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European Conference on Computer Vision

ECCV 1998: Computer Vision — ECCV'98 pp 141–157Cite as

Use your hand as a 3-D mouse, or, relative orientation from extended sequences of sparse point and line correspondences using the affine trifocal tensor

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1406)

Abstract

This paper addresses the problem of computing three-dimensional structure and motion from an unknown rigid configuration of point and lines viewed by an affine projection model. An algebraic structure, analogous to the trilinear tensor for three perspective cameras, is defined for configurations of three centered affine cameras. This centered affine trifocal tensor contains 12 non-zero coefficients and involves linear relations between point correspondences and trilinear relations between line correspondences. It is shown how the affine trifocal tensor relates to the perspective trilinear tensor, and how three-dimensional motion can be computed from this tensor in a straightforward manner. A factorization approach is also developed to handle point features and line features simultaneously in image sequences. This theory is applied to a specific problem in human-computer interaction of capturing three-dimensional rotations from gestures of a human hand. Besides the obvious application, this test problem illustrates the usefulness of the affine trifocal tensor in a situation where sufficient information is not available to compute the perspective trilinear tensor, while the geometry requires point correspondences as well as line correspondences over at least three views.

Keywords

  • Point Feature
  • User Equipment
  • Line Feature
  • Point Correspondence
  • Centered Affine

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.

The support from the Swedish Research Council for Engineering Sciences, TFR, is gratefully acknowledged

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Authors and Affiliations

  1. Dept. of Numerical Analysis and Computing Science, Computational Vision and Active Perception Laboratory (CVAP), KTH, S-100 44, Stockholm, Sweden

    Lars Bretzner & Tony Lindeberg

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  1. Lars Bretzner
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  2. Tony Lindeberg
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    © 1998 Springer-Verlag Berlin Heidelberg

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    Bretzner, L., Lindeberg, T. (1998). Use your hand as a 3-D mouse, or, relative orientation from extended sequences of sparse point and line correspondences using the affine trifocal tensor. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055664

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    • DOI: https://doi.org/10.1007/BFb0055664

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