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Spatially Varying Mixtures Incorporating Line Processes for Image Segmentation

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Abstract

Spatially varying mixture models are characterized by the dependence of their mixing proportions on location (contextual mixing proportions) and they have been widely used in image segmentation. In this work, Gauss-Markov random field (MRF) priors are employed along with spatially varying mixture models to ensure the preservation of region boundaries in image segmentation. To preserve region boundaries, two distinct models for a line process involved in the MRF prior are proposed. The first model considers edge preservation by imposing a Bernoulli prior on the normally distributed local differences of the contextual mixing proportions. It is a discrete line process model whose parameters are computed by variational inference. The second model imposes Gamma prior on the Student’s-t distributed local differences of the contextual mixing proportions. It is a continuous line process whose parameters are also automatically estimated by the Expectation-Maximization (EM) algorithm. The proposed models are numerically evaluated and two important issues in image segmentation by mixture models are also investigated and discussed: the constraints to be imposed on the contextual mixing proportions to be probability vectors and the MRF optimization strategy in the frameworks of the standard and variational EM algorithm.

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Authors and Affiliations

  1. Department of Computer Science, University of Ioannina, 45110, Ioannina, Greece

    Giorgos Sfikas & Christophoros Nikou

  2. Department of Electrical and Computer Engineering, University of Patras, 26500, Rio, Greece

    Nikolaos Galatsanos

  3. Laboratoire des Sciences de l’Image de l’Informatique et de la Télédétection / LSIIT, UMR CNRS-ULP 7005, University of Strasbourg, BP 67412, Illkirch cedex, France

    Giorgos Sfikas & Christian Heinrich

Authors
  1. Giorgos Sfikas
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  2. Christophoros Nikou
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  3. Nikolaos Galatsanos
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  4. Christian Heinrich
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Correspondence to Christophoros Nikou.

Additional information

Giorgos Sfikas was supported by a grant from Région Alsace (France).

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Sfikas, G., Nikou, C., Galatsanos, N. et al. Spatially Varying Mixtures Incorporating Line Processes for Image Segmentation. J Math Imaging Vis 36, 91–110 (2010). https://doi.org/10.1007/s10851-009-0174-x

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