Motion Correction in Emission Tomography - Correction Techniques in Emission Tomography - page 167

taking a least median of squares approach at solving the over-determined lin-
ear equation system [2]. Horn{Schunck assumed a global smoothing function
to solve the image constraint equation[34]. This method was improved by El-
Feghali/Mitchie to preserve boundaries by weighting the smoothing term [24].
Deriche et al improved the Horn{Schunck algorithm by using a non-quadratic
function for smoothing [20]. A different method was proposed by Alvarez et
al. [1] who improved the algorithm by Nagel/Enkelmann by using a brightness
invariant term into consideration. Thus if two images differ in contrast by a
constant factor, their method can still estimate the flow correctly. The local
and global methods were combined by Vemuri et al. to register medical images
[65]. Lastly, Bruhn et al. [8] have given a framework for combined local and
global optical flow algorithms.
Other approaches to optical flow estimation include the mass conserva-
tion method [56],[59], uid mechanics{based method [12], or approaches using
higher order constraints on flow [27].
The gradient-based algorithms for optical flow estimation achieve high ac-
curacy and flexibility. It is thus no wonder that most of the research has
been done in the area of gradient-based methods. The image volumes recon-
structed from the PET data after appropriate gating contain equal amounts
of radioactivity. As all gates contain data from almost all breathing cycles,
the basic image constraint equation is fulfilled in the PET data. Thus the
gradient-based methods can be applied to our problem readily.
8.3.3 Optical flow in medical imaging
Medical imaging has also been a fertile field for the use of optical flow
methods. Most of the applications in this respect are concerned with motion
detection, registration and image segmentation on medical images. Modalities
that have benefited from optical flow applications include, but are not confined
to, magnetic resonance imaging (MRI), computed tomography (CT), positron
emission tomography (PET) and ultrasound (US) imaging.
Hata et al. used optical flow to measure the deformations between MRI
images of the brain taken before, during and after brain surgery [33]. Zientara
et al. used optical flow to measure dilation and contraction of liver tissue dur-
ing laser ablation on MRI images [68]. Another application was to estimating
cardiac displacements in tagged MRI images [21],[54]. Optical flow has been
used to segment heart on gated MRI images by Galic et al. [29]. Recently
successful tracking of endocardium on MRI images was shown by Duan et al.
[22].
On the CT side, Song et al. [59] and Gorce et al. [32] used optical flow
to estimate 3D velocity fields on CT cardiac images. A study by Torigian
et al. suggests use of optical flow for assessing regional air trapping in lung
CT images acquired in inspiration and expiration phases [62]. A method for
prospective motion correction of X-ray imaging of the heart was presented by
Shechter et al. [58].