Projective geometry for image analysis. International Symposium on Photogrammetry & Remote Sensing.
Mohr, R., Quan, L., & Veillon, F. (1995). Relative 3D reconstruction using multiple uncalibrated images. International Journal of Robotics Research, 14, 619–632.
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.
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.
Peuchot, B. (1993). Camera virtual equivalent model: 0.01 pixel detectors. Computerized Medical Imaging and Graphics, 17(415), 289–294.
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.
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.
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.
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.
Sturm, P. (2000). A case against Kruppa’s equations for camera self-calibration. IEEE Transactions on Pattern Analysis Machine Intelligence, 22, 1199–1204.
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.
Triggs, B. (1998) Autocalibration from planar scenes. In: Proceedings of the 5th European Conference on Computer Vision, pp. 89–105.
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.
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.
Wright, A. (1991). Genetic algorithms for real parameter optimization (pp. 205–218). San Mateo: Morgan Kaufmann.
Zhang, W. (2005). A simple method for 3D reconstruction from two views. In: GVIP 05 Conference.
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.
Zhao, Y., & Lv, X. D. (2012). An approach for camera self-calibration using vanishing-line. Information Technology Journal, 112, 276–282.
Civera, J., Davison, A., & Montiel, M. (2008). Inverse depth parametrization for monocular SLAM. IEEE Transactions on Robotics, 24(5), 932–945.
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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