L denotes the classical curve length, s is the arc-length parameter, and Γ : [0, L]→ Ω is a curve with non-vanishing velocity vector. κ is the curvature and α , β are two positively weighted functions computed by the optimally oriented flux filter [2]. Our first step is to cast the elastica energy (5) in the form of path length with respect to a degenerate Finsler metric. For that purpose, let ...

Travelling wave solutions to the vortex lament ow generated by elastica produce surfaces in R 3 that carry mutually orthogonal foliations by geodesics and by helices. These surfaces are classiied in the special cases where the helices are all congruent or are all generated by a single screw motion. The rst case yields a new characterization for the BB acklund transformation for constant torsion...

We study the force vs extension behaviour of a helical spring made of a thin torsionally-stiff anisotropic elastic rod. Our focus is on springs of very low helical pitch. For certain parameters of the problem such a spring is found not to unwind when pulled but rather to form hockles that pop-out one by one and lead to a highly non-monotonic force-extension curve. Between abrupt loop pop-outs t...

Image inpainting is an image restoration problem, in which image models play a critical role, as demonstrated by Chan, Kang and Shen’s recent inpainting schemes based on the bounded variation [10] and the elastica [9] image models. In the present paper, we propose two novel inpainting models based on the MumfordShah image model [37], and its high order correction — the Mumford-Shah-Euler image ...