Combined evolution of level sets and B - spline curves for imaging

We propose the evolution of curves in direction of their unit normal using a combined implicit and explicit spline representation according to a given velocity field. In the implicit case we evolve a level set function for segmentation and geometry reconstruction in 2D images. The level set approach allows for topological changes of the evolving curves. The evolution of the explicit B-spline curve is driven by the Mumford-Shah functional. We are mainly concerned with the segmentation of images using active contours. To get satisfactory results from the implicit evolution the optimal stopping time and the correct level of the evolving function has to be estimated. We overcome this problem by using the combined evolution. As a second application we focus at controlling the topology of the level set function used to detect geometries via EIT. The concurrent evolution of spline curves enables us to identify geometries of dimension 1 which would be lost using only the level set approach. 2 Noname manuscript No. (will be inserted by the editor) M. Fuchs · B. Jüttler · O. Scherzer · H. Yang Combined evolution of level sets and B-spline curves for imaging the date of receipt and acceptance should be inserted later