In this paper, a class of algorithms for the high order geometric motion of planar curves is developed. The algorithms alternate two simple steps—a convolution and a thresholding step—to evolve planar curves according to combinations of Willmore flow, surface diffusion flow and curvature motion. A distinguishing feature of the methods is that they posses much better stability than typical expli...

We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shorteningstraightening flow. In this paper, first we prove a long time existence result for the shortening-straightening flow for non-closed plan...

In this article, we will develop parallel processing of one-sided Radon transform for the detection of the position and the orientation of a planar motion object. Detection of planar motion based on one-sided Radon transform can be applied to arbitrary shapes and is robust against overlapping of objects but it requires much computation time. Thus, we will construct a parallel computation of one...

This paper proposes a solution to the motion planning and control problem of a point-mass robot which is required to move safely to a designated target in a priori known workspace cluttered with fixed elliptical obstacles of arbitrary position and sizes. A tailored and unique algorithm for target convergence and obstacle avoidance is proposed that will work for any number of fixed obstacles. Th...