Image segmentation is a popular topic in computer vision and image processing. As a region-based approach, the Mumford and Shah (MS) model is a powerful and robust segmentation technique as compared to local based methods. However, there are also some difficulties with the MS model. In this paper, we present a piecewise linear approximation for the MS model to adapt to the image intensities distribution inside the segmented regions. We also modify the MS model to detect roof edges. Because the MS functional is not convex, the result is often trapped in a local minimum and depends on the initial conditions. To overcome this problem, we present a new hierarchical strategy that takes into account both the local information at the pixel level and the global information of the MS model. The results indicate that our approach is effective in many applications.