A Variational Approach for Volume-to-Slice Registration

  • Stefan Heldmann
  • Nils Papenberg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5567)


In this work we present a new variational approach for image registration where part of the data is only known on a low-dimensional manifold.

Our work is motivated by navigated liver surgery. Therefore, we need to register 3D volumetric CT data and tracked 2D ultrasound (US) slices. The particular problem is that the set of all US slices does not assemble a full 3D domain. Other approaches use so-called compounding techniques to interpolate a 3D volume from the scattered slices. Instead of inventing new data by interpolation here we only use the given data.

Our variational formulation of the problem is based on a standard approach. We minimize a joint functional made up from a distance term and a regularizer with respect to a 3D spatial deformation field. In contrast to existing methods we evaluate the distance of the images only on the two-dimensional manifold where the data is known. A crucial point here is regularization. To avoid kinks and to achieve a smooth deformation it turns out that at least second order regularization is needed.

Our numerical method is based on Newton-type optimization. We present a detailed discretization and give some examples demonstrating the influence of regularization. Finally we show results for clinical data.


Distance Measure Image Registration Variational Approach Nodal Discretization Slice Data 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Stefan Heldmann
    • 1
  • Nils Papenberg
    • 1
  1. 1.Institute of MathematicsUniversity of LübeckGermany

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