Journal of Mathematical Imaging and Vision

, Volume 29, Issue 2–3, pp 131–140 | Cite as

Combining Points and Tangents into Parabolic Polygons

An Affine Invariant Model for Plane Curves
  • Marcos Craizer
  • Thomas Lewiner
  • Jean-Marie Morvan


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.


Affine differential geometry Affine curvature Affine length Curve reconstruction 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Marcos Craizer
    • 1
  • Thomas Lewiner
    • 1
  • Jean-Marie Morvan
    • 2
  1. 1.Department of MathematicsPUC-RioRio de JaneiroBrazil
  2. 2.Université Claude BernardLyonFrance

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