Abstract
The multiple view geometry of static scenes is now well understood. Recently attention was turned to dynamic scenes where scene points may move while the cameras move. The triangulation of linear trajectories is now well handled. The case of quadratic trajectories also received some attention.
We present a complete generalization and address the Problem of general trajectory triangulation of moving points from non-synchronized cameras. Our method is based on a particular representation of curves (trajectories) where a curve is represented by a family of hypersurfaces in the projective space ℙ5. This representation is linear, even for highly non-linear trajectories. We show how this representation allows the recovery of the trajectory of a moving point from non-synchronized sequences. We show how this representation can be converted into a more standard representation. We also show how one can extract directly from this representation the positions of the moving point at each time instant an image was made. Experiments on synthetic data and on real images demonstrate the feasibility of our approach.
This work is partially supported by the Emmy Noether Institute for Mathematics and the Minerva Foundation of Germany, by the Excellency Center of the Israel Science Foundation “ Group Theoretic Methods in the Study of Algebraic Varieties” and by EAGER (European network in Algebraic Geometry).
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Kaminski, J.Y., Teicher, M. (2002). General Trajectory Triangulation. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds) Computer Vision — ECCV 2002. ECCV 2002. Lecture Notes in Computer Science, vol 2351. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47967-8_55
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DOI: https://doi.org/10.1007/3-540-47967-8_55
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