To the Graduate Council: I am submitting herewith a dissertation ...

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Contents1 Introduction 11.1 ResearchMotivation ............................. 11.2 A Framework for 3D Reconstruction and Analysis . . . . . . . . . . . . 31.3 Contributions . . . . . ............................ 51.4 DocumentOrganization ........................... 82 Background 102.1 SurfaceSmoothing .............................. 102.2 SurfaceRegistration ............................. 162.3 SurfaceIntegration.............................. 222.4 SurfaceSegmentation ............................ 283 Surface Smoothing Based on Area-Decreasing Flow 343.1 Regularization Based on Area-Decreasing Flow . . . . . . . . . . . . . . 353.2 RangeDataSmoothing ........................... 383.2.1 Area-Decreasing Stabilizer for Range Data . . . . . . . . . . . . 38vii
3.2.2 Edge Preservation for Range Data . . . . . . . . . . . . . . . . . 443.3 SurfaceMeshSmoothing........................... 453.3.1 Area-Decreasing Stabilizer for Surface Mesh . . . . . . . . . . . . 453.3.2 Edge Preservation for Surface Mesh . . . . . . . . . . . . . . . . 484 Surface Registration by Point Fingerprint 574.1 TheExponentialMap ............................ 584.1.1 DefinitionoftheExponentialMap ................. 604.1.2 Computation of the Departure Angle . . . . . . . . . . . . . . . . 624.2 FingerprintoftheSurfacePoint....................... 644.2.1 GeodesicCircleGeneration ..................... 644.2.2 DefinitionofPointFingerprint ................... 694.3 CandidatePointSelection.......................... 724.4 FeatureMatching............................... 734.5 ApplicationtoSurfaceRegistration..................... 764.5.1 CoarseRegistrationbyFingerprintComparison.......... 764.5.2 ICPRefinement ........................... 785 Surface Reconstruction from Multi-View Range and Color Images 805.1 Mesh-BasedSurfaceIntegration....................... 815.1.1 Triangulating a Single Range Image . . . . . . . . . . . . . . . . 815.1.2 Removing Triangles in Overlapping Regions . . . . . . . . . . . . 825.1.3 LinkingtheMeshPatches...................... 86viii
Page 1 and 2: To the Graduate Council:I am submit
Page 3 and 4: Copyright c○ Yiyong Sun, 2002All
Page 5 and 6: AcknowledgmentsFirst and foremost,
Page 7: search employs an implicit surface-
Page 11 and 12: 8.2 Future Research . . . .........
Page 13 and 14: List of Figures1.1 A framework for
Page 15 and 16: 7.14 Finding corresponding points o
Page 17 and 18: Chapter 1IntroductionThis introduct
Page 19 and 20: Range ImageSmoothingRegistrationCol
Page 21 and 22: obust to surface noise and registra
Page 23 and 24: more efficient than 2D image correl
Page 25 and 26: scending path, and region merging.L
Page 27 and 28: two-dimensional (2D) image, 2D lowp
Page 29 and 30: curvatures of points on a surface i
Page 31 and 32: smoothing on the surface mesh. Shri
Page 33 and 34: with different surface representati
Page 35 and 36: center point and every surface poin
Page 37 and 38: Table 2.1: Comparison of different
Page 39 and 40: Reconstruction from Unorganized Poi
Page 41 and 42: tional. An offset of the distance f
Page 43 and 44: surement confidence. However, in or
Page 45 and 46: triangle mesh. The triangle mesh is
Page 47 and 48: mesh segmentation based on the phys
Page 49 and 50: Rettmann et al. [70] proposed a mes
Page 51 and 52: successful smoothing for both raw r
Page 53 and 54: where lim t→0 (R/t) =0,H represen
Page 55 and 56: the range r ij is estimated instead
Page 57 and 58: y minimizing the following energy f
Page 59 and 60:
tions were used:r α = r i,j+1 −
Page 61 and 62:
where κ represents a parameter tha
Page 63 and 64:
inequality, such asI∑I∑S i ≤
Page 65 and 66:
n ′ in iT ipqn ipw in ′ i−→
Page 67:
The singular value decomposition is
Page 70 and 71:
a limit on sharp edges. This limit
Page 72 and 73:
of the smoothing.Surface smoothing
Page 74 and 75:
fingerprint are presented. Section
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erroneously includes surface patch
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(ρ, θ)ρθT p (S)expSexp p (ρ,
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exponential map is introduced.4.2 F
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accurately than Dijkstra’s algori
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andθ = arccos ρ2 (A)+|AB| 2 −
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andy =((n × −→ pm) × n) · v
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images.4.3 Candidate Point Selectio
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(a)(b)(c)(d)Figure 4.6: Global fing
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and R ij is below a threshold. The
Page 94 and 95:
If the singular-value decomposition
Page 96 and 97:
Chapter 5Surface Reconstruction fro
Page 98 and 99:
Figure 5.2: Two registered and over
Page 100 and 101:
Figure 5.4: Intersecting triangles.
Page 102 and 103:
Figure 5.7: Gap between surfaces af
Page 104 and 105:
5.2 Volume-Based Surface Integratio
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2D texture coordinate of x is set t
Page 108 and 109:
ABFigure 5.9: Hole filling illustra
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are presented in Section 7.4.6.1 A
Page 112 and 113:
6.3 Applying the Fast Marching Wate
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Algorithm 6.2 (Fast Marching Waters
Page 116 and 117:
15: end if16: if v i.h
Page 118 and 119:
6.3.2 Geodesic ErosionThis step ass
Page 120 and 121:
(a)(b)(c)(d)Figure 6.3: Segmenting
Page 122 and 123:
Chapter 7Experimental ResultsThis c
Page 124 and 125:
no discernible improvement. For fai
Page 126 and 127:
(a)(b)(c)(d)Figure 7.4: Surface smo
Page 128 and 129:
(a)(b)(c)(d)Figure 7.6: Smoothing s
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(a)(b)(c)(d)(e)(f)Figure 7.8: Adapt
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The real range images were scanned
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(a)(b)Figure 7.10: Registration of
Page 136 and 137:
(a)(b)(c)(d)(e)(f)Figure 7.12: Matc
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(a) (b) (c) (d)(e) (f) (g) (h)(i)(j
Page 140 and 141:
(a)(b)ICP Registration Error (mm)21
Page 142 and 143:
(a)(b)(c)(d)(e)(f)Figure 7.17: Surf
Page 144 and 145:
Table 7.1: Small parts 3D reconstru
Page 146 and 147:
(a)(b)(c)(d)Figure 7.21: Surface mo
Page 148 and 149:
(a)(b)Figure 7.23: Automatic hole f
Page 150 and 151:
(a)(b)(c)(d)(e)(f)(g)(h)Figure 7.25
Page 152 and 153:
(a)(b)(c)(d)Figure 7.27: Four-view
Page 154 and 155:
(a)(b)(c)(d)Figure 7.28: Segmentati
Page 156 and 157:
(a)(b)(c)(d)Figure 7.30: Surface se
Page 158 and 159:
Table 7.2: Performance of the fast
Page 160 and 161:
surface reconstructed from the raw
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to choose a proper flowing step siz
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of interest based on the shape irre
Page 166 and 167:
8.2 Future ResearchThere are many o
Page 168 and 169:
Bibliography[1] E. L. Allgower and
Page 170 and 171:
[26] G. Dziuk and J. E. Hutchinson.
Page 172 and 173:
[54] W. E. Lorensen and H. E. Cline
Page 174 and 175:
[81] M. Soucy and D. Laurendeau. A
Page 176 and 177:
[106] S. M. Yamany, A. A. Farag, an
Page 178 and 179:
Appendix ALaser Range ScannersLaser
Page 180 and 181:
(a)(b)Transmitter LensTargetDiodeLa
Page 182 and 183:
A.2 Scanners Based on Laser Triangu
Page 184 and 185:
LaserBaseline B-s0saOpticalCenter(a
Page 186 and 187:
Appendix BSimplification of theArea
Page 188:
VitaYiyong Sun was born in Beijing,
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To the Graduate Council: I am submitting herewith a dissertation ...

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