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

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52 Chapter 3. Grouping and Linkage into Connected Networks obtained from this image gradient information. We used the GVF field already for identification of tubular objects as a replacement for the multi-scale gradient vector computation for detection of tubular structures (Section 2.3). In combination with a tube likeliness measure based on central or offset-medialness functions, the overall approach allows detection of tubular objects at their centerlines showing several advantages compared to conventional multi-scale TDFs. But similar to other TDFs, the method does not produce valid centerline paths in the proximity of junctions or diseases like stenosis where the objects shapes strongly deviates from the typical tubular shape. However, the GVF shows another property that can be used to solve this problem and that has been used for extraction of curve skeletons (CS) from binary segmentations by the skeletonization approach of Hassouna and Farag [53, 54]. In contrast to skeletonization approaches that are based on the distance transformation, the magnitude of the GVF always decreases towards the medial curves independent of the object’s shape. This property of the GVF enables the extraction of the centerlines also in case of junctions or plate like structures. (a) (b) (c) (d) (e) Figure 3.2: Illustration of the basic idea on 2D cross section profiles of some 3D structures. Top row: cross section T-junction of a tubular object; bottom row: structures with a circular cross section (left) and a strong deviation from a circular cross section (right). From left to right: original dataset, GVF, derived tube-likeliness, derived medialness λ(x), extracted CS. Fig. 3.2 illustrates this property and the basic idea for our image based grouping/linkage on some 2D cross sections of 3D structures. In these images the GVF field, the TDF response (using the central medialness function as described in Section 2.3.1), and the derived medialness measure based on the GVF magnitude that
3.3. Image Based Approach 53 can be utilized for the grouping/linkage in regions with significant deviation from a typical tubular shape, is shown. As a measure of medialness Hassouna and Farag [53, 54] applied the following weighting of the GVF magnitude |V (x)|: ( ) q |V(x)| − min|V(x)| λ(x) = 1.0 − (3.2) max|V(x)| − min|V(x)| with 0.0 < q < 1.0 in combination with their levelset based skeletonization approach. As can be seen from the medialness images, the GVF magnitude decreases with increasing distance from the surfaces of the structures. This property is independent of the size of the structures and it is also preserved in areas where the tubes do not show a circular crosssection. For our purpose, we utilized the weighting of the GVF magnitude as applied by Hassouna and Farag only for visualization in Fig. 3.2(d), while for the actual extraction a similar but simpler medialness measure is used: M(x) = 1 − |V(x)|. From the medialness images, the medial curves can be extracted as the height-ridges using the ridge traversal procedure presented in Section 2.4. For our image based grouping and linkage, we search for connecting paths between the identified tubular structures in the medialness map M(x). Therefor, starting from each endpoint of each tubular structure the associated height-ridge in the medialness map is traversed in the direction pointing away from the tubular structure into the direction where the shape strongly deviates from the typical tube shape. The traversal is stopped when the medialness falls below a given threshold m min or a centerline point of a tubular structure is found. The extracted traversal path is analyzed if it forms a valid connection/linkage path and added as a link between the tubular structures if it is valid. A traversal path in the medialness map is assumed as a valid link if the traversal ends at another tubular object and if the gray values along the linkage path do not change too much; therefor the maximal gray value difference d = max x∈path |I(x)−I tube | between the linkage path points and the average gray value I tube of the considered tubular structure has to stay below a given threshold d < γ diff . In this way the tubular structures are grouped and linked together based on image information. The overall approach allows for extraction of complete CSs from tubular networks directly from gray value images by utilizing the same GVF field two-fold, for a bottom-up identification of tubular structures and for an extraction of medial curves also in the regions that strongly deviate from the typical tubular shape.
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Graz University of Technology Insti
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Abstract The segmentation of tubula
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Kurzfassung Die Segmentierung tubul
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Acknowledgements I am deeply gratef
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Contents 1 Introduction 1 1.0.1 Req
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CONTENTS xv 8 Conclusion and Outloo
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xviii LIST OF FIGURES 4.2 Shape pri
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List of Tables 3.1 Average centerli
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102 Chapter 6. Coronary Artery Tree
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Chapter 7 Airway Tree Segmentation
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7.2. Methods 111 shown in Fig. 7.1.
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7.2. Methods 113 Additionally, the
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7.3. Evaluation and Results 115 Gro
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7.3. Evaluation and Results 117 Tab
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7.4. Discussion 119 Figure 7.5: “
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7.5. Conclusion 121 Comparison to o
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7.5. Conclusion 123 Figure 7.6: Exa
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Chapter 8 Conclusion and Outlook Co
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8.1. Conclusion 127 arteries - info
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8.2. Directions for Future Work 129
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132 Chapter A. List of Publications
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BIBLIOGRAPHY 135 Bibliography [1] A
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BIBLIOGRAPHY 137 [21] Choyke, P., Y
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BIBLIOGRAPHY 139 [41] Florin, C., P
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BIBLIOGRAPHY 141 [63] Kitslaar, P.
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BIBLIOGRAPHY 143 [85] Lindeberg, T.
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BIBLIOGRAPHY 145 [108] O’Donnell,
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BIBLIOGRAPHY 147 [129] Schmugge, S.
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BIBLIOGRAPHY 149 [150] van Bemmel,
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BIBLIOGRAPHY 151 [171] Yi, J. and R
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