Image Segmentation And Semi-supervised Data Based On Variational Regularization

Image segmentation plays an important role and is the foundation of the follow-up work in image processing.But due to spatial variations in illuminations,imperfection of imaging devices and so on,the observed image intensities may not be uniform and cause the so-called intensity inhomogeneity effect,which challenges the accuracy of automat-ic segmentation methods.In this thesis,based on the image decomposition model,we propose a piecewise-smooth image segmentation model for the purpose of simultaneous segmenting images and bias correction,in the presence of noise and bias field.In addi-tion,based on augmented Lagrange function,we use the alternating direction minimizing method to solve it,and provide the theoretical analysis to guarantee the existence of the minimizers and the partial convergence of the proposed model.Finally through the com-parisons of numerical experiments and some of quantization standards,we illustrate the proposed model in the CPU time,segmentation and bias correction outperforms other methods.Data classification technique has been widely used in machine learning and data min-ing,so how to classify such data efficiently is important.Despite of existence of millions of unlabeled data samples,it is believed that labeling a handful of data such as the semisu-pervised scheme will remarkably improve the searching performance.In this paper,based on the Mumford-Shah-Potts-type model,we propose semisupervised data classification algorithm,use the alternating direction method of multipliers and the preconditioning primal-dual method to solve it,and briefly demonstrate the convergence of algorithms.Some balanced and unbalanced classification problems are tested,which demonstrate the efficiency of the proposed algorithms.