A Fast Projection Method for Connectivity Constraints in Image Segmentation

  • Jan Stühmer
  • Daniel Cremers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8932)


We propose to solve an image segmentation problem with connectivity constraints via projection onto the constraint set. The constraints form a convex set and the convex image segmentation problem with a total variation regularizer can be solved to global optimality in a primal-dual framework. Efficiency is achieved by directly computing the update of the primal variable via a projection onto the constraint set, which results in a special quadratic programming problem similar to the problems studied as isotonic regression methods in statistics, which can be solved with O(n logn) complexity. We show that especially for segmentation problems with long range connections this method is by orders of magnitudes more efficient, both in iteration number and runtime, than solving the dual of the constrained optimization problem. Experiments validate the usefulness of connectivity constraints for segmenting thin structures such as veins and arteries in medical image analysis.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jan Stühmer
    • 1
  • Daniel Cremers
    • 1
  1. 1.Department of Computer ScienceTechnische Universität MünchenGermany

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