The Minimum Cost Connected Subgraph Problem in Medical Image Analysis

  • Markus Rempfler
  • Bjoern Andres
  • Bjoern H. Menze
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9902)


Several important tasks in medical image analysis can be stated in the form of an optimization problem whose feasible solutions are connected subgraphs. Examples include the reconstruction of neural or vascular structures under connectedness constraints.

We discuss the minimum cost connected subgraph (MCCS) problem and its approximations from the perspective of medical applications. We propose (a) objective-dependent constraints and (b) novel constraint generation schemes to solve this optimization problem exactly by means of a branch-and-cut algorithm. These are shown to improve scalability and allow us to solve instances of two medical benchmark datasets to optimality for the first time. This enables us to perform a quantitative comparison between exact and approximative algorithms, where we identify the geodesic tree algorithm as an excellent alternative to exact inference on the examined datasets.



With the support of the Technische Universität München – Institute for Advanced Study, funded by the German Excellence Initiative (and the European Union Seventh Framework Programme under grant agreement n 291763).

Supplementary material

432173_1_En_46_MOESM1_ESM.pdf (235 kb)
Supplementary material 1 (pdf 235 KB)


  1. 1.
    Türetken, E., Benmansour, F., Andres, B., et al.: Reconstructing curvilinear networks using path classifiers and integer programming. IEEE TPAMI, preprint (2016)Google Scholar
  2. 2.
    Rempfler, M., Schneider, M., Ielacqua, G.D., et al.: Reconstructing cerebrovascular networks under local physiological constraints by integer programming. Med. Image Anal. 25(1), 86–94 (2015)CrossRefGoogle Scholar
  3. 3.
    Robben, D., Türetken, E., Sunaert, S., et al.: Simultaneous segmentation and anatomical labeling of the cerebral vasculature. Med. Image Anal. 32, 201–215 (2016)CrossRefGoogle Scholar
  4. 4.
    Payer, C., et al.: Automated integer programming based separation of arteries and veins from thoracic CT images. Med. Image Anal. preprint (2016)Google Scholar
  5. 5.
    Vicente, S., Kolmogorov, V., Rother, C.: Graph cut based image segmentation with connectivity priors. In: Proceedings of CVPR, pp. 1–8 (2008)Google Scholar
  6. 6.
    Nowozin, S., Lampert, C.H.: Global connectivity potentials for random field models. In: Proceedings of CVPR, pp. 818–825 (2009)Google Scholar
  7. 7.
    Chen, C., Freedman, D., Lampert, C.H.: Enforcing topological constraints in random field image segmentation. In: Proceedings of CVPR, pp. 2089–2096 (2011)Google Scholar
  8. 8.
    Stühmer, J., Schroder, P., Cremers, D.: Tree shape priors with connectivity constraints using convex relaxation on general graphs. In: Proceedings of ICCV, pp. 2336–2343 (2013)Google Scholar
  9. 9.
    Staal, J.J., Abramoff, M.D., Niemeijer, M., et al.: Ridge based vessel segmentation in color images of the retina. IEEE TMI 23(4), 501–509 (2004)Google Scholar
  10. 10.
    Ganin, Y., Lempitsky, V.: \(N^4\)-fields: neural network nearest neighbor fields for image transforms. In: Cremers, D., Reid, I., Saito, H., Yang, M.-H. (eds.) ACCV 2014. LNCS, vol. 9004, pp. 536–551. Springer, Heidelberg (2015). doi: 10.1007/978-3-319-16808-1_36 Google Scholar
  11. 11.
    Brown, K.M., Barrionuevo, G., Canty, A.J., et al.: The DIADEM data sets. Neuroinformatics 9(2), 143–157 (2011)CrossRefGoogle Scholar
  12. 12.
    Gurobi Optimization, I.: Gurobi Optimizer Reference Manual (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Markus Rempfler
    • 1
  • Bjoern Andres
    • 2
  • Bjoern H. Menze
    • 1
  1. 1.Department of Informatics and Institute for Advanced StudyTechnical University of MunichMunichGermany
  2. 2.Max Planck Institute for InformaticsSaarbrückenGermany

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