Research On Segmentation Algorithm For PET Cardiac Images Based On Fractional Order Level Set

PET (Positron Emission Tomography) is one of the most advanced large-scale medical diagnostic imaging equipment. In terms of diagnosis and evaluation of cardiovascular disease, PET has a unique application value. In the thesis, two image segmentation models based on fractional order level set are proposed, which are associated with the level set theory and fractional calculus theory, some image segmentation experiments on PET cardiac image using the two models are carried out, and the results show that the presented image segmentation models based on fractional order level set have better effect on PET cardiac image segmentation. The main works and innovations in this thesis can be summarized as follows:(1) A large number of literature has been studied, and the PET imaging and its clinical application are investigated, and image segmentation algorithms (focus on the level set method) and the research status of fractional order calculus theory in image processing are introduced.(2) A notion of fractional order level set has been proposed, which is associated with level set theory and fractional calculus theory, and we proposed two image segmentation models based on fractional order level set, the fractional order C-V model and fractional order RSF model. The image segmentation models based on fractional order level set expand the first derivative of regularization item in traditional image segmentation models which are based on integral order level set to fractional order derivative. The fractional order differential has "long memory" characteristics, which makes the fractional order level set models have the "global nature" and overcome the local nature of first derivative in the traditional integral order level set models.(3) We derived the Euler-Lagrange equations of fractional order level set models by solving the fractional functional problems, and we can obtain the fractional order level set evolution equations by using gradient descent flow. On this basis, we designed a fractional order level set mask based on Gruwald-Letnikov fractional order differential definition, and achieve the numerical algorithm of the fractional order level set models.(4) We conduct some image segmentation experiments on PET cardiac image using the proposed fractional order level set models (fractional order C-V model and fractional order RSF model), and compares with the traditional image segmentation models based on integral order level set. The results show that fractional order C-V model has better image segmentation results than original C-V model for some intensity homogeneity PET cardiac images; The fractional order C-V model and conventional C-V model do not have an ideal segmentation effect for intensity inhomogeneity PET cardiac images; To solve the problem, we proposed the fractional order RSF model, which is not only suitable for intensity homogeneity PET cardiac images segmentation, but also suitable for intensity inhomogeneity PET cardiac images segmentation; The fractional RSF image segmentation model has the advantages of fewer iteration times, faster compulation, and higher numerical stability.