Projective Estimators for Point/Tangent Representations of Planar Curves

Recognizing shapes in multiview imaging is still a challenging task, which usually relies on geometrical invariants estimations. However, very few geometric estimators that are projective invariant have been devised.This paper proposes projective length and 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 the four point-tangent samples for the projective length and five for the projective curvature.The proposed length estimator is based on affine estimators and is proved to be convergent. The curvature estimator relies on the length to fit logarithmic spirals to the point-tangent samples. It is projective invariant and experiments indicate its convergence. Preliminary results using both estimators together are promising, although the estimators´ lack of robustness would require additional work for noisy cases.