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Image Registration

Registration tasks arise in many medical applications. Before comparing or combining the information of two images, their accurate alignment in one common frame has to be ensured. Given two images - the template image T and the reference image R - image registration aims to find an optimal transformation M(T,y), such that the transformed template and the reference become as simliar as possible. The transformation y establishes point-to-point correspondences between both images. Due to the variety of possible transformations and the sensitivity against noise, registration results in a under-determined and thus ill-posed inverse problem. In a variational setting, image registration reads

The above minimization problem can be tailored to the respective problem by specifying
  • the functional D, measuring the similarity of both images
  • the transformation model M, corresponding to the expected mis-alignment(rigid, affine, non-parametric)
  • the regularizer or smoother S, that drives the problem to a meaningful solution
  • the soft-penalizer P and the hard equality or inequality constraints, E and I, respectively


Image Fusion

Different image modalities show in general different information about the object being imaged. In medical applications the usage of multi modal images, for instance the combination of structural and functional images or two different structural images, are desired. The voxel-wise combination of both images, called image fusion, requires accurate registration. This is a non-trivial problem because a meaningful distance functional D, comparing both dissimilar images, has to be defined.

Scan 1 - original Scan 1 - corrected
Magnetic Resonance Images left: T1-weighted image, right: T2-weighted image. Institute for Biomagnetism and Biosignalanalysis, UKM Münster

Atlas-based Segmentation

Segmentation of medical images is a challenging task. In addition to image-driven approaches, there are approaches using registration. To this end, an accurate segmentation of one image, the atlas, will be generated by hand or automatically and the compartments will be labeled. Images showing the same object, can now be segmnented automatically by establishing point-to-point correspondences to the atlas.

Motion Correction of PET

In Positron Emission Tomography (PET) respiratory and cardiac motion during the acquisition (typical acquisition time 20 min) lead to blurred images. By using special acquisition schemes - called 'gating' - it is, however, possible to reconstruct images, corresponding to single respiratory or cardiac cycles. Image registration allows then the meaningful combination of all gated images in one reference phase.

Systole Motion Estimate Diastole
Cardiac gated PET images of a human heart. left: heart in diastole, right: heart in systole, center: Motion estimate. Images: European Institute for Molecular Imaging, WWU Münster

Field-inhomogeneity correction in MRI

In Magnetic Resonance imaging (MRI) an image is reconstructed using a known relationship of position and magnetic field-strength. In practice, however, the magnetic field is not homogeneous enough to relate position and field strength. This unknown inhomogeneity leads to mislocalization of the received signal. Using tailored image registration approaches and acquisition of two reversedly deformed images, it is possible to estimate and eliminate the distortions due to inhomogeneities.

Scan 1 - original Scan 1 - corrected Scan 2 - original
Spin Echo Echo-Planar-Images left and right: initial deformed and modulated images, center: corrected version. Images: Institute for Biomagnetism and Biosignalanalysis, UKM Münster


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