An Improved Geodesic Active Contour Model And Its Numerical Implementation

The boundaries extracted by segmentation methods based on partial differential equations (PDE) have advantages such as continuity, closeness and high precision. That is the reason many researchs focus on PDE methods. Among these, Geodesic Active Contour (GAC) model is one of the geometric active contour models whose theory foundations are curve evolution theory and level set method. GAC model attracts many researchers due to that it doesn’t depend on the parameter of curve and can handle the topological changes of the curve.In this paper, we focus on studying the segmentation method based on PDE combining GAC model with Gradient vector flow (GVF). GVF is firstly used in parametric active contour models. Compared with traditional gradient field, GVF has a wider capture range, and it has the property with bidirectional driving curve, In this paper, the development of active contour models on the image segmentation is briefly introduced. Then, from the aspect of parametric active contour models, three models are introduced:Snake model, Balloon Snake model and GVF Snake model. On the other hand, GAC model and generalized GAC model belonging to the geometric active contour models are introduced. After description about the basic principle and numerical implementation of each model, the advantages and disadvantage are also pointed out through experments.Generalized GAC model can effectively avoid the problem produced by GAC model. But the undirected shrinking force of generalized GAC model leads to over-segmenation and requires the initial curve completely put outside or inside the object boundary. Due the merits of GVF, the GAC_GVF model is proposed. In this model, the directed-boundary-attraction force generated by GVF is integrated to replace the undirected shrinking force, extending the range of the initial contour and effectly solving the insensitivity to initialization of generalize GAC model. Due to saddle points and stagnayion points in the GVF field of the complexshape or multi_objects images, GAC_GVF model can’t get good results in these images. So r GAC_GVF&B model is proposed integrating the balloon force based on the GVF gradient magnitude into GAC_GVF model.When the contour encounters the saddle points and stagnation points, the balloon force will be actived and drive the contour towards to the object.. As for GAC_GVF&B model, two numerical implementation methods are put forward. One is explicit scheme.and the other is the additive operator splitting schema (AOS) used to solve the semi-implicit scheme. GAC_GVF&B model has been tested by two schemas and compared with the existing models on many images. Experimental results show that the GAC_GVF&B model can effectively and automatically gain the segmentation results whether the initialized level is set inside, outside or across the object boundary. The results are properly and efficiently and indicates that the Additive operator splitting (AOS) schema effectively reduce the required iterations and cpu time. Furthermore, it speedups the segmentation.