Incorporating Mean Template Into Finite Mixture Model for Image Segmentation

The well-known finite mixture model (FMM) has been regarded as a useful tool for image segmentation application. However, the pixels in FMM are considered independent of each other and the spatial relationship between neighboring pixels is not taken into account. These limitations make the FMM more sensitive to noise. In this brief, we propose a simple and effective method to make the traditional FMM more robust to noise with the help of a mean template. FMM can be considered a linear combination of prior and conditional probability from the expression of its mathematical formula. We calculate these probabilities with two mean templates: a weighted arithmetic mean template and a weighted geometric mean template. Thus, in our model, the prior probability (or conditional probability) of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the local spatial and intensity information for eliminating the noise. Finally, our algorithm is general enough and can be extended to any other FMM-based models to achieve super performance. Experimental results demonstrate the improved robustness and effectiveness of our approach.

[1]  Jun Zhang,et al.  Maximum-likelihood parameter estimation for unsupervised stochastic model-based image segmentation , 1994, IEEE Trans. Image Process..

[2]  Peter Clifford,et al.  Markov Random Fields in Statistics , 2012 .

[3]  Martial Hebert,et al.  Measures of Similarity , 2005, 2005 Seventh IEEE Workshops on Applications of Computer Vision (WACV/MOTION'05) - Volume 1.

[4]  Hui Wei,et al.  Compact Image Representation Model Based on Both nCRF and Reverse Control Mechanisms , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Nizar Bouguila,et al.  Count Data Modeling and Classification Using Finite Mixtures of Distributions , 2011, IEEE Transactions on Neural Networks.

[6]  Stelios Krinidis,et al.  A Robust Fuzzy Local Information C-Means Clustering Algorithm , 2010, IEEE Transactions on Image Processing.

[7]  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).

[8]  Sotirios Chatzis,et al.  A Fuzzy Clustering Approach Toward Hidden Markov Random Field Models for Enhanced Spatially Constrained Image Segmentation , 2008, IEEE Transactions on Fuzzy Systems.

[9]  Radford M. Neal Pattern Recognition and Machine Learning , 2007, Technometrics.

[10]  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.

[11]  W. Qian,et al.  Estimation of parameters in hidden Markov models , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[12]  Aly A. Farag,et al.  A modified fuzzy c-means algorithm for bias field estimation and segmentation of MRI data , 2002, IEEE Transactions on Medical Imaging.

[13]  J. Besag Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[14]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

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

[16]  Joseph N. Wilson,et al.  Twenty Years of Mixture of Experts , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[17]  Martial Hebert,et al.  A Measure for Objective Evaluation of Image Segmentation Algorithms , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Workshops.

[18]  Nizar Bouguila,et al.  Variational Learning for Finite Dirichlet Mixture Models and Applications , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[19]  P. Deb Finite Mixture Models , 2008 .

[20]  R. Cooke Real and Complex Analysis , 2011 .

[21]  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.

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

[23]  J. Besag Statistical Analysis of Non-Lattice Data , 1975 .

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

[25]  Daoqiang Zhang,et al.  Robust image segmentation using FCM with spatial constraints based on new kernel-induced distance measure , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).