The Para-Perspective Projection as an Approximation of the Perspective Projection for Recovering 3D Motion in Real Time

  • Tserennadmid TumurbaatarEmail author
  • Nyamlkhagva Sengee
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 157)


We present a new algorithm for determining 3D motion of a moving rigid object in real-time image sequences relative to a single camera. In the case where features are two-dimensional (2D), they are obtained by projective transformations of the 3D features on the object surface under perspective model. The perspective model has formulated in nonlinear least square problem to determine 3D motions as characterized by rotation and translation iteratively. In practice, it is numerically ill-conditioned and may converge slowly or even fail to converge, if it starts with not good enough initial guess. However, since para-perspective projection model closely approximates perspective projection for recovering the 3D motion and shape of the object in Euclidean space, we used the results provided from para-perspective projection model as an initial value of nonlinear optimization refinement under perspective model equations.


Para-perspective model Perspective model 3D motion 



The work in this paper was supported by the grant of National University of Mongolia (No. P2017-2469) and MJEED, JICA (JR14B16).


  1. 1.
    Poelman, C.J., Kanade, T.: A paraperspective factorization method for shape and motion recovery. IEEE Trans. Pattern Anal. Mach. Intell. 19(3), (1997)CrossRefGoogle Scholar
  2. 2.
    Aloimonos, J.Y.: Perspective approximations. Image Vis. Comput. 8(3) (1990)CrossRefGoogle Scholar
  3. 3.
    Huang, T.S., Netravali, A.N.: Motion and structure from feature correspondences: a review. Proc. IEEE 82(2) (1994)CrossRefGoogle Scholar
  4. 4.
    Huang, T.S., Tsai, R.Y.: Image sequence analysis: motion estimation. In: Image Sequence Analysis. Springer Verlag, New York (1981)CrossRefGoogle Scholar
  5. 5.
    Huang, T.S.: Determining three dimensional motion and structure from two perspective views. In: Young, T.Y., Fu, K.S. (eds.) Handbook of Pattern Recognition and Image Processing. Academic Press, New York (1986)Google Scholar
  6. 6.
    Zhuang, X., Huang, T.S., Ahuja, N., Haralick, R.M.: A simplified linear optic flow motion algorithm. Comput. Vis. Graph. Image Process. 42, 334–344 (1988)CrossRefGoogle Scholar
  7. 7.
    Longuet-Higgins, H.C.: A computer program for reconstructing a scene from two projections. Nature 293, 133–135 (1981)CrossRefGoogle Scholar
  8. 8.
    Faugeras, O.: Three-Dimensional Computer Vision: A Geometric View-point, Cambridge. MIT Press, MA (1993)Google Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Information and Computer SciencesNational University of MongoliaUlaanbaatarMongolia

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