Segmentation of 3D Tubular Tree Structures in Medical Images ...

2.5. Experiments 35
However, the approach of Krissian does not produce any response between these closely
tangenting tubular objects in Fig. 2.7(e), in contrast to the example in Fig. 2.6(d) where
it did.
This behavior deserves a closer investigation and explanation. With Pock’s approach
two different scale spaces are utilized where the scale at which the boundary information
is obtained depends on a parameter η. Moreover, the relation between the radius of the
tubular objects and the boundary information is non-linear (σ P 2 = r η with 0.0 ≤ η ≤ 1.0
as explained in Section 2.2.2), meaning that the response also depends on the size of the
tubular objects explaining the different results between the two figures. The approach of
Pock addresses the problem of the pure Gaussian scale space methods (Frangi, Krissian),
by computing the boundary information on a smaller scale. However, this computation
of the boundary information on a smaller scale represents a tradeoff with this method
as illustrated in Fig. 2.8. Computing the boundary information on a too large scale, the
method shows the same problems as Krissians approach and produces responses between
the tubular objects (Fig. 2.8(a)), while computing the boundary information on a too small
scale, the method can not account for deviations from a perfectly circular cross section
(e.g. ellipsoidal) (Fig. 2.8(b)).
50
50
0
0
0 200 400 600 800 1000 1200 1400 1600 18000 200 400 600 800 1000 1200 1400 1600 1800
(a) Response of Pock’s method [114] using
very large η = 1.0.
(b) Response of Pock’s method [114] using
very small η = 0.0.
Figure 2.8: Influence of η on the TDF response with Pock’s method [114] for the tubular
structures shown in Fig. 2.7(a).
With the GVF-based approaches this tradeoff does not exist. The edge information is
computed on a very small scale and the GVF diffuses the gradient information, thus making
it still possible to produce reasonable responses to slight variations from a perfectly circular
cross section profile (ellipsoid). The method of Pock and the GVF-based approaches do not
produce any response for surface patches contrary to the methods of Frangi and Krissian.
Varying contrast level: In Fig. 2.9 the effect of varying contrast is shown. For the
TDF of Frangi and the GVF-based methods the parameters were adapted accordingly to
the contrast indicated by the dotted line, while the methods of Krissian and Pock do not