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Fundamental Limitations on Projective Invariants of Planar Curves
January 1995 (vol. 17 no. 1)
pp. 77-81

Abstract—In this paper, some fundamental limitations of projective invariants of non-algebraic planar curves are discussed. It is shown that all curves within a large class can be mapped arbitrarily close to a circle by projective transformations. It is also shown that arbitrarily close to each of a finite number of closed planar curves there is one member of a set of projectively equivalent curves. Thus a continuous projective invariant on closed curves is constant. This also limits the possibility of finding so called projective normalisation schemes for closed planar curves.

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Index Terms:
Projective and affine invariants, recognition, Hausdorff metric.
Citation:
Kalle Åström, "Fundamental Limitations on Projective Invariants of Planar Curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 17, no. 1, pp. 77-81, Jan. 1995, doi:10.1109/34.368148
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