Biomedical Engineering Reference
In-Depth Information
8.2.3.6
Displaced Frame Difference and Optical Flow
The displaced frame difference (DFD) measures the difference between
voxel intensities. It can be used either directly [1, 101, 144] or linearized
(known as optical flow) [46, 76, 125]. The DFD is known to be highly non-
linear whereas optical flow is linear. However, optical flow is only valid for
small displacements and can estimate motion only in the direction of the
image gradient (aperture problem). In both cases, this similarity will not
be valid if luminance is not conserved (this may happen because of im-
age acquisition, acquisition systems or parameters, MR inhomogeneities and
so on).
Close to mechanical approaches, Song and Leahy [125] and Devlaminck
[46] have proposed to estimate the optical flow with a mechanical reg-
ularization. More specifically, when images are density images (the lumi-
nance is directly related to a physical quantity), the mass conservation hy-
pothesis may be introduced to constraint the estimation in a plausible way
[37, 125].
In the field of cardiac imaging, Reissmann
et al.
[112] have proposed to use
the neuractive pyramid to register images using the optical flow. The elastic grid
that is the kernel of the deformation deforms so as to reject the discontinuities
at boundaries of the grid. The minimization is therefore alternated between the
deformation and the optimal shape of the grid.
The SPM spatial normalization approach [2] estimates warps by matching
each skull-stripped image to the skull-stripped reference. Registration involves
minimizing the mean squared difference between the images, which had been
previously smoothed by convolving with an isotropic 8 mm FWHM Gaussian
kernel. The non-rigid deformation is modeled by a linear combination of low-
frequency cosine transform basis functions [2]. Displacements in each direction
are parameterized by 392 basis function coefficients, making a total of 1176
parameters in total. Regularization is obtained by minimizing the membrane
energy of the warps.
Vemuri [144] also uses the optical flow but models the deformation as a
combination of splines similarly to [127]. Finally, Musse
et al.
[101] describe a
hierarchical method to estimate the deformation using the SSD criterion. The
solution is sought as a combination of the spine's functions that ensure the
regularity of the solution.
