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Single Camera Structure and Motion Estimation

  • Ashwin P. Dani
  • Warren E. Dixon
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 401)

Abstract

Two new continuous nonlinear observers are proposed for the problem of structure from motion (SfM) and structure and motion (SaM) of a stationary object observed by a moving camera. The observer for SfM, where full velocity feedback is available, yields global exponential convergence of the states for the structure. The SaM observer requires only one of the linear velocities as a feedback and identifies the states asymptotically. The linear velocity is used to derive the scene scale information. The observer gain conditions are derived to prove the stability of the proposed observers through a Lyapunov-based analysis.

Keywords

Motion Estimation Linear Velocity Camera Motion Scale Invariant Feature Transformation Structure From Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Azarbayejani, A., Pentland, A.P.: Recursive estimation of motion, structure, and focal length. IEEE Transactions on Pattern Analysis and Machine Intelligence 17(6), 562–575 (1995)CrossRefGoogle Scholar
  2. 2.
    Bartoli, A., Sturm, P.: Constrained structure and motion from multiple uncalibrated views of a piecewise planar scene. International Journal of Computer Vision 52(1), 45–64 (2003)zbMATHCrossRefGoogle Scholar
  3. 3.
    Bartoli, A., Sturm, P.: Structure-from-motion using lines: Representation, triangulation, and bundle adjustment. Computer Vision and Image Understanding 100(3), 416–441 (2005)CrossRefGoogle Scholar
  4. 4.
    Bay, H., Tuytelaars, T., Van Gool, L.: Surf: Speeded up robust features. In: Leonardis, A., Bischof, H., Pinz, A. (eds.) ECCV 2006. LNCS, vol. 3951, pp. 404–417. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. 5.
    Chen, X., Kano, H.: A new state observer for perspective systems. IEEE Trans. Automat. Contr. 47(4), 658–663 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen, X., Kano, H.: State observer for a class of nonlinear systems and its application to machine vision. IEEE Trans. Automat. Contr. 49(11), 2085–2091 (2004)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Chicone, C.: Ordinary Differential Equations with Applications, 2nd edn. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  8. 8.
    Chitrakaran, V., Dawson, D.M., Dixon, W.E., Chen, J.: Identification a moving object´s velocity with a fixed camera. Automatica 41(3), 553–562 (2005)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Chiuso, A., Favaro, P., Jin, H., Soatto, S.: Structure from motion causally integrated over time. IEEE Trans. Pattern Anal. Machine Intell. 24(4), 523–535 (2002)CrossRefGoogle Scholar
  10. 10.
    Dahl, O., Nyberg, F., Heyden, A.: Nonlinear and adaptive observers for perspective dynamic systems. In: American Controls Conference, New York City, USA, pp. 966–971 (2007)Google Scholar
  11. 11.
    De Luca, A., Oriolo, G., Giordano, P.: On-line estimation of feature depth for image-based visual servoing schemes. In: Proc. IEEE Int. Conf. Robotics and Automation, pp. 2823–2828 (2007)Google Scholar
  12. 12.
    Dixon, W.E., Fang, Y., Dawson, D.M., Flynn, T.J.: Range identification for perspective vision systems. IEEE Trans. Automat. Contr. 48(12), 2232–2238 (2003)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Faugeras, O.D., Lustman, F.: Motion and structure from motion in a piecewise planar environment. Int. J. Pattern Recog. and Artificial Intell. 2(3), 485–508 (1988)CrossRefGoogle Scholar
  14. 14.
    Ghosh, B., Loucks, E.: A perspective theory for motion and shape estimation in machine vision. SIAM J. on Control and Optimization 33(5), 1530–1559 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Ghosh, B.K., Inaba, H., Takahashi, S.: Identification of riccati dynamics under perspective and orthographic observations. IEEE Transactions on Automatic Control 45(7), 1267–1278 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Hartley, R., Zisserman, A.: Multiple View Geometry. Cambridge University Press, Cambridge (2003)Google Scholar
  17. 17.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge (2003)Google Scholar
  18. 18.
    Hu, G., Aiken, D., Gupta, S., Dixon, W.: Lyapunov-Based Range Identification For Paracatadioptric Systems. IEEE Transactions on Automatic Control 53(7), 1775–1781 (2008)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Hutchinson, S., Hager, G., Corke, P.: A tutorial on visual servo control. IEEE Trans. Robot. Automat. 12(5), 651–670 (1996)CrossRefGoogle Scholar
  20. 20.
    Jankovic, M., Ghosh, B.: Visually guided ranging from observations points, lines and curves via an identifier based nonlinear observer. Systems and Control Letters 25(1), 63–73 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Kahl, F.: Multiple view geometry and the l  ∞ -norm. In: International Conference on Computer Vision, pp. 1002–1009 (2005)Google Scholar
  22. 22.
    Kahl, F., Hartley, R.: Multiple-view geometry under the l  ∞ -norm. IEEE Transactions on Patterm Analysis and Machine Intelligence 30(9), 1603–1617 (2008)CrossRefGoogle Scholar
  23. 23.
    Kano, H., Ghosh, B.K., Kanai, H.: Single camera based motion and shape estimation using extended kalman filtering. Mathematical and Computer Modelling 34, 511–525 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Karagiannis, D., Astolfi, A.: A new solution to the problem range identification in perspective vision systems. IEEE Trans. Automat. Contr. 50, 2074–2077 (2005)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Khalil, H.: Adaptive Output Feedback Control of Nonlinear Systems Represented by Input-Output Models. IEEE Transactions on Automatic Control 41(2), 177 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Khalil, H.K.: Nonlinear Systems, 3 edn. Prentice Hall, New Jersey (2002)Google Scholar
  27. 27.
    Lowe, D.G.: Distinctive image feature from scale-invariant keypoints. Int. J. Computer Vision 60, 91–110 (2004)CrossRefGoogle Scholar
  28. 28.
    Ma, L., Cao, C., Hovakimayan, N., Dixon, W.E., Woolsey, C.: Range identification in the presence of unknown motion parameters for perspective vision systems. In: American Controls Conference, New York City, USA, pp. 972–977 (2007)Google Scholar
  29. 29.
    Ma, Y., Soatto, S., Kosecká, J., Sastry, S.: An Invitation to 3-D Vision. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  30. 30.
    Matthies, L., Kanade, T., Szeliski, R.: Kalman filter-based algorithms for estimating depth from image sequences. Int. J. Computer Vision 3, 209–236 (1989)CrossRefGoogle Scholar
  31. 31.
    Oliensis, J.: A critique of structure-from-motion algorithms. Computer Vision and Image Understanding 80, 172–214 (2000)zbMATHCrossRefGoogle Scholar
  32. 32.
    Oliensis, J.: Exact two-image structure from motion. IEEE Transactions on Patterm Analysis and Machine Intelligence 24(12), 1618–(2002)CrossRefGoogle Scholar
  33. 33.
    Oliensis, J., Hartley, R.: Iterative extensions of the strum/triggs algorithm: convergence and nonconvergence. IEEE Transactions on Patterm Analysis and Machine Intelligence 29(12), 2217–2233 (2007)CrossRefGoogle Scholar
  34. 34.
    Quian, G., Chellappa, R.: Structure from motion using sequential monte carlo methods. International Journal of Computer Vision 59, 5–31 (2004)CrossRefGoogle Scholar
  35. 35.
    Ramalingam, S., Lodha, S., Sturm, P.: A generic structure-from-motion framework. Computer Vision and Image Understanding 103(3), 218–228 (2006)CrossRefGoogle Scholar
  36. 36.
    Ribnick, E., Atev, S., Papanikolopoulos, N.: Estimating 3D Positions and Velocities of Projectiles from Monocular Views. IEEE transactions on pattern analysis and machine intelligence 31(5), 938 (2009)CrossRefGoogle Scholar
  37. 37.
    Sim, K., Hartley, R.: Recovering camera motion using l  ∞  minimization. In: Computer Vision and Pattern Recognition, vol. 1, pp. 1230–1237 (2006)Google Scholar
  38. 38.
    Soatto, S.: 3d structure from visual motion: Modeling, representation and observability. Automatica 33(7), 1287–1312 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  39. 39.
    Soatto, S., Frezza, R., Perona, P.: Motion estimation via dynamic vision. IEEE Trans. Automat. Contr. 41(3), 393–413 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Soatto, S., Perona, P.: Reducing structure from motion: A general framework for dynamic vision, part 1: Modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence 20(9) (1998)Google Scholar
  41. 41.
    Spong, M.W., Vidyasagar, M.: Robot Dynamics and Control. Wiley, New York (1989)Google Scholar
  42. 42.
    Sturm, P., Triggs, B.: A factorization based algorithm for multi-image projective structure and motion. In: Buxton, B.F., Cipolla, R. (eds.) ECCV 1996. LNCS, vol. 1065, pp. 709–720. Springer, Heidelberg (1996)Google Scholar
  43. 43.
    Tomasi, C., Kanade, T.: Detection and tracking of point features. Tech. rep., Carnegie Mellon University (1991)Google Scholar
  44. 44.
    Zhang, Z., Hanson, A.: 3D reconstruction based on homography mapping. In: Proc. ARPA Image Understanding Workshop Palm Springs, CA (1996)Google Scholar

Copyright information

© Springer London 2010

Authors and Affiliations

  • Ashwin P. Dani
    • 1
  • Warren E. Dixon
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of FloridaGainesvilleUSA

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