ABSTRACT
European Institute for Molecular Imaging, University of Mu¨nster, Mu¨nster, Germany
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 8.1.1 Magnitude of motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.1.1.1 Patient motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.1.1.2 Respiratory motion . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 8.1.1.3 Cardiac motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
8.2 Motion correction on 3D PET data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 8.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 8.2.2 Rigid motion correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 8.2.3 Elastic motion correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
8.3 Optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3.1 Image constraint equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 8.3.2 Optical flow methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 8.3.3 Optical flow in medical imaging . . . . . . . . . . . . . . . . . . . . . . . . . 167
8.4 Lucas-Kanade optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 8.5 Horn-Schunck optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 8.6 Bruhn optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 8.7 Preserving discontinuities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 8.8 Correcting for motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173 8.9 Mass conservation-based optical flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174
8.9.1 Correcting for motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
Motion is a major cause of image distortion and degradation in emission tomography. The foremost effect of motion on the reconstructed images is the induction of blur which is proportional in magnitude to the amount of motion causing it. Small objects or those with low contrast may thus become invisible
as the activity is spread over a larger image volume. It has been shown that the respiratory motion may lead to incorrect staging of tumors [25]. Small tumors may even succeed in evading detection [50]. In addition to image blur, another disadvantage of motion has been observed and quantified in recent years on PET images: attenuation artifacts in the case of hybrid scanners where CT-or MRI-based attenuation maps are used for attenuation correction of the PET data.
