Image Segmentations Via Geometric Partial Differential Equations

Image segmentation is a key process from image processing to image analysis, and is also a basic technique in Computer Vision. The target of image segmentation is to isolate the interested objects from an image and get the boundaries of the objects. There are great deals of researches on how to detect the objects in an image in the fields of Medicine, Military and Industry quickly, accurately and adaptively. Recently, image segmentations based on partial differential equations (PDE), which is one of the novel and efficient segmentation methods, are gradually turned into research hotspot. Geometric active contours, i.e., active contour implemented via level set methods, have been proposed to address a wide range of image segmentation problems in image processing and computer vision.In this dissertation, we focus on PDE-based image segmentation problems. The drawbacks of active contours, such as sensitivity to initial positions, difficulty to deal with noise images, contour leakage at locations of weak boundary and complexity of numerical implementation, are addresed.Recently, a new variational level set method, i.e., distance preserving level set method, was presented. It has many advantages over the traditional geometric methods; e.g., it completely eliminates the re-initialization procedure of the level set function and the resulting level set evolution can be implemented using simple finite difference method with a much larger time step. However, it has the disadvantage of requiring the initial curve to surround (let in or keep out) the objects to be detected. In this dissertation, an adaptive distance preserving level set method is proposed, in which the initial curve is no longer required to surround (let in or keep out) the objects to be detected, i.e., the initial curve can be anywhere in the image. The proposed method can detect certain object boundaries, for which the original method is not applicable; e.g., it can automatically detect interior and exterior contours of an object and edges of multi-objects, starting with only one initial curve whose position is anywhere in the image. Moreover, active contours can move into boundary concavities and perform better in the presence of weak boundaries.Moreover, an adaptive geometric active contour model with motion constraintis is proposed in this dissertation. The proposed model has simultaneously the following advantages:①completely eliminates the costly re-initialization procedure of the level set function;②the position of the initial curve can be anywhere in the image;③this model can select adaptively parameters to a great extent. Experimental results show that the proposed model can detect certain object boundaries, for which the two well-known models (GAC model and LBF model) are not applicable; e.g., it can better detect objects, a part of which cross over boundaries of the image, and perform better in the presence of weak boundaries and strong noises. It also has been successfully detected infrared images edges with complexity background.