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Fundamental limitations on projective invariants of planar curves

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1 Author(s)
Astrom, K. ; Dept. of Math., Lund Univ., Sweden

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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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:17 ,  Issue: 1 )