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Fundamental difficulties with projective normalization of planar curves

In English

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