Research On Markov Random Field Model For Image Segmentation

With the rapid development of science and technology, digital image processing has been widely used in the fields of computer science, electronics, bio-medical, automation, satellite positioning, etc. Digital image processing can be mainly divided into three levels: special image processing, image analysis and image understanding. Image segmentation is a key step in connecting image processing with image analysis, and the accuracy of image segmentation has great influence on later applications of image analysis and image understanding. Since image segmentation is the prerequisite of image feature extraction and image tracing, the research about image segmentation technology has important significance in image processing field.Markov model is widely used in image segmentation for its complete mathematical theory and the ability of well describing image's spatial information. Using the characteristics(gray value, color, texture features) of the image itself, image can be modeled with Markov random field, which integrating the mutual information of images into image segmentation process. In this paper, Single-scale Markov model, multi-resolution Markov model and hierarchical based Markov model were analyzed and improved, in which multi-resolution Markov model based on wavelet domain analysis is our research focus.The main work and innovation of this thesis are as follows:Firstly, the basic theory of Markov random field model was introduced, and the estimation methods and the specific MRF with several types of airports, illustrate several parameter estimation methods and specific calculation procedure were illustrated. Moreover,some typical optimal principles of image segmentation and the corresponding composition of the cost function were introduced, we also discussed the advantages and disadvantages of different criteria in detail.Secondly, the anisotropic diffusion equation based on partial differential equations was introduced into Markov model. As the preprocessing of the algorithm, the traditional anisotropic diffusion equation was improved with the substitution of nonlinear filtering using mathematical morphology for Gaussian filter,which not only can effectively filter out noise and eliminate small isolated points while preserving edge features, but also solve the problem of boundary shift result of Gaussian filter. Performing initial segmentation of images with Fuzzy C-Means Clustering after image preprocessing denoising, modeling features field and tag field with Gaussian mixture model and Potts model respectively. Through the MAP criteria the energy of features field and tag field were minimized. Then using the ICM algorithm to perform the final image segmentation.Thirdly, we studied the principles and characteristics of multi-resolution Markov model.Image presentation using multi-resolution wavelet transform was analyzed, through modeling features field and tag field on some columns wavelet coefficients to make each scale's features field can take advantages of the tag field on the same scale. MLL model and GMRF model were adopted to establish tag field model and feature field model respectively. We used EM algorithm to do parameter estimation and finally got the minimum energy under MAP criterion. The model started from the largest scale, and obtained segmentation results of the maximum scale, then the results will be directly mapped into the adjacent smaller scale as the initial segmentation. Through the iteration process, we can get the final segmentation result.In this thesis, a variable weight multi-scale Markov random field model was presented to solve the problem of that the weight of tag field energy and feature field is 1, which considering the influence of segmentation scale, iteration times, and the number of segmentation categories on the energy of tag field and feature field. Experiment proved the effectiveness of the proposed algorithm.Finally, we studied multi-scale Markov model in-depth research and improved the traditional algorithm. Basic multi-scale Markov model was introduced, which modeling tag field on a series of wavelet coefficients, thus forming the relationship between scales. In the basic model, feature field of the highest resolution is adopted, SMAP principle is used to complete the image segmentation. Against the issue that basic multi-scale Markov model has difficulty in describing image redundancy, a novel hierarchical Markov random field model based on wavelet domain was proposed, in which feature field and tag field were modeled on multi-scale wavelet domain, each layer's tag field can use the feature field on the same scale.Although the proposed algorithm solved the issues of non-stationary and direction, the local spatial information still hasn't been utilized in image segmentation. Hence, we presented an adaptive variable potential function based multi-scale Markov model to combines the causal Markov process between scales and non-causal Markov model in scale, which not only retains the advantages of the original model, but also introduced the local spatial information into the segmentation process. Using EM algorithm to estimate the interaction coefficients between scales, introducing adaptive variable potential function between different scales to make the division results retains the original real boundaries and with favorable locality.