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

Combining points and tangents into parabolic polygons: an affine invariant model for plane curves
Marcos Craizer, Thomas Lewiner, Jean-Marie Morvan

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.

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BibTeX:

@article{parabolic_polygon_jmiv,
    author = {Marcos Craizer and Thomas Lewiner and Jean-Marie Morvan},
    title = {Combining points and tangents into parabolic polygons: an affine invariant model for plane curves},
    year = {2007},
    month = {november},
    journal = {Journal of Mathematical Imaging and Vision},
    volume = {29},
    number = {2-3},
    pages = {131--140},
    publisher = {Springer},
    doi = {10.1007/s10851-007-0037-2},
    url = {\url{http://thomas.lewiner.org/pdfs/parabolic_polygon_jmiv.pdf}}
}