| Title | Fundamental Difficulties With Projective Normalization of Planar Curves |
| Authors | Karl Åström |
| Publication | Applications of Invariance in Computer Vision. Second Joint European - US Workshop Proceedings |
| Year | 1993 |
| Pages | 199 - 214 |
| Document type | Conference paper |
| Conference name | Second Joint European - US Workshop Applications of Invariance in Computer Vision |
| Conference Date | 1993-10-09 - 1993-10-14 |
| Conference Location | Ponta Delgada, Azores, Portugal |
| Status | Published |
| Language | eng |
| Publisher | Springer-Verlag |
| Abstract English | In this paper projective normalization and projective invariants of planar curves are discussed. It is shown that there exists continuous affine invariants. It is shown that many curves can be projected arbitrarily close to a circle in a strengthened Hausdorff metric. This does not infer any limitations on projective invariants, but it is clear that projective normalization by maximizing compactness is unsuitable. 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 there can not exist continuous projective invariants, and a projective normalisation scheme can not have both the properties of continuity and uniqueness. Although uniqueness might be preferred it is not essential for recognition. This is illustrated with an example of a projective normalization scheme for non-algebraic, both convex and non-convex, curves |
| Keywords | computational geometry, computer vision, projective normalization, planar curves, projective invariants, continuous affine invariants, Hausdorff metric, compactness, projectively equivalent curves, uniqueness , |
| ISBN/ISSN/Other | ISBN: 3 540 58240 1 |
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