Abstract
The paper develops a numerical method to analyze and model planar shapes via polygonal curve evolutions. Consider a smooth curve each point of which moves in the normal direction with speed equal to a function of the curvature and curvature derivatives at the point. Chosen the speed function properly, the evolving curve converges to a desired shape. Smooth curve evolutions are approximated by evolutions of polygonal curves. Discrete analogs of the curvature and its derivatives are considered and analyzed. We apply our approach to simplify curves for purposes of multiscale shape analysis, to model geodesics on a plane equipped with a Riemannian metric, to design of nonlinear splines satisfying various boundary conditions, and to detect objects in grey-scale images.
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