  In this paper, we introduce a novel approach for active contours with free
endpoints. A scheme is presented for image segmentation and restoration based
on a discrete version of the Mumford-Shah functional where the contours can be
both closed and open curves. Additional to a flow of the curves in normal
direction, evolution laws for the tangential flow of the endpoints are derived.
Using a parametric approach to describe the evolving contours together with an
edge-preserving denoising, we obtain a fast method for image segmentation and
restoration. The analytical and numerical schemes are presented followed by
numerical experiments with artificial test images and with a real medical
image.
