Abstract

Image segmentation is a popular topic in computer vision and image processing. As a region-based (global) approach, the Mumford and Shah (MS) model is a powerful and robust segmentation technique as compared to edge-based (local) methods. However, there are some difficulties with the MS model. One difficulty is the detection of roof edges. In this thesis, we first modify the MS model to include second order derivative term and use linear approximation to implement the solution. In this way, we can detect not only step edges but also creases and roof edges. The most important difficulty of MS model is that the segmentation results depend on the initial curves. To overcome this problem, we present in this thesis a hierarchical strategy that takes into account both the local information at the pixel level and the global information of the MS model. With this hierarchical segmentation scheme, we can segment an image into regions until each region is smooth enough and need no additional segmentation. Compared with previous works, our approach can automatically detect both main structure and details in an image with multi-level-set functions, and it can stop automatically when the boundaries are detected. In our approach, the final segmentation does not depend on the initial condition. Many experimental results indicate that our approach is effective in many applications. Especially, we apply the new approach to the image inpainting problem. Compared with previous work, because the new approach can detect all the edges in an image, it can preserve more edges and details in the inpainting process.