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Continuous Time Matching Constraints for Image Streams

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Abstract

Corresponding image points of a rigid object in a discrete sequence of images fulfil the so-called multilinear constraint. In this paper the continuous time analogue of this constraint, for a continuous stream of images, is introduced and studied. The constraint links the Taylor series expansion of the motion of the image points with the Taylor series expansion of the relative motion and orientation between the object and the camera. The analysis is done both for calibrated and uncalibrated cameras. Two simplifications are also presented for the uncalibrated camera case. One simplification is made using an affine reduction and the so-called kinetic depths. The second simplification is based upon a projective reduction with respect to the image of a planar configuration. The analysis shows that the constraint involving second-order derivatives are needed to determine camera motion. Experiments with real and simulated data are also presented.

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Authors and Affiliations

  1. Department of Mathematics, Lund University, Lund, Sweden. E-mail

    Kalle Åström & Anders Heyden

Authors
  1. Kalle Åström
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  2. Anders Heyden
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Åström, K., Heyden, A. Continuous Time Matching Constraints for Image Streams. International Journal of Computer Vision 28, 85–96 (1998). https://doi.org/10.1023/A:1008006815607

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