Fundamental difficulties with projective normalization of planar curves
Författare
Redaktör
- Joseph L. Mundy
- Andrew Zisserman
- David Forsyth
Summary, in 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.
Avdelning/ar
Publiceringsår
1994
Språk
Engelska
Sidor
199-214
Publikation/Tidskrift/Serie
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volym
825 LNCS
Dokumenttyp
Konferensbidrag
Förlag
Springer
Ämne
- Mathematics
Nyckelord
- computational geometry
- computer vision
- projective normalization
- planar curves
- projective invariants
- continuous affine invariants
- Hausdorff metric
- compactness
- projectively equivalent curves
- uniqueness
Conference name
Second Joint European - US Workshop Applications of Invariance in Computer Vision
Conference date
1993-10-09 - 1993-10-14
Conference place
Ponta Delgada, Azores, Portugal
Status
Published
ISBN/ISSN/Övrigt
- ISSN: 1611-3349
- ISSN: 0302-9743
- ISBN: 978-3-540-48583-4
- ISBN: 978-3-540-58240-3