Based On Partial Differential Equations And Variational Level Set Image Segmentation

The technology of image segmentation means extractingimage,and it is one of hot spots and difficulties in image processing.Recently,the nonlinear methods,especially image segmentation methods based on PDEs have attracted more and more attentions.Compared to traditional image segmentation approaches,PDE-based ones have many prominent virtues:such as more accuracy,being able to directly deal with some image features which is easy for flexible descriptions with various mathematical models.Among PDE-based image segmentation techniques,variation and level set approaches are two useful and important mathematical tools,based on which active contour models embody the advantages of PDE methods over traditional ones. However,these two methods have their own insufficiency on some aspects,for example,variation-based parametric active contour model has difficulty in dealing with the adaptability of topological changes,while level set based geometric active contour model is generally not an energy minimization model.Variational level set methods which are an ideal and efficient tool take on all the virtues of them.The advantages of variational level set methods are obvious,but they use the level set to solve the PDE equations,which causes their evolution velocities greatly slow down.The paper discusses the devlopment of the model,and analyzes the principle and deficiency of the "Snake" model.Geometric and geodesic active contours based on the level set theory are concerned.The active contours without edges are emphasized, which are proposed by Chan and Vese.Through improving the model,initial condition and numerical implementation,the evolution velocity is enhanced.In this paper,from the fundamental level set theory,many problems are discussed.Here,we mainly present a new variational formulation for Chan-Vese model that forces the level set function to be close to a signed function,and completely eliminates the need of the constly re-initialization procedure,so the evolution velocity is greatly improved.Also,when we detect more than one object,we can change the initial condition to improve the evolution velocity.In the numerical implementation,we adopt AOS(Additive Operator Splitting) scheme to eliminates limit of time step.And we can not only select the large time step,but also absolutely stable.Finally,we process some compose images and real images.And the result shows that the evolution velocity greatly improves and the precision doesn't reduce.