Using the Fourth Dimension to Distinguish Between Structures for Anisotropic Diffusion Filtering in 4D CT Perfusion Scans - Longitudinal Registration and Shape Modeling - page 74

venograms, if the filter is designed to enhance vascular structures. Several noise
reduction methods [ 7 - 9 ] have been proposed in the literature for filtering 4D
datasets. However, these methods are either based on non-local means or bilat-
eral filtering, and they are not designed to enhance certain types of structures
during filtering.

Anisotropic diffusion [ 10 , 11 ], on
the other hand, can be designed to
enhance certain types of structures.
Montagnat [ 12 ] et al. proposed a 4D
anisotropic diffusion filter for echocar-
diographic images. For each voxel in
the 4D dataset, the 4D gradient is
determined. If the gradient magni-
tude is larger than a certain thresh-
old, diffusion is reduced (based on
the diffusion function) in the direc-
tion of the gradient, but high in the
directions orthogonal to the gradi-
ent. This method is an extension of
edge-enhancing diffusion (EED) [ 11 ]
to four dimensions. It is, however,
insucient for filtering the 4D CTP
scans, in which the vessels show a
large intensity change over time, due
to the inflow and wash-out of contrast
material. The gradient will therefore
point in the direction of the temporal
dimension (highest gray level fluctua-
tion). Diffusion will be reduced in the
direction of the gradient, but will be
high in the directions orthogonal to
the gradient, blurring the vessel edges,
instead of enhancing them. Therefore,
we propose to use a 3D diffusion ten-
sor and filter each time volume sep-
arately. However, the eigenvectors and eigenvalues of the diffusion tensor are
adjusted according to the difference between the time intensity profiles in the
fourth dimension. Previous approaches [ 13 , 14 ] did propose to filter each time
volume separately, but applied isotropic diffusion and therefore only adjusted
the conductance parameter according to the fourth dimension. Our approach
enables full anisotropic diffusion by determining the first order derivatives based
on the difference between the time intensity profiles.

350

300

Artery

250

Vein

200

150

100

50

0

−50

0 10 20 30 40 50

Time (s)

Fig. 1. Time-intensity profiles within a 4D
CTP scan of voxels in an artery and a
vein located close to each other as illus-
trated in the top image. If values would
be averaged across the spatial and tempo-
ral dimension (i.e. red/blue dots) to reduce
noise, the shape of the time-intensity pro-
files will change. However, for automatically
separating the arteries and veins based on
the time-intensity profiles, it is important
that the shape of these profiles is preserved.
The arrow indicates a point in time when
the intensity value of the artery is similar
to the intensity value of the vein.