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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.
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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