Spatial Relationship Constrained Nonparametric Bayesian Model And Its Application For Image Processing

Model selection is one of the most challenging problems in computer vision and machine learning.To classify the data with distinguishable feature,the number of models can be predefined manually.While the data is undistinguishable or its feature is time varying,manual model selection cannot achieve the classification task well.Obviously,model selection should be data driven to adapt to the undistinguishable feature.Dirichlet process model is such a model to cluster data into a number of models in a nonparametric manner.Herein,attention will be paid to the combination of DP with Markov random fields to achieve the model selection on image processing.Previous representative work on the same problem such as iHMRF and MRFDPMM are worth mentioning.iHMRF model uses the stick-breaking construction of DP to obtain the prior distribution of data.With it as the external field of the MRF and the spatial information coded as the second order potential,a new nonparametric infinite MRF is constructed.While in the original paper,the iHMRF model is constructed from the viewpoint of production of probabilities of MRF and DP obtained distribution.Probability production makes sense while a mean field theory is employed.Thus,our formulation is more natural and theoretically accurate.In addition,variational inference is deployed for model inference.MRFDPMM model has the similar principle with the iHMRF.It has an external field with distribution generated by a DP through a Chinese restaurant process(CRP)construction.CRP based model can be inferred easily by Gibbs sampler.However,the Gibbs sampler is slow to converge as it is hard to cross over low probabilistic state.Thus,a SWC based sampler is designed for inference of MRF-DPMM.Both the referred models are DP embedded MRF models.The premise of the combination is that the external fields are independent in Markov random field.In other words,priors for data are independent identically distributed.Such a premise in a DP derived distribution does not exist actually.In this paper,a hierarchical model is proposed.Firstly input image is over segmented with MRF in the lower level.Then a CRP in the higher level will go on the processing using global clustering.Split-merge sampler is employed for model inference.Experiments on natural image and MRI segmentation show the model is robust with varying image categories.