Research On The Image Segmentation Based On Partial Differential Equations

In recent years, Partial differential equations (PDE) has played more and more importantrole on image processing. Compared with other approaches, the PDE method has remarkableadvantages in both theory and computation. First, it allows one to directly handle and processvisually important geometric features such as gradients, tangents, curvatures, and level set.Second, in terms of computation, it can profoundly benefit from the existing wealth ofliterature on numerical analysis and computational PDEs. PDE has greatly enhanced thedevelopment of image segmentation techniques. PDE based segmentation models are usuallyincorporated into a variational framework, by minimizing some energy functional. Theadvantage is that, in complex segmentation procedure, it can incorporate additionalinformation, such as texture information, shape information, statistical information, etc. Thisthesis focuses on some new kind of complex texture segmentation techniques based on PDEsegmentation method.Firstly, the thesis introduces the definition, background, and development of PDE basedimage segmentation with a review of some of the most classical and prevalent models incurrent years and a comprehensive conclusion of the development trends in this area.Followed is a brief introduction to texture image segmentation.Secondly, the thesis analyses the properties of PDE based linear and nonlinear diffusionin its smoothing and edge-preserve effects, and mainly analyses the Chan-Vese segmentationmodel and associated Vector-Valued case with plenty of illustrations to reveal the mechanismand effects of main parameters on the segmentation result.Thirdly, a new method is proposed combining structure tensor and Vector-ValuedChan-Vese model for texture image segmentation. The structure tensor is used to extracttexture image features which will be smoothed by the linear diffusion filter equation, and thefiltered features will be incorporated into the Vector-Valued Chan-Vese model to completethe segmentation process. Also experiment illustrations are given to test the accuracy of thenew method with run time.Finally, the nonlinear filtering of the structure tensor is test. Using traditionalPerona-Malik diffusion equations can’t achieve perfect smooth effects for the texture features,so TV flow (Total Variation Flow) is preferred to be the diffusion function in the diffusion equation, which can improve the segmentation accuracy. In addition, the combination oflinear and nonlinear structure tensor is considered, which comes to eights channels for thesegmentation model to improve the accuracy further. Experiments are carried out on bothnatural and manual texture images with different patterns of texture in both foreground andbackground to demonstrate the effectiveness of the method.