Journal of Mathematical Imaging and Vision

, Volume 29, Issue 2, pp 131–140

Combining Points and Tangents into Parabolic Polygons

An Affine Invariant Model for Plane Curves


  • Marcos Craizer
    • Department of MathematicsPUC-Rio
    • Department of MathematicsPUC-Rio
  • Jean-Marie Morvan
    • Université Claude Bernard

DOI: 10.1007/s10851-007-0037-2

Cite this article as:
Craizer, M., Lewiner, T. & Morvan, J. J Math Imaging Vis (2007) 29: 131. doi:10.1007/s10851-007-0037-2


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 geometryAffine curvatureAffine lengthCurve reconstruction

Copyright information

© Springer Science+Business Media, LLC 2007