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

40 Chapter 2. Extraction of Tubular Structures
the utilization of TDFs has not been considered so far.
However, as the GVF-based approaches only respond at the center of the tubular
structures, these methods are not so suitable for visualization tasks where the TDFs are
utilized for vessel enhancement, as is the case with Frangi’s method. Also, the response
of the GVF-based methods falls off completely in case a minimum contrast-to-noise ratio
in the initial vector field is not given, while with the approaches of Krissian and Pock the
response only decreases. Therefore, it may be necessary for some applications to use combinations
of the GVF-based approach for sufficiently contrasted tubes and a conventional
TDF computed only on a very small scale for the identification of thinner low contrast
tubular structures in noisy datasets.
TDFs compute a tube-likeliness measure independently for each voxel of the image domain.
This makes them ideally suited for GPU implementations and thus allows achieving
low computation times. The Gaussian scale space based methods obtain a tube-likeliness
measure for each voxel at multiple scales, meaning that their computation time depends
linearly on the number of voxels and the number of used scales. With the GVF-based approach
on the other hand, the tube-likeliness has to be computed only once for each voxel
while the main computation time is on behalf of the GVF that has to be computed only
once; the GVF is also easily parallelizeable and can be implemented on the GPU. Using
such GPU based implementations of the TDFs, the computation times on typical volume
datasets remain in the range of seconds to maybe few minutes on large datasets. E.g. on a
CT dataset with an axis aligned bounding box surrounding only the liver (380 × 425 × 210
voxels), the computation time for the TDF of Pock et al. [114] is about 10 seconds when
computed on 10 scales and the computation time for the GVF-based approach with the
offset medialness function (Section 2.3.2) is about 15 seconds, using an NVIDIA GeForce
8800 GTX in both cases.
All TDFs have in common that the output (the tube-likeliness measure) decreases due
to deviations from the assumptions about the tubular structures or decreasing contrast.
In addition, the methods may also show some slight response to noise. Extracting tubular
structures from the tube-likeliness images requires appropriate thresholding of this tubelikeliness.
However, in particular in regions of the tubular trees that strongly deviate from
a typical tube shape (e.g. junctions, stenosis) the tube-likeliness is as low or lower as in
the noise image regions such that a discrimination of these cases based on thresholding
is not possible. The presented height-ridge traversal with the incorporated hysteresis
thresholding accounts for this problem to some extend and tolerates slight variations from