| Recently Chan and Vese have developed an active contour model for image segmentation and smoothing. Tsai et al. have also developed a similar approach independently. In this thesis, we develop a new hierarchical method which has many advantages compared to the Chan and Vese multiphase active contour models. First, unlike previous works, the curve evolution partial differential equations (PDEs) for different level set functions are decoupled. Each curve evolution PDE is the equation of motion of just one level set function; and different level set equations of motion are solved in a hierarchy. This decoupling of the motion equations of the level set functions speeds up the segmentation process significantly. Secondly, because of the coupling of the curve evolution equations associated with different level set functions, the initialization of the level sets in Chan and Vese's method is difficult to handle. The hierarchical method proposed in this thesis can avoid the problem due to the choice of initial conditions. Thirdly , we use the diffusion equation for denoising. This method therefore can deal with very noisy images. In general, our method is fast, flexible, not sensitive to the choice of initial conditions, and produces very good results. |
