Journal of Signal Processing Systems

, Volume 81, Issue 1, pp 45–58 | Cite as

Two Fast and Robust Modified Gaussian Mixture Models Incorporating Local Spatial Information for Image Segmentation

  • Hui Zhang
  • Tian Wen
  • Yuhui Zheng
  • Danhua Xu
  • Dingcheng Wang
  • Thanh Minh Nguyen
  • Q. M. Jonathan WuEmail author


The Gaussian Mixture Model (GMM) with the spatial constraint, e.g. Hidden Markov Random Field (HMRF), has been proven effective for image segmentation. The parameter β in the HMRF model is used to balance between robustness to noise and effectiveness of preserving the detail of the image. In other words, the determination of parameter β is, in fact, noise dependent to some degree. In this paper, we propose a simple and effective algorithm to make the traditional Gaussian Mixture Model more robust to noise, with consideration of the relationship between the local spatial information and the pixel intensity value information. The conditional probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the spatial and the intensity information. In this case, the parameter β can be assigned to a small value to preserve image sharpness and detail in non-noise images. Meanwhile, the neighborhood window is used to tolerate the noise for heavy-noised images. Thus, the parameter β is independent of image noise degree in our model. Furthermore, we propose another algorithm for our modified GMM (MGMM) with the simplification of conditional probability computation (MGMM_S). Finally, our algorithm is not limited to GMM – it is general enough so that it can be applied to other distributions based on the construction of the Finite Mixture Model (FMM) technique. Experimental results of synthetic and real images demonstrate the improved robustness and effectiveness of our approach.


EM algorithm Gaussian Mixture Model HMRF Image segmentation Local information Spatial constraints 



This work was supported in part by the Canada Chair Research Program and the Natural Sciences and Engineering Research Council of Canada. This work was supported in part by the National Natural Science Foundation of China under Grant 61105007 and 61103141. This work was supported in part by PAPD (A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions). This work was supported in part by the Natural Science Foundation of Jiangsu Province NO. BK2012858. This work was supported in part by the Innovation Fund of China Academy of Space Technology: CAST201302.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Hui Zhang
    • 1
    • 3
    • 4
  • Tian Wen
    • 2
  • Yuhui Zheng
    • 1
    • 3
  • Danhua Xu
    • 1
    • 3
  • Dingcheng Wang
    • 1
    • 3
  • Thanh Minh Nguyen
    • 4
  • Q. M. Jonathan Wu
    • 1
    • 4
    Email author
  1. 1.School of Computer & SoftwareNanjing University of Information Science & TechnologyNanjingChina
  2. 2.JiangSu Provincial Center for Disease Prevention and ControlNanjingChina
  3. 3.Jiangsu Engineering Center of Network MonitoringNanjing University of Information Science & TechnologyNanjingChina
  4. 4.Department of Electrical and Computer EngineeringUniversity of WindsorWindsorCanada

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