图像处理水平集方法介绍1.ppt

Active Contours, Level Sets, and Image Segmentation Outline 2D Level Set 3D Level Set More Applications of Level Sets Advantages of Active Contours and Level Sets Image Segmentation: Classic Methods Parametric Active Contours (Kass et al 1987) Evolution of Active Contours External Force Gradient Vector Flow (Xu and Prince, 1998) An Example Advantages of GVF Snake Differential Geometry of Curves Curvature Curvature (Cont’d) Dynamic Curves Geometric Curve Evolution Constant Speed Motion and Mean Curvature Motion Why MCM Shortens Curve Length? Geodesic Active Contour (Caselles et al, 1997) Geodesic Active Contour Example Difficulties of Parameterized Curve Evolution Solutions Level Set Representation of Curves Advantages of Level Set Methods Level Set Functions Signed Distance Function Useful Calculus Facts in Level Set Formulation From Curve Evolution to Level Set Evolution Special Cases Demo of GAC Unstable Evolution and Need for Reinitialization Procedure of Standard Level Set Methods More Details All computation is carried out on a fixed grid, no need for re-parameterization. Topological changes are handled naturally. More … Also have some disadvantages, will be discussed later. contour Level set functions with the same zero level set Contour C Signed distance function If a curve is a level set of a function then, the normal vector and the curvature can be computed from the embedding function The surface (or line) integral of a quantity p(x) over the zero level surface (or contour) of The volume (or area) integral of p(x) over Curve evolution where F is the speed function, N is normal vector to the curve C Embed the dynamic curve as the zero level set of a time dependent function , i.e. Take derivative with respect to time Level set evolution: Mean curvature flow Constant Speed Motion Geodesic active contours Click to play the movie Degraded level set function, 50 it