Motion Correction in Emission Tomography - Correction Techniques in Emission Tomography - page 176

FIGURE 8.7: The optical flow calculated with the proposed method. A
coronal slice is shown with superimposed vectors. Only two components of
the ow are shown.

for this purpose. As the time derivative I t was calculated as I 2 I 1 and the
flow u is now assumed to be known, the transformed image can be calculated
as

I 2mc = I 2 + div(I 2 u): (8.19)

Applying this equation, the deformed (motion corrected) images can be readily
calculated from the floating images.
The motion correction methods described above have been applied to real
patient data and their performance measured with various methods. Different
aspects such as noise levels, extent of motion, pattern of breathing, etc. were
taken into account, too. The results showed that the discontinuity preserv-
ing method performed well on real patient data. The respiratory motion was
detected and correspondingly corrected to well below voxel size levels [15][16].
An example of the application of the brightness consistency based optical
flow applied to PET data is shown in Figure 8.8. The left column shows,
from top to bottom, the target phase, the floating phase and the floating
phase after motion correction, respectively. The white line on the images helps
assess the position of the heart and diaphragm. It shows that the heart and
the diaphragm are displaced downwards and a little to the left (on images)
as the patient inhales from target to floating phases. The motion-corrected
version has all image parts in the same position as in the target phase. In the
right column of the figure half of the estimated flow vectors are shown.