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

36 Chapter 2. Extraction of Tubular Structures
have a parameter that can be adapted to the expected contrast. As shown from the results,
with the methods of Krissian and Pock the responses depend linearly on the contrast, while
with the other approaches the response saturates above the expected contrast and starts
decreasing with lower contrast than the expected one. One may argue that the methods
of Krissian and Pock do not require an adaption to the expected contrast, however, on
the other side this implies that for extraction of the tubular structures it is necessary
to adapt thresholds on the TDF response appropriately to achieve a discrimination from
noise responses. Morover, because of this behavior the methods of Krissian and Pock also
produce strong responses to structures with a strong contrast, even in case the structure
itself strongly deviates from a tubular shape. In contrast to that, the method of Frangi
and the GVF-based method produce normalized results allowing to use the same set of
parameters for extraction of the actual tubular structures.
Varying noise level: The datasets provided by Aylward et al. ‡ [2], see Fig. 2.10, contains
a tortuous, branching, tubular object with vanishing radius. The contrast between
the tubular object and the background ranges from 100 at the center of the tube to 50 at
the tube’s edge. The datasets were corrupted with additive Gaussian noise with increasing
standard deviations η of 10, 20, 40 and 80. “The η = 20 data is representative of the noise
level in MR and CT data. The η = 40 data more closely resembles the noise magnitude
of ultrasound data. [...] The η = 80 images are well beyond any worst case number [...]
for any clinically acceptable MRA, CT, or ultrasound data.”[2].
For Frangi’s method and the GVF-based methods, the noise-sensitivity parameters,
c and F max , respectively, were adapted on the low noise dataset (η = 10). As already
mentioned above, the methods of Krissian and Pock do not allow controlling the influence
of contrast on the filter response. As a result, with these methods the response to image
noise increases with an increasing noise level. The GVF-based approaches produce clean
responses at the centers of the tubular objects even under high (clinically acceptable) noise
levels (η = 10, 20, and 40), although for noise reduction only a Gaussian smoothing with
a very small variance (σ = 1.0) was used. This shows that in practice only a Gaussian
smoothing with a very small variance is necessary. Computation of gradient information on
a large scale as done by the Gaussian scale space based methods is not necessary to account
for image noise. However, in case of insufficient noise suppression the GVF-based method
with the central medialness function produces unsatisfying results, while the GVF-based
method with the offset medialness function shows a slightly better behavior, as shown in
‡ http://ij.itk.org/midas/item/view/1065