Implicit Surface Segmentation Variational Level Set Method

Image segmentation is an important research aspect in computer vision.The goal of it is to divide an image into different regions or detect objects in an image based on intensity,texture,color,optic flow and so on.Many researches have got promising results in 2D image segmentation.However,sometimes images on surfaces can reflect information of interest more correctly than 2-D images,such as the cerebral cortex,the mountains,and vegetations of the terrain,etc.Since images on a surface are combined with the geometrical features of the surface,the models for 2D image segmentation cannot be applied to the image segmentation on surface directly.Thus the research of image segmentation on surface has great importance.In this paper,some researches have been done about the image segmentation on the implicit surface.Several aspects are introduced in this paper: Firstly,the definition of image on implicit surface and the representation of the 3D curves are systematically explained as the foundation of the research of image segmentation on implicit surface.Secondly,the Chan-Vese model for piecewise constant image segmentation on implicit surface is presented based on the Chan-Vese model for 2D image segmentation.For the piecewise-constant images, different multiphase image segmentation models are defined based on the region competition strategy proposed by Chan and Vese and used in segmentation of images that follow different probability distributions,for instance,Gauss Probability Distribution and Rayleigh Probability Distribution.Thirdly,the model is extended to the piecewise-smooth images.Chan-Vese model and multiphase image segmentation models for segmenting piecewise-smooth images on implicit surface are deduced.Fourthly,all the models mentioned above are implemented, including piecewise-constant image segmentation and piecewise-smooth image segmentation on implicit surface.Experiments denote that satisfactory results using corresponding image segmentation models can be got and the intrinsic features of the surface can be fully preserved.Finally,future research directions are put forward according to the problems and limitations emerged during the research work.