International Journal of Computer Vision

, Volume 71, Issue 3, pp 361–372 | Cite as

Image Registration with Guaranteed Displacement Regularity

  • Eldad HaberEmail author
  • Jan Modersitzki
Short Paper


The goal of image registration is twofold. One goal is to enforce a certain similarity of two images by geometrically transforming one of the images. The second goal is to keep this transformation meaningful or regular. There exists a large amount of approaches aiming for regularity. Most of those are based on certain regularization techniques, others use so-called regridding options.

Here, we present a mathematically sound formulation that explicitly controls the deformation in terms of the determinant of the Jacobian of the transformation. In contrast to similar work, we use pointwise inequality constraints, i.e., the volume is controlled voxel by voxel and not by integral measures. This approach guaranties grid regularity and prevent folding.

As it turns out, the discretization of the volume constraint inequality is not straightforward. Therefore, we present a new type of discretization enabling the detection of twists in a pixel or a voxel. Such detection is crucial since a twists indicates that a transformation is physically meaningless.

To solve the large-scale inequality constrained optimization problem, we present a numerical approach based on an interior point method. We finally present some numerical examples that demonstrate the advantage of including inequality constraints explicitly.


image registration image matching image fusion variational approach constrained optimization 


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Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEmory UniversityAtlanta
  2. 2.Institute of MathematicsUniversity of LübeckGermany

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