Abstract
An algorithm is presented for computing a decomposition of planar shapes into convex subparts represented by ellipses. The method is invariant to projective transformations of the shape, and thus the conic primitives can be used for matching and definition of invariants in the same way as points and lines. The method works for arbitrary planar shapes admitting at least four distinct tangents and it is based on finding ellipses with four points of contact to the given shape. The cross-ratio computed from the four points on the ellipse can then be used as a projectively invariant index. It is shown that a given shape has a unique parameter-free decomposition into ellipses with unit cross-ratio.
Acknowledgements: I would like to thank Lars Svensson of the Royal Institute of Technology for illuminating discussions on invariants. This work was part of Esprit Basic Research Action 6448, VIVA, with support from Swedish NUTEK.
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© 1994 Springer-Verlag Berlin Heidelberg
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Carlsson, S. (1994). Conic Primitives for Projectively Invariant Representation of Planar Curves. In: O, YL., Toet, A., Foster, D., Heijmans, H.J.A.M., Meer, P. (eds) Shape in Picture. NATO ASI Series, vol 126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03039-4_27
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DOI: https://doi.org/10.1007/978-3-662-03039-4_27
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