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

66 Chapter 4. Tube Segmentation
Only a few methods in the literature have addressed the issue of utilizing known
structural information to obtain accurate segmentations of tubular tree structures in a
topology preserving way. Deformable models are the most common approach [43, 103,
104, 151, 165, 172]. In very recent works, approaches based on graph-cuts [127] and
optimal surface finding [32] were applied.
In the last few chapters, we presented methods utilizing properties of the GVF for
detection of tubular objects (Section 2.3) and for grouping/linkage of tubular objects
into tree structures (Section 3.3). However, the GVF was originally presented to guide
snake based segmentations [168]. But properties of the GVF (or similar gradient diffusion
methods) have also been used to generate voxel accurate 2D and 3D segmentations without
using snakes [22, 82, 129, 174]. For example, Li et al. [80] used a gradient flow tracking in
the GVF field in combination with a locally adaptive thresholding scheme based on gray
value statistics to segment blob like 3D structures. But to our knowledge, none of the so
far presented methods is directly applicable for segmentation of tubular structures.
In the next two sections, we present two different methods to obtain accurate segmentations
associated with already known tubular structures that preserve the topology.
Therefor, two methods are presented. The first utilizes the same GVF field as utilized
for the tube detection approach (Section 2.3) and the second utilizes a graph cut based
approach that performs a segmentation in a globally optimal fashion.
4.2 Inverse Gradient Vector Flow Tracking
To achieve an accurate segmentation of the tubular structures identified in a GVF field
by using the approach from Section 2.3, we present in this section a method that can
be directly applied to the same already obtained GVF field. As we have seen in Section
2.3.3, the GVF-based approach may be adapted to varying background conditions.
In case of varying background conditions and arbitrary edge types, the initial vector field
is obtained from a gradient magnitude image, while for tubular structures surrounded by
the dark/bright background the initial vector field for the GVF is obtained directly from
the gray value images. For the tube segmentation method presented in this section, we
also have to distinguish between these two cases.
Considering the GVF field V (x) of a tubular structure as illustrated in Fig. 4.1, all
the vectors flow towards the centers of the tubular structures, which correspond to the
extracted centerlines of the tubular structures (in case of tubular objects). By following the
direction V n (x) = V (x)/|V (x)| of the vectors, each voxel can be assigned to a neighboring