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Voronoi diagram and Delaunay triangulation. It produces a set of triangles, called crustof the sample points. All vertices of crust triangles are sample points.Amenta et al. introduced the power crust in [3]. The power crust is a constructionwhich takes a sample of points from the surface of a three-dimensional object andproduces a surface mesh and an approximate medial axis.The approach is to firstapproximate the medial axis transform (MAT) of the object, and then use an inversetransform to produce the surface representation from the MAT.Bernardini et al. [6] developed a system named ball-pivoting based on α-shapes whileavoiding the computation of the Voronoi diagram. The ball-pivoting algorithm computesa triangle mesh interpolating a given point cloud. Three points form a triangle if a ballof a user-specified radius ρ touches them without containing any other point. Startingwith a seed triangle, the ball pivots around an edge until it touches another point,forming another triangle.The process continues until all reachable edges have beentried, and then starts from another seed triangle, until all points have been considered.The process can then be repeated with a ball of larger radius to handle uneven samplingdensities.Zhao et al. [112] introduced a minimal surface like model and its variational andpartial differential equation formulation for surface reconstruction from an unorganizeddata set. The data set can include points, curves, and surface patches. In the formulation,only distance to the data set is used as the input. To find the final shape, theycontinuously deform an initial surface following the gradient flow of an energy func-24
tional. An offset of the distance function to the data set is used as the initial surface.The level set method [77] is used in the numerical computation.Although the algorithms reconstructing surfaces from unorganized points are able tocompute a surface model using only point information, they discard useful informationsuch as surface normal and reliability estimates. These algorithms make three assumptions[81]. First, they assume that the K nearest surface neighbors of a point can beestimated by finding its K nearest 3D neighbors. Second, these methods assume thatthe density of data points is reasonably uniform over the surface to be modeled. Finally,they assume that the points are measured with the same accuracy. These assumptionsare too restrictive for integrating multiple range images.Mesh IntegrationSurface reconstruction methods by merging the triangle meshes assume a surface meshcan be easily obtained from a range image. This is true for most range scanners. Rangescanners usually acquire range images on a rectangular grid, where the triangulationprocess is straightforward.Turk and Levoy [96] integrate the surface by zippering triangle meshes from differentviews. Merging begins by converting two meshes that may have considerable overlapinto a pair of meshes that just barely overlap along portions of their boundaries. Thisis done by simultaneously eating back the boundaries of each mesh that lie directly ontop of the other mesh. Next, the meshes are zippered together. The triangles of onemesh are clipped to the boundary of the other mesh, and the vertices on the boundary25
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 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: Reconstruction from Unorganized Poi
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
Page 76 and 77: erroneously includes surface patch
Page 78 and 79: (ρ, θ)ρθT p (S)expSexp p (ρ,
Page 80 and 81: exponential map is introduced.4.2 F
Page 82 and 83: accurately than Dijkstra’s algori
Page 84 and 85: 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
Page 114 and 115:
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
Page 138 and 139:
(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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