Abstract
An affine concept of shape is introduced, which is independent of the coordinate description. By comparing the shapes of corresponding object and image configurations, it is possible to draw information about the projective mapping that associates them. This is done by means of mutual cross-ratios, which generalize the classical cross-ratio on the line. The geometric machinery is applied to the various orientation problems (exterior, interior and relative). It makes it possible to construct computational schemes, involving only the solutions of systems of linear equations and polynomial equations in one variable.
The work has been supported by the Swedish National Board for Technical Development (STU).
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References
Horn, B.K.P., Robot Vision, MIT Press, 1986.
Nielsen, L. and Sparr, G., Projective Area-Invariants as an Extension of the Cross-Ratio, in The 6th Scandinavian Conference on Image Analysis, Oulu, 969–986, 1989.
Sparr, G. and Nielsen, L., Shape and mutual cross-ratios with applications to orientation problems, Technical report, Dept. of Mathematics, Lund, 1990.
Veblen, O. and Young, J.W., Projective Geometry, Ginn and Company, Boston, 1910.
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© 1990 Springer-Verlag Berlin Heidelberg
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Sparr, G., Nielsen, L. (1990). Shape and mutual cross-ratios with applications to exterior, interior and relative orientation. In: Faugeras, O. (eds) Computer Vision — ECCV 90. ECCV 1990. Lecture Notes in Computer Science, vol 427. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014921
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DOI: https://doi.org/10.1007/BFb0014921
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