The Study Of Image Segmentation Based On Statistical Mixture Models

Image segmentation is one of the old and fundmental research topics in computervision. It has been successfully applied in many fields. At the same time, it is thefoundation of feature extraction and image understanding. Therefore, imagesegmentation has been received many researchers’ attentions. Image segmentation is aprocess which is dividing an image into several parts based on their similarity. Instatistics, image segmentation is referred to as cluster analysis. It has been widelyresearched and many models of image segmentation have been proposed. Mixturemodels have been successfully appllied clustering problems including imagesegmentation because it can model heterogeneity very well in a cluster analysis contextand it is easy to be implemented. However, finite mixture model (FMM) cannot obtaingood image segmentation results under noise condition. The main reason is that finitemixture model considers that the relationship between the pixels is independent.Markov random field (MRF) model which considers the spatial relationships between thepixels have been successfully appllied to image segmentation. Many models whichintegerate FMM with MRF have been proposed and obtained better image segmentationresults. This dissertation focuses on the research of mixture model applied in imagesegmentation utilizing the MRF relationship among the pixels. The research includesthe efficiency and robustness against noise of spatially variant finite mixture model(SVFMM); the new models which integerate Student’s t-distribution with SVFMM areproposed and applied to image segmentation; how to automatically determine the numberof hidden states of hidden markov random field (HMRF) and how to improve therobustness of HMRF. Considering the real applications of image processing, a newsoftware platform is designed and implemented for image process. This dissertationfocuses on the image segmentation using mixture model. The constributions and theresults we obtain in this dissertation are summarized as follows.1. To resolve the problem that the label probability proportion cannot be obtainedin closed form in the inference process, which needs reparatory computations andincreases the computational load. A spatial directional relationships-based Gaussian mixture mode (SDRGMM) is proposed. In SDRGMM, the label probability proportionis explicitly mdoelled as a probabilistic vector which avoids the reparatorycomputations. The experiments on synthetic grayscale images and simulated brainimages show that the efficiency of SDRGMM.2. According to the feature that the Student’s t-distribution owns heavier tailed thanGaussian distribution and the Student’s t-distribution is more robustness against noisethan Gaussian distribution, a directional spatially varying Student’s t-distributionmixture model (DSVStMM) is proposed. In DSVStMM, the merits of SVFMM and thespatial relationships are fully considered. DSVStMM contains fewer parameterscompared to some models based on MRF. Therefore it is easy to be implemented. Someexperiments on synthetic and natural images are carried out to demonstrate that theproposed model outperforms some other related ones.3. Considering the defect that the Student’s t-distribution mixture model (StMM)does not consider the spatial relationships between the pixels in an image, a spatiallysmooth-based Student’s t-distribution mixture model (SSStMM) is proposed. SSStMMregards the Student’s t-distribution as an entity and utilizes gradient descent method toinference the paramenters of the model. In the previous most literatures, the Student’st-distribution in the inference process is regarded as an infinite Gaussian mixture model.The visual and quantitative comparisons of image segmentation on synthetic images andnatural images show the superiority of SSStMM over some existing models.4. To resolve the problem that hidden markov random field (HMRF) model cannotautomatically determine the number of segments when it is applied to imagesegmentation, we utilize Dirichlet process (a nonparametric Bayesian statistics model)as a prior of the hidden states of HMRF. Furthermore, the distribution of observationsadopts Student’s t-distribution. A new HMRF model is proposed, in the proposed model,Dirichlet process is represented by stick-breaking representation. The proposed model iscalled stick-breaking representation of HMRF based on Student’s t-distribution(SBHMRF-St). Variational Bayes inference is used to obtain the parameters ofSBHMRF-St. Comprehensive experiments on Berkeley image segmentation data setand the images taken from Microsoft Research Cambridge show the superiority ofSBHMRF-St over some models based on Dirichlet process.5. Considering the real applications of image processing, we have analyzed some existing software. Then an image process platform is designed and implemented bycombining three open source software-ITK, VTK and Qt. New functions can be easilyadded in the platform if the algorithms exist in the open source software.