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Collinearity and Coplanarity Constraints for Structure from Motion

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Advances in Image and Video Technology (PSIVT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 4319))

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Abstract

Structure from motion (SfM) comprises techniques for estimating 3D structures from uncalibrated 2D image sequences. This work focuses on two contributions: Firstly, a stability analysis is performed and the error propagation of image noise is studied. Secondly, to stabilize SfM, we present two optimization schemes by using a priori knowledge about collinearity or coplanarity of feature points in the scene.

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References

  1. Fischler, M., Bolles, R.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Comm. ACM 24, 381–385 (1981)

    Article  MathSciNet  Google Scholar 

  2. Harris, C., Stephen, M.: A combined corner and edge detector. In: Proc. Alvey Vision Conf, pp. 147–151 (1988)

    Google Scholar 

  3. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, New York (2000)

    MATH  Google Scholar 

  4. Horn, B.K.P.: Recovering baseline and orientation from essential matrix (1990), http://www.ai.mit.edu/people/bkph/papers/essential.pdf

  5. Huang, T.: Motion and structure from feature correspondences: a review. Proc. IEEE 82, 252–268 (1994)

    Article  Google Scholar 

  6. Klette, R., Schlüns, K., Koschan, A.: Computer Vision – Three-dimensional Data from Images. Springer, Singapore (1998)

    MATH  Google Scholar 

  7. Lawson, C.L., Hanson, R.J.: Solving Least Squares Problems. Prentice Hall, Englewood (1974)

    MATH  Google Scholar 

  8. Longuet-Higgins, H.: A computer algorithm for reconstructing a scene from two projections. Nature 293, 133–135 (1981)

    Article  Google Scholar 

  9. Murray, R., Li, Z., Sastry, S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)

    MATH  Google Scholar 

  10. Pollefeys, M., Koch, R., van Gool, L.: A simple and efficient rectification method for general motion. In: Proc. Int. Conf. Computer Vision, pp. 496–501 (1999)

    Google Scholar 

  11. Szeliski, R., Torr, P.H.S.: Geometrically constrained structure from motion: points on planes. In: Proc. European Workshop 3D Structure Multiple Images Large-Scale Environments, pp. 171–186 (1998)

    Google Scholar 

  12. Tsai, R.: A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses. IEEE J. Robotics and Automation 3, 323–344 (1987)

    Article  Google Scholar 

  13. Zhang, Z.: Determining the epipolar geometry and its uncertainty: a review. Int. J. Computer Vision 27, 161–198 (1998)

    Article  Google Scholar 

  14. Zhang, Z., Deriche, R., Faugeras, O., Luong, Q.-T.: A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. Artificial Intelligence J 78, 87–119 (1995)

    Article  Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Liu, G., Klette, R., Rosenhahn, B. (2006). Collinearity and Coplanarity Constraints for Structure from Motion. In: Chang, LW., Lie, WN. (eds) Advances in Image and Video Technology. PSIVT 2006. Lecture Notes in Computer Science, vol 4319. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11949534_2

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  • DOI: https://doi.org/10.1007/11949534_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68297-4

  • Online ISBN: 978-3-540-68298-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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