Research On Fast Image Segmentation Models Based On Split Bregman Method

Image segmentation is a fundamental task in image processing and computer vision.Active contour models have become one of the most successful methods for image seg-mentation. There are some classic active contour models, including the geodesic activecontour model, the Chan-Vese model, the region-scalable fitting energy model, the piece-wise constant multiphase Vese-Chan model and so on. Although these models can getgood numerical and experimental results, they all have their own limitations. For exam-ple, the Chan-Vese model and the piecewise constant multiphase Vese-Chan model cannot handle inhomogeneous images, the geodesic active contour model and the region-scalable fitting energy model are sensitive to the initialization of contours. Besides, non-convexity is the common disadvantage of these models. To eliminate difculties associat-ed with the non-convexity, the globally convex segmentation method has been proposedand applied to the Chan-Vese model with promising results. The Split Bregman methodhas been applied to solve image segmentation problems more efciently, for example, tominimize the globally convex Chan-Vese model. However, the globally convex Chan-Vese model is mainly for homogeneous and two-phase images. Therefore, in order tosegment inhomogeneous images or multiphase images, based on these classic active con-tour models, the globally convex segmentation method and the Split Bregman method,this dissertation presents the following four new and fast image segmentation models.1. In order to eliminate difculties associated with the nonconvexity of the region-scalable fitting energy model and detect the object boundaries more quickly and moreeasily, this dissertation presents a globally convex region-scalable fitting energy modelby combining the region-scalable fitting energy model, the geodesic active contour modeland the globally convex segmentation method. The special structure of the proposedenergy functional guarantees the application of the Split Bregman method, and a fastalgorithm is given for the proposed model. Thus the proposed globally convex region-scalable fitting energy model can segment images with intensity inhomogeneity moreefciently and more accurately.2. Considering the advantages and disadvantages of the Chan-Vese model and theregion-scalable fitting energy model, this dissertation presents an active contour mod-el combining local and global information dynamically. The Chan-Vese model and the region-scalable fitting energy model are first combined, and a weight function varyingwith the location of a given image is used to balance the weights of the two models. Thena new energy functional is defined by applying the globally convex segmentation method.To detect boundaries more easily, the energy functional is modified by incorporating in-formation from the edge with a non-negative edge detector function. The Split Bregmanmethod is then applied to minimize the new energy functional more efciently. There-fore, the proposed model can segment more general images more accurately and moreefciently, including homogeneous and inhomogeneous images.3. This dissertation presents a fast multiphase segmentation model based on theVese-Chan model, the globally convex segmentation method and the Split Bregman methodto segment a given image into multiple regions. The proposed fast multiphase segmenta-tion model has the following advantages. It automatically avoids the problems of vacuumand overlap by construction, and it needs fewer level set functions to represent the samenumber of phases, and it can represent boundaries with complex topologies. Besides,the application of the globally convex segmentation method and the Split Bregman en-sures that the new model is much more efcient than the Vese-Chan model. The proposedmodel is a piecewise constant multiphase segmentation model, thus it mainly focuses onhomogeneous multiphase images.4. In order to segment images with multiple regions and intensity inhomogeneity,the above proposed active contour model combining local and global information dynam-ically is extended from the two-phase level set formulation to the multiphase level setformulation, and a multiphase segmentation model combining local and global informa-tion dynamically is proposed. The new model can segment more general images withmultiple regions more accurately and more efciently, especially images with intensityinhomogeneity, such as the brain magnetic resonance images.In this dissertation, the above four proposed fast image segmentation models basedon the Split Bregman method have been applied to synthetic and real images with promis-ing results. Experimental results and comparisons with other models demonstrate the su-periority of the proposed models, such as the accuracy of the segmentation results, theefciency of the algorithms, the robustness to noise, and so on.