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

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34 Chapter 2. Extraction of Tubular Structures represents a slightly curved surface path. (a) 3d volume rendering. (b) 2d cross sections of 3d objects. 1000 100 500 0 0 0 200 400 600 800 1000 1200 1400 1600 18000 200 400 600 800 1000 1200 1400 1600 1800 (c) 1d cross sections of 3d objects. (d) Response of Frangi’s method [44]. 50 50 0 0 0 200 400 600 800 1000 1200 1400 1600 18000 200 400 600 800 1000 1200 1400 1600 1800 (e) Response of Krissian’s method [70]. (f) Response of Pock’s method [114] using typical parameter η = 0.5. For variations of η see Fig. 2.8. 20 10 500 0 0 0 200 400 600 800 1000 1200 1400 1600 18000 200 400 600 800 1000 1200 1400 1600 1800 (g) Response of GVF-based tube detection with central medialness (Section 2.3.1). (h) Response of GVF-based tube detection with offset medialness (Section 2.3.2). Figure 2.7: Tubular structures with varying cross section profile representing situations found in typical CT datasets and responses of different TDFs. The x-axis indicates the location and the y-axis the contrast/response. Fig. 2.7(d)-(h) show the responses of the different TDFs. With all the approaches the responses descreases with increasing deviation from the expected cross section profiles (ellipse) or in case of other nearby image structures (e.g. another closely tangenting tube). In case of the TDFs of Krissian and Pock the response is also correlated with the edge-type (blurred edges, or Gaussian cross section profile), while with the method of Frangi and the GVF-based approaches the responses do not decrease in these cases. The TDFs of Frangi and Krissian also produced quite strong responses for the surface patch like structure and between the closely tangenting tubular objects. The GVF-based approaches do not produce responses between the closely tangenting tubular objects as we have already seen in the experiments of the varying tube configurations (see Fig. 2.6).
2.5. Experiments 35 However, the approach of Krissian does not produce any response between these closely tangenting tubular objects in Fig. 2.7(e), in contrast to the example in Fig. 2.6(d) where it did. This behavior deserves a closer investigation and explanation. With Pock’s approach two different scale spaces are utilized where the scale at which the boundary information is obtained depends on a parameter η. Moreover, the relation between the radius of the tubular objects and the boundary information is non-linear (σ P 2 = r η with 0.0 ≤ η ≤ 1.0 as explained in Section 2.2.2), meaning that the response also depends on the size of the tubular objects explaining the different results between the two figures. The approach of Pock addresses the problem of the pure Gaussian scale space methods (Frangi, Krissian), by computing the boundary information on a smaller scale. However, this computation of the boundary information on a smaller scale represents a tradeoff with this method as illustrated in Fig. 2.8. Computing the boundary information on a too large scale, the method shows the same problems as Krissians approach and produces responses between the tubular objects (Fig. 2.8(a)), while computing the boundary information on a too small scale, the method can not account for deviations from a perfectly circular cross section (e.g. ellipsoidal) (Fig. 2.8(b)). 50 50 0 0 0 200 400 600 800 1000 1200 1400 1600 18000 200 400 600 800 1000 1200 1400 1600 1800 (a) Response of Pock’s method [114] using very large η = 1.0. (b) Response of Pock’s method [114] using very small η = 0.0. Figure 2.8: Influence of η on the TDF response with Pock’s method [114] for the tubular structures shown in Fig. 2.7(a). With the GVF-based approaches this tradeoff does not exist. The edge information is computed on a very small scale and the GVF diffuses the gradient information, thus making it still possible to produce reasonable responses to slight variations from a perfectly circular cross section profile (ellipsoid). The method of Pock and the GVF-based approaches do not produce any response for surface patches contrary to the methods of Frangi and Krissian. Varying contrast level: In Fig. 2.9 the effect of varying contrast is shown. For the TDF of Frangi and the GVF-based methods the parameters were adapted accordingly to the contrast indicated by the dotted line, while the methods of Krissian and Pock do not
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Graz University of Technology Insti
Page 5 and 6: Abstract The segmentation of tubula
Page 7 and 8: Kurzfassung Die Segmentierung tubul
Page 9: Acknowledgements I am deeply gratef
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5.3. Evaluation and Results 85 (a)
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5.4. Discussion 93 results. Selle
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5.5. Conclusion 95 a prior to const
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98 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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