Arranging and interpolating sparse unorganized feature points with geodesic circular arc

A novel method to reconstruct object boundaries with geodesic circular arc is proposed in this paper. Within this framework, an energy of circular arc spline is utilized to simultaneously arrange and interpolate each member in the set of sparse unorganized feature points from the desired boundaries. A general form for a family of parametric circular arc spline is firstly derived and followed by a novel method of arranging these feature points by minimizing an energy term depending on the circular arc spline configuration defined on these feature points. With regard to the fact that the energy function is usually nonconvex and nondifferentiable at its critical points, an improved scheme of particle swarm optimizer is given to find the minimum for the energy in this paper. With this improved scheme, each pair of neighboring feature points along the boundaries of the desired objects are picked out from the set of sparse unorganized feature points, and the corresponding directional chord tangent angles are computed simultaneously to finish interpolation. We show experimentally and comparatively that the proposed method can perform effectively to restrict leakage on weak boundaries and premature convergence on long concave boundaries. Besides, it has good noise robustness and can as well extract multiple and open boundaries.