Efficient Splitting And Preconditioning Algorithms For Total Variation And Elastica Energy Minimization For Variational Image Processing And Computer Vision

Euler's elastica energy for curves and Willmore energy for surfaces are well established concepts and they have numerous applications in many branches of sciences. Their applications to image processing and computer vision are also well recognized. These energies measure the smoothness of curves and surfaces. If we use these energies for the level set of functions, they give us a measurement for smoothness of the functions. This proposal is about designing and testing of some fast and robust algorithms for minimizing these energies for functions. So far, it is still a very difficult task to minimize these energies. Existing algorithms are either too slow or too sensitive to parameters. The proposed algorithm is fast and nearly parameter free. This project is not about a specific application of these energies. The designed algorithms will have more general applications. To demonstrate and test on the proposed ideas, we will take image restoration, image segmentation, image inpainting and surface processing as examples.

In this project, we will mainly work with designing and testing of algorithms. Some preliminary studies show the efficiency and advantages of the proposed ideas. Our research will produce a new class of fast algorithms for these problems and will lead to new ways to design efficient algorithms for minimization of curvature related models.