Mean Field Network Based Graph Refinement with Application to Airway Tree Extraction

  • Raghavendra SelvanEmail author
  • Max Welling
  • Jesper H. Pedersen
  • Jens Petersen
  • Marleen de Bruijne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11071)


We present tree extraction in 3D images as a graph refinement task, of obtaining a subgraph from an over-complete input graph. To this end, we formulate an approximate Bayesian inference framework on undirected graphs using mean field approximation (MFA). Mean field networks are used for inference based on the interpretation that iterations of MFA can be seen as feed-forward operations in a neural network. This allows us to learn the model parameters from training data using back-propagation algorithm. We demonstrate usefulness of the model to extract airway trees from 3D chest CT data. We first obtain probability images using a voxel classifier that distinguishes airways from background and use Bayesian smoothing to model individual airway branches. This yields us joint Gaussian density estimates of position, orientation and scale as node features of the input graph. Performance of the method is compared with two methods: the first uses probability images from a trained voxel classifier with region growing, which is similar to one of the best performing methods at EXACT’09 airway challenge, and the second method is based on Bayesian smoothing on these probability images. Using centerline distance as error measure the presented method shows significant improvement compared to these two methods.


Mean field network Tree extraction Airways CT 



This work was funded by the Independent Research Fund Denmark (DFF) and Netherlands Organisation for Scientific Research (NWO).


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Raghavendra Selvan
    • 1
    Email author
  • Max Welling
    • 2
    • 3
  • Jesper H. Pedersen
    • 4
  • Jens Petersen
    • 1
  • Marleen de Bruijne
    • 1
    • 5
  1. 1.Department of Computer ScienceUniversity of CopenhagenCopenhagenDenmark
  2. 2.Informatics InstituteUniversity of AmsterdamAmsterdamNetherlands
  3. 3.Canadian Institute for Advanced ResearchTorontoCanada
  4. 4.Department of Cardio-Thoracic Surgery RTUniversity Hospital of CopenhagenCopenhagenDenmark
  5. 5.Departments of Medical Informatics and RadiologyErasmus Medical CenterRotterdamNetherlands

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