Combining points and tangents into parabolic polygons: AAAAn affine invariant model for plane curves

Marcos Craizer, Thomas Lewiner*, Jean-Marie Morvan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Image and geometry processing applications estimate the local geometry of objects using information localized at points. They usually consider information about the tangents as a side product of the points coordinates. This work proposes parabolic polygons as a model for discrete curves, which intrinsically combines points and tangents. This model is naturally affine invariant, which makes it particularly adapted to computer vision applications. As a direct application of this affine invariance, this paper introduces an affine curvature estimator that has a great potential to improve computer vision tasks such as matching and registering. As a proof-of-concept, this work also proposes an affine invariant curve reconstruction from point and tangent data.

Original languageEnglish (US)
Pages (from-to)131-140
Number of pages10
JournalJournal of Mathematical Imaging and Vision
Volume29
Issue number2-3
DOIs
StatePublished - Nov 1 2007

Keywords

  • Affine curvature
  • Affine differential geometry
  • Affine length
  • Curve reconstruction

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics

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