A unified Bayesian mixture model framework via spatial information for grayscale image segmentation

The representation of the contextual mixing proportion is very characteristic.The component function of the proposed method is the Student's t-distribution.To obtain the parameters of the method, the inherent relationships between two distributions are utilized.The gradient method is adopted in the inference process. Because of the Student-t distribution owning heavier tailed than the Gaussian distribution, under a Bayesian framework, a spatially variant finite mixture model with Student's t-distribution component function is proposed for grayscale image segmentation. To avoid additional computational step and improve the efficiency of the proposed model, a representation of contextual mixing proportion is adopted. Secondly, the spatial information of the pixels is closely related to the Gaussian distribution of their neighborhood system. Thirdly, the inherent relationship between the Gaussian distribution and the Student's t-distribution is adopted to optimize the unknown parameters of the proposed model, which simplifies the inference process and makes the proposed model to be easily implemented. Comprehensive experiments on synthetic noise images, simulated medical images and real-world grayscale images are presented to illustrate the superior performance of the proposed model in terms of the visual and quantitative comparison.

[1]  Theo Gevers,et al.  A Spatially Constrained Generative Model and an EM Algorithm for Image Segmentation , 2007, IEEE Transactions on Neural Networks.

[2]  Nikolas P. Galatsanos,et al.  Robust Image Segmentation with Mixtures of Student's t-Distributions , 2007, 2007 IEEE International Conference on Image Processing.

[3]  D. Louis Collins,et al.  Design and construction of a realistic digital brain phantom , 1998, IEEE Transactions on Medical Imaging.

[4]  Thomas J. Hebert,et al.  Bayesian pixel classification using spatially variant finite mixtures and the generalized EM algorithm , 1998, IEEE Trans. Image Process..

[5]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[6]  Zhang Yi,et al.  Grayscale image segmentation by spatially variant mixture model with student’s t-distribution , 2012, Multimedia Tools and Applications.

[7]  Christopher M. Bishop,et al.  Pattern Recognition and Machine Learning (Information Science and Statistics) , 2006 .

[8]  D. Louis Collins,et al.  A new improved version of the realistic digital brain phantom , 2006, NeuroImage.

[9]  Xue-Cheng Tai,et al.  A Continuous Max-Flow Approach to Potts Model , 2010, ECCV.

[10]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.

[11]  Jianfei Cai,et al.  Beyond pixels: A comprehensive survey from bottom-up to semantic image segmentation and cosegmentation , 2015, J. Vis. Commun. Image Represent..

[12]  Nikolas P. Galatsanos,et al.  A Class-Adaptive Spatially Variant Mixture Model for Image Segmentation , 2007, IEEE Transactions on Image Processing.

[13]  Xue-Cheng Tai,et al.  Global Minimization for Continuous Multiphase Partitioning Problems Using a Dual Approach , 2011, International Journal of Computer Vision.

[14]  Stan Z. Li,et al.  Markov Random Field Modeling in Image Analysis , 2001, Computer Science Workbench.

[15]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[16]  Luc Van Gool,et al.  The Pascal Visual Object Classes Challenge: A Retrospective , 2014, International Journal of Computer Vision.

[17]  Chunming Li,et al.  Minimization of Region-Scalable Fitting Energy for Image Segmentation , 2008, IEEE Transactions on Image Processing.

[18]  Martial Hebert,et al.  Toward Objective Evaluation of Image Segmentation Algorithms , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  Anil K. Jain,et al.  Unsupervised Learning of Finite Mixture Models , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[20]  Geoffrey J. McLachlan,et al.  Robust mixture modelling using the t distribution , 2000, Stat. Comput..

[21]  G. McLachlan,et al.  The EM algorithm and extensions , 1996 .

[22]  Aristidis Likas,et al.  Bayesian feature and model selection for Gaussian mixture models , 2006, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[23]  D. Louis Collins,et al.  Twenty New Digital Brain Phantoms for Creation of Validation Image Data Bases , 2006, IEEE Transactions on Medical Imaging.

[24]  Jitendra Malik,et al.  A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[25]  Q. M. Jonathan Wu,et al.  Fast and Robust Spatially Constrained Gaussian Mixture Model for Image Segmentation , 2013, IEEE Transactions on Circuits and Systems for Video Technology.

[26]  Nikolas P. Galatsanos,et al.  Spatially Varying Mixtures Incorporating Line Processes for Image Segmentation , 2009, Journal of Mathematical Imaging and Vision.

[27]  Sotirios Chatzis,et al.  A variational Bayesian methodology for hidden Markov models utilizing Student's-t mixtures , 2011, Pattern Recognit..

[28]  Q. M. Jonathan Wu,et al.  Gaussian-Mixture-Model-Based Spatial Neighborhood Relationships for Pixel Labeling Problem , 2012, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[29]  Nikolas P. Galatsanos,et al.  A Bayesian Framework for Image Segmentation With Spatially Varying Mixtures , 2010, IEEE Transactions on Image Processing.

[30]  Michael I. Jordan,et al.  Variational inference for Dirichlet process mixtures , 2006 .

[31]  Stephen M. Smith,et al.  Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm , 2001, IEEE Transactions on Medical Imaging.

[32]  Q. M. Jonathan Wu,et al.  An Extension of the Standard Mixture Model for Image Segmentation , 2010, IEEE Transactions on Neural Networks.

[33]  Nasser M. Nasrabadi,et al.  Pattern Recognition and Machine Learning , 2006, Technometrics.

[34]  Q. M. Jonathan Wu,et al.  A fuzzy logic model based Markov random field for medical image segmentation , 2013, Evol. Syst..

[35]  Jiawei Han,et al.  Data Mining: Concepts and Techniques , 2000 .

[36]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[37]  Christopher M. Bishop,et al.  Robust Bayesian Mixture Modelling , 2005, ESANN.

[38]  Nikolas P. Galatsanos,et al.  A spatially constrained mixture model for image segmentation , 2005, IEEE Transactions on Neural Networks.

[39]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[40]  Zhang Yi,et al.  Robust t-distribution mixture modeling via spatially directional information , 2013, Neural Computing and Applications.

[41]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[42]  Sotirios Chatzis,et al.  Signal Modeling and Classification Using a Robust Latent Space Model Based on $t$ Distributions , 2008, IEEE Transactions on Signal Processing.