Thạc Sĩ 3D Segmentation of Soft Tissues by Flipping-free Mesh Deformation

List of Figures
1.1 Medical image characteristics . 2
1.2 Sample result of the watershed algorithm 3
1.3 Leakage problem 4
1.4 PathFinder . 5
1.5 IntraSense Myrian software 5
1.6 ITK-SNAP . 6
2.1 Self-intersection problem 10
2.2 Flip of surface normal . 10
3.1 Adaptive thresholding . 17
3.2 Sample result of the watershed algorithm 20
3.3 Bone removal in a CT image . 22
3.4 Fuzzy membership functions 23
3.5 Snake segmentation of bone 25
3.6 Gradient vector flow 26
3.7 Merging of contours 27
3.8 Level set segmentation of heart image 28
3.9 Segmentation of cartilage by active shape model 30
v3D Segmentation of Soft Tissues LIST OF FIGURES
4.1 3D quadrilateral mesh . 40
4.2 UV sphere . 41
4.3 Search for correspondence . 43
4.4 Flip detection 43
4.5 Flip avoidance . 45
4.6 Folding problem. (a) Displacing non-flipping vertices (dots) around soli-
tary vertices (circle) may cause (b) folding of the mesh, and in the extreme
case, (c) non-flipping self-intersection . 45
4.7 Non-flipping self-intersection . 46
4.8 Laplacian operator . 47
4.9 Example mesh configuration 49
4.10 Registration results of a naive method and the proposed method . 52
4.11 Registration of the quadrilateral mesh to the maxplanck volume 53
4.12 Registration error: registration of mesh to the maxplanck volume . 54
4.13 Cup volume . 55
4.14 Error measure . 56
4.15 Robustness to mesh resolution and deformation step size changes . 56
4.16 Registration of the quadrilateral mesh to a cup volume . 57
4.17 Robustness to deformation step-size changes . 58
4.18 Convergence with different positional weights 60
4.19 Convergence with different Laplacian weights 61
4.20 Variance of the edge lengths 62
4.21 Edge length variance 63
4.22 Execution time . 64
5.1 Mesh initialization . 67
vi3D Segmentation of Soft Tissues LIST OF FIGURES
5.2 Correspondence search . 72
5.3 Diffusion of correspondence 73
5.4 Convergence curve . 75
5.5 Comparison of segmentation algorithms . 76
5.6 Segmentation of spleen . 78
5.7 Segmentation of left brachiocephalic vein . 79
5.8 Feature extraction of the abdominal wall . 80
5.9 Extraction of abdominal wall . 82
5.10 Volume rendering 83
6.1 Inter-object collision 87
6.2 Computation of deformation bound regions using distance transform . 88
6.3 Computation of deformation bounding regions using fast marching 89
6.4 Bounding regions generated by fast marching 90
6.5 Leakage problem 93
6.6 Single-object segmentation vs multiple-object segmentation 94
6.7 Convergence curve . 95
6.8 Multiple-object segmentation . 97
6.9 Multiple-object segmentation . 98
6.10 Multiple-object segmentation . 99
6.11 Multiple-object segmentation . 100
viiList of Tables
5.1 Comparison of level set algorithm (LS), graph cut (GC) and the single-
object segmentation algorithm 77