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Area-Decreasing Flow for Surface Smoothing [86, 89, 91]This research proposes to smooth the surface using area-decreasing flow, which is theoreticallyidentical to the mean curvature flow. A popular smoothing method has beenlocal deformation of surfaces based on mean curvature flow. The problem with meancurvature flow is that the curvature value is difficult to estimate on a discrete surfaceand there is no way to explicitly compute the step size of the flow. Using the areadecreasingflow to smooth a surface, there is no need to estimate the curvature valueand an optimal step size of the flow can be obtained. A rigidity term is included tomake the deformation faithful to the original measurements. Smoothing is designed tobe adaptive to preserve the crease edges and sharp corners. The proposed smoothingalgorithm is able to efficiently smooth large triangle meshes and preserve the geometricdetails.Point Fingerprint for Surface Matching [84, 90]This research proposes a new surface representation scheme based on a signature of a3D point, called point fingerprint. The fingerprint of a 3D point is defined as a set of2D contours obtained by projecting the geodesic circles of different radii on the tangentplane. Surfaces are registered by finding corresponding point pairs in the overlappingregion based on fingerprint comparison. Compared to other representation schemes inprevious works, point fingerprint uses the accurate geodesic distance that is intrinsic tothe surface. Fingerprint comparison is based on a set of 1D signal correlations, which are6
more efficient than 2D image correlations. The fingerprint representation functions likea one-to-one mapping and is able to carry other information such as color and curvature.This research also proposes an alternative method for geodesic distance computationon a triangle mesh and a fast approach based on irregularity of the point fingerprint toextract feature points from a surface. The point fingerprint can be applied to surfaceregistration.Implicit Surface-Based Integration [86, 88, 89]This research extends previous work on implicit surface-based integration by combiningthe textures fusion. Within a volumetric grid, each surface patch generates a signeddistance field. All signed distance fields are fused by weighted average. The whole surfaceis extracted using a polygonization algorithm. The method can generate watertightmodels using space carving. It can also work without space carving and fill the holesby volumetric interpolation.The proposed algorithm is employed to reconstruct 3Dmodels using range images captured by various range scanners.Geodesic Erosion in 3D Watershed Segmentation [87]This research proposes a watershed-based surface mesh segmentation approach. Basedon eigen analysis of surface normals inside a geodesic neighborhood, the approach robustlyestimates the edge strength of each vertex on the surface mesh on which thewatershed segmentation is applied. Compared with the previous works on watershedbasedmesh segmentation, this research first applies the geodesic erosion on a triangle7
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 and 8: search employs an implicit surface-
Page 9 and 10: 3.2.2 Edge Preservation for Range D
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: obust to surface noise and registra
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,
Page 80 and 81:
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 −
Page 86 and 87:
andy =((n × −→ pm) × n) · v
Page 88 and 89:
images.4.3 Candidate Point Selectio
Page 90 and 91:
(a)(b)(c)(d)Figure 4.6: Global fing
Page 92 and 93:
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
Page 110 and 111:
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
Page 130 and 131:
(a)(b)(c)(d)(e)(f)Figure 7.8: Adapt
Page 132 and 133:
The real range images were scanned
Page 134 and 135:
(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
Page 162 and 163:
to choose a proper flowing step siz
Page 164 and 165:
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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