Study On Image Segmentation Based On Partial Differential Equations

Image segmentation is one of fundamental and important tasks in image analysisand processing. Given an image, the segmentation goal is to separate the image domaininto a series of meaningful regions or extract interesting objects of image.In recent years, active contour models based on partial differential equations havebeen widely used in image segmentation. Active contour models have many advantages,while the classical image segmentation methods (such as edge detection, threshold andregion growing methods, etc.) do not have, thus it have gained common concern ofdomestic and foreign scholars. Now, active contour models can be divided into twocategories: edge-based models and region-based models. This dissertation mainlydiscusses region-based models, to solve the problems of active contour models, such asbe sensitive to the initial position, be re-initialized, the complexity of the numericalcalculation, the edge of the leaks and over-segmentation of the segmentation result, etc.This dissertation discusses a series of different region-based active contour models,such as C-V model, improved C-V model, region-scalable fitting model, local imagefitting model, selective local or global segmentation model, and explores the specificproblems of these models and the cause of the problems. Finally, we make someimprovement and innovation, and hope to achieve the desired segmentation results. Themain work and results of this dissertation are summarized as follows:1) Due to the fact that local image fitting (LIF) model is highly sensitive toinitialization of the contours, combined with improved C-V model, an active contourmodel combining local and global image information is proposed. First, the force oflevel set evolution is defined by a linear combination of global intensity fitting forcethat is resulted from the improved C-V model and local intensity fitting force that isresulted from the LIF model. Then, by choosing appropriately the parameter thatcontrols the influence of these two forces, the proposed model allows for flexibleinitialization of the contours. Finally, Gaussian filtering regularized level set method isemployed to regularize the level set function. Experimental results on both real andsynthetic images show that the proposed model is robust to initialization of the contours,while having the ability of handling intensity inhomogeneity.2) Combining SLGS and RSF models, this paper proposes a novel active contourmodel in a partial differential equation formulation. SLGS (selective local or global segmentation) model, an active contour model based on global information, allows forthe flexible initialization of contours, but cannot deal with intensity inhomogeneity. RSF(region-scalable fitting) model, an active contour model based on local information, isable to handle intensity inhomogeneity, but sensitive to initialization. This paperincorporates the local information defined in RSF model into the SLGS model.Experimental results show that the proposed model can efficiently deal with intensityinhomogeneity and allows for flexible initialization. Also, it is more accurate thanSLGS model for some images with weak or blurred edges.