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A SOM-based Chan–Vese model for unsupervised image segmentation

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Abstract

Active Contour Models (ACMs) constitute an efficient energy-based image segmentation framework. They usually deal with the segmentation problem as an optimization problem, formulated in terms of a suitable functional, constructed in such a way that its minimum is achieved in correspondence with a contour that is a close approximation of the actual object boundary. However, for existing ACMs, handling images that contain objects characterized by many different intensities still represents a challenge. In this paper, we propose a novel ACM that combines—in a global and unsupervised way—the advantages of the Self-Organizing Map (SOM) within the level set framework of a state-of-the-art unsupervised global ACM, the Chan–Vese (C–V) model. We term our proposed model SOM-based Chan–Vese (SOMCV) active contour model. It works by explicitly integrating the global information coming from the weights (prototypes) of the neurons in a trained SOM to help choosing whether to shrink or expand the current contour during the optimization process, which is performed in an iterative way. The proposed model can handle images that contain objects characterized by complex intensity distributions, and is at the same time robust to the additive noise. Experimental results show the high accuracy of the segmentation results obtained by the SOMCV model on several synthetic and real images, when compared to the Chan–Vese model and other image segmentation models.

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Notes

  1. For both simplicity and uniformity of notation, in writing (4) and other PDEs, we do not show explicitly the arguments of the functions, which are already specified in other parts of the paper.

  2. In this paper, training pixels from one image are considered in the training session of the SOMCV and \(SOMCV_s\) models. Such an image is either identical or similar to the image presented in the testing session. In the first case, using even identical images for the training and testing sessions is not a limitation of the models: one of the reasons is that the training is unsupervised.

  3. Instead of sequential training, batch training (Vesanto et al. 2000) of the SOM may also be used for a faster convergence.

  4. This choice of the function \(h_{bn}(t)\) implies that, for fixed t, when \(\Vert r_{b}-r_{n}\Vert \) increases, \(h_{bn}(t)\) decreases to zero gradually to smooth out the effect of the BMU neuron on the weights of the neurons far from the BMU neuron itself, and when t increases, the influence of the BMU neuron becomes more and more localized.

  5. The developed code is available at http://mohammedabdelsamea.weebly.com.

  6. In the experiments presented in Figs. 3 and 8, also the choice \(\sigma =.5\) was considered, together with \(\sigma = 1.5\).

  7. Since in the paper we are interested in unsupervised ACMs, we have not compared the proposed SOMCV model to the SOM-based ACMs proposed in Abdelsamea et al. (2014) and Abdelsamea et al. (2015), which are supervised models.

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Authors and Affiliations

  1. Department of Mathematics Faculty of Science, University of Assiut, Assiut, 71516, Egypt

    Mohammed M. Abdelsamea

  2. IMT Institute for Advanced Studies, Piazza S. Ponziano 6, 55100, Lucca, Italy

    Giorgio Gnecco

  3. Robert Gordon University, Aberdeen, UK

    Mohamed Medhat Gaber

Authors
  1. Mohammed M. Abdelsamea
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  2. Giorgio Gnecco
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  3. Mohamed Medhat Gaber
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Corresponding author

Correspondence to Giorgio Gnecco.

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The authors declare that they have no conflict of interest.

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Communicated by V. Loia.

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Abdelsamea, M.M., Gnecco, G. & Medhat Gaber, M. A SOM-based Chan–Vese model for unsupervised image segmentation. Soft Comput 21, 2047–2067 (2017). https://doi.org/10.1007/s00500-015-1906-z

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