Introduction - Motion Correction in Thoracic Positron Emission Tomography - page 17

1.5.3.1 CT

The compressibility of the lungs makes motion estimation in CT lung images
challenging. A mass-preserving registration framework was applied to such data
in [ 138 ] to compensate for tissue compression. The proposed multi-resolution
B-spline approach includes an essential additional mapping of the Hounsfield units
to density values. A similar approach for CT lung registration is proposed in [ 57 ].

1.5.3.2 MRI

Field inhomogeneities lead to image degradation in MRI, particularly in Echo Planar
Imaging (EPI) sequences. Mislocalizations along the read-out direction are suc-
cessfully corrected with a mass-preserving transformation model in [ 27 , 104 , 118 ].
A peculiarity of the proposed method is the simultaneous application of the same
transformation to two corresponding reference scans but with reversed direction.

1.5.3.3 SPECT

The expansion ratio characterizes the ratio of volume change of the heart in
cardiac SPECT. In order to achieve the preservation of the overall radioactivity the
expansion ratio was incorporated into the objective function for motion estimation
in [ 91 , 129 ] by rescaling the pixel intensity in accordance with the wall thickening.
The proposed deformable mesh model is based on a left-ventricle surface model.

1.5.3.4 PET

For PET, we proposed two approaches for mass-preserving motion estimation with
the Variational Algorithm for Mass-Preserving Image REgistration (V AMPIRE )[ 50 ,
51 ] and the Mass-Preserving Optical Flow (MPOF) approach [ 33 , 37 ]. Both methods
compensate for tissue compression and, more importantly, allow the matching
of corresponding points with PVE disturbed intensities. The second property
distinguishes the application of mass-preserving motion estimation methods to PET
data compared to CT or MRI. Note, however, that these methods could also be
applied to SPECT data for the same reasons.
V AMPIRE and MPOF account for the preservation of mass with a specifically
designed transformation model considering the volume change induced by the
estimated transformation. The same effect could also be achieved by utilizing a
forward mapping as proposed by Klein [ 71 , 72 ]. However, as such a transformation
model is not necessarily surjective, a sampling of each point in the reference domain
is not guaranteed. Furthermore, a complicated energy function with numerous local