Projective Splines and Estimators for Planar Curves

Authors:
Thomas Lewiner;Marcos Craizer
Affiliations:
Department of Mathematics, PUC, Rio de Janeiro, Brazil;Department of Mathematics, PUC, Rio de Janeiro, Brazil
Venue:
Journal of Mathematical Imaging and Vision
Year:
2010

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Abstract

Recognizing shapes in multiview imaging is still a challenging task, which usually relies on geometrical invariants estimations. However, very few geometric estimators that achieve projective invariance have been devised. This paper proposes a projective length and a projective curvature estimators for plane curves, when the curves are represented by points together with their tangent directions. In this context, the estimations can be performed with only three point-tangent samples for the projective length and five samples for the projective curvature. The proposed length and curvature estimator are based on projective splines built by fitting logarithmic spirals to the point-tangent samples. They are projective invariant and convergent.