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

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Chapter 2<br />

Extraction <strong>of</strong> <strong>Tubular</strong> <strong>Structures</strong><br />

Contents<br />

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17<br />

2.2 Tube Detection Filters <strong>in</strong> Gaussian Scale Space . . . . . . . . . 18<br />

2.3 Tube Detection us<strong>in</strong>g Gradient Vector Flow . . . . . . . . . . . 23<br />

2.4 Centerl<strong>in</strong>e Extraction us<strong>in</strong>g Ridge Traversal . . . . . . . . . . . 30<br />

2.5 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31<br />

2.6 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . 39<br />

2.1 Introduction<br />

A tubular tree structure can be described as a set <strong>of</strong> tubular structures that are <strong>in</strong>terconnected<br />

with each other such that there are no loops. In this chapter, we are concerned<br />

with the extraction <strong>of</strong> these tubular structures <strong>in</strong> medical images. Thereby, we aim at<br />

deriv<strong>in</strong>g structural representations for all tubular structures <strong>in</strong> a given volume <strong>of</strong> <strong>in</strong>terest<br />

<strong>in</strong> a fully automated fashion.<br />

In the literature, methods have been presented that enable extraction <strong>of</strong> structural<br />

representations (centerl<strong>in</strong>es) <strong>of</strong> tubular structures directly from the gray-value images<br />

[2, 163]. However, these methods require an appropriate <strong>in</strong>itialization for each s<strong>in</strong>gle<br />

tubular structure. In contrast to these methods, tube detection filters (TDF) – a.k.a.<br />

vessel detection filters, l<strong>in</strong>eness filters, or vessel enhancement filters (e.g. [44, 70, 123]) –<br />

do not require such an <strong>in</strong>itialization, because they perform a shape analysis for each voxel<br />

<strong>in</strong> the image doma<strong>in</strong> result<strong>in</strong>g <strong>in</strong> a k<strong>in</strong>d <strong>of</strong> medialness measure or tube-likel<strong>in</strong>ess. However,<br />

TDFs do not result <strong>in</strong> structural representations <strong>of</strong> the tubular objects. To extract such<br />

17

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