Using the Fourth Dimension to Distinguish Between Structures for Anisotropic Diffusion Filtering in 4D CT Perfusion Scans - Longitudinal Registration and Shape Modeling - page 79

the intensity value of the arteries and veins is similar at a certain point in time
(arrow in Figure 1 ), the structure tensor of the TIPS anisotropic diffusion filter
will not be disturbed. Since the similarity between the time-intensity profiles
(fourth dimension) is used to distinguish between structures, both the arteries
and veins will be detected as separate tubular like structures and diffusion will
be performed accordingly.
The use of this principle is not limited to the HDCS filter, but can be used
for all diffusion based filtering techniques, such as plain EED [ 10 ]orCED[ 17 ].
It could even be used for other derivative based methods, such as VED [ 20 ]
or the vesselness filter [ 21 ], if the 1st-order derivatives would be substituted by
2nd-order derivatives and the structure tensor by the Hessian. Another way of
extending anisotropic diffusion methods to four dimensions, is by adding another
dimension to the structure and diffusion tensor, like Montagnat [ 12 ]proposedfor
4D cylindrical echocardiographic images. However, most of these filters would
then lose the very properties that made them successful in the first place. The key
to our approach is that we provide a way to exploit the additional information
(fourth dimension) present in the 4D CTP data, and still profit from the benefits
of the various anisotropic diffusion filters or vesselness filters. The similarity
measure between the time-intensity profiles is also not limited to the sum of
squared difference (SSD) used in this paper, but the SSD typically increases the
contrast between similar and non-similar profiles.
A limitation of our study was that we did not compare our approach to
for example the TIPS bilateral filter [ 9 ]. Bilateral filters and non-local mean
filters have been proven to work very well, and have the advantage of being
less time consuming. However these methods lack the property of directional
smoothing that anisotropic diffusion based methods do have. This is illustrated
by Weickert in his fingerprint example (Figure 2 in [ 17 ]), in which he illustrates
that CED is able to connect the interrupted lines in a fingerprint image. CED was
incorporated in the HDCS filter [ 9 ] that was evaluated in this paper, to be able to
connect small vessels that were interrupted by noise. Therefore, our hypothesis
was that the TIPS HDCS filter would increase the visibility of small arteries
and veins without degrading the larger arteries and veins. The observer study
confirmed our hypothesis. The results showed that the signal to noise ratio in
the CTP data improved significantly. The effect of filtering was most pronounced
in the small arteries and veins that were lost in the noise in the original data.
The observers indicated in the majority of the cases that more small arteries
and veins were visible after filtering and the quality was better. Future work
consists of comparing TIPS anisotropic diffusion to the TIPS bilateral filter to
confirm our hypothesis that the anisotropic diffusion filter is better able to filter
the small vessels than the bilateral filter.
In conclusion, in this paper we have shown that arteries and veins can be
enhanced and noise reduced, by using the similarity between the time-intensity
profiles (fourth dimension) to distinguish between structures for anisotropic
hybrid diffusion in 4D CT perfusion scans.