Multi-atlas Segmentation Using Patch-Based Joint Label Fusion with Non-Negative Least Squares Regression

  • Mattias P. HeinrichEmail author
  • Matthias Wilms
  • Heinz Handels
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9467)


This work presents a patch-based multi-atlas segmentation approach based on non-negative least squares regression. Our approach finds a weighted linear combination of local image patches that best models the target patch, jointly for all considered atlases. The local coefficients are optimised with the constraint of being positive or zero and serve as weights, of the underlying segmentation patches, for a multi-atlas voting. The negative influence of erroneous local registration outcome is shown to be reduced by avoiding negative weights. For challenging abdominal MRI, the segmentation accuracy is significantly improved compared to standard joint least squares regression and independent similarity-based weighting. Our experiments show that restricting weights to be non-negative yields significantly better segmentation results than a sparsity promoting \(\ell _1\) penalty. We present an efficient numerical implementation that rapidly calculates correlation matrices for all overlapping image patches and atlases in few seconds.


Linear regression Generative model Cross-correlation 



We are very grateful to H. Matuschek (University of Potsdam) for making available an efficient implementation for non-negative least square optimisation within the Eigen3 library (


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Mattias P. Heinrich
    • 1
    Email author
  • Matthias Wilms
    • 1
  • Heinz Handels
    • 1
  1. 1.Institute of Medical InformaticsUniversity of LübeckLübeckGermany

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