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Characterizing the stability of 3D invariants derived from 3D translational symmetry

  • Geometric Invariance
  • Conference paper
  • First Online:
Recent Developments in Computer Vision (ACCV 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1035))

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Abstract

Translational symmetry provides a powerful constraint that enables recognition of three-dimensional (3D) objects from a single view. Under ideal conditions, affine invariants of 3D points reconstructed from corresponding points would serve as accurate indices for object recognition. In real images, however, inaccurate 2D coordinates of corresponding points can lead to erroneous invariants. In this paper, we investigate the effects of such errors on the 3D invariants, and discuss some approaches to successful indexing in the presence of these errors.

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References

  1. Faugeras, O.D., “What can be Seen in Three Dimensions with an Uncalibrated Stereo Rig?” Proc. ECCV, LNCS 588, Springer-Verlag, p.563–578, 1992.

    Google Scholar 

  2. Hartley, R.I., Gupta, R. and Chang, T. “Stereo from Uncalibrated Cameras,” Proc. CVPR92, p.761–764, 1992.

    Google Scholar 

  3. Lin J.S., Mundy J.L. and Walker E., “Recognizing Arbitrary Objects from Multiple Projections”, Proc. of Asian Conference on Computer Vision, p.422–426, 1993.

    Google Scholar 

  4. Liu J.S., Mundy J.L., Forsyth D.A., Zisserman A. and Rothwell C.A., “Efficient Recognition of Rotationally Symmetric Surfaces and Straight Homogeneous Generalized Cylinders”, CVPR, 1993

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  5. Mundy, J.L. and Zisserman A., “Repeated Structures: Image Correspondence and 3D Structure Recovery”, in Applications of Invariance in Computer Vision, Mundy, J.L., Zisserman, A. and Forsyth D.,editors, LNCS 825, Springer Verlag, 1994.

    Google Scholar 

  6. Fawcett R., Zisserman A. and Brady J.M., “Extracting Structure from an Affine View of a 3D Point Set with One or Two Bilateral Symmetries”, Image and Vision Computing, 12, 9, 615–622, 1994.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Rensselaer Polytechnic Institute Troy, 12180, New York

    J. Liu & E. Walker

  2. GE Corporate Research and Development Schenectady, 12309, NY

    J. Mundy

Authors
  1. J. Liu
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  2. E. Walker
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  3. J. Mundy
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Editor information

Stan Z. Li Dinesh P. Mital Eam Khwang Teoh Han Wang

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© 1996 Springer-Verlag Berlin Heidelberg

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Liu, J., Walker, E., Mundy, J. (1996). Characterizing the stability of 3D invariants derived from 3D translational symmetry. In: Li, S.Z., Mital, D.P., Teoh, E.K., Wang, H. (eds) Recent Developments in Computer Vision. ACCV 1995. Lecture Notes in Computer Science, vol 1035. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60793-5_95

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  • DOI: https://doi.org/10.1007/3-540-60793-5_95

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60793-9

  • Online ISBN: 978-3-540-49448-5

  • eBook Packages: Springer Book Archive

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