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

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map z(x, y) the energy function can be written asf(z) =g(z)+λh(z) z ∈ R. (2.2)Although this assumption is quite limited, the idea of treating smoothing as a regularizationprocess is the basis of the approach developed in this research. Different definitionsof the smoothing term have been proposed in the literature. Blake and Zissermen [10]introduced the membrane and plate model. Using the membrane model, the smoothingterm for a height map z is∫∫h =|∇z| 2 dxdy (2.3)The membrane has intrinsic resistance to creasing. In order to fit to crease discontinuities,a plate model should be used. The smoothing term for a plate model is theQuadratic Variation∫∫h =(z 2 xx +2z 2 xy + z 2 yy)dxdy (2.4)or the Square Laplacian∫∫h =(z xx + z yy ) 2 dxdy (2.5)Stevenson and Delp [83] chose h as the sum square integral of the two principal12
curvatures of points on a surface in the form of a height map.∫∫h =(k 2 1 + k 2 2)dxdy (2.6)where k 1 and k 2 are principal curvatures. Eq. (2.6) came from the analysis of a plateof elastic material. Smoothly varying surface can be modeled as an ideal thin flexibleplate of elastic material. The potential energy density of a thin plate is given byA( k2 1 + k2 2)+Bk 1 k 2 (2.7)2where A and B are constants of the material. To simplify the equation, let A = 1 andB = 0, and Eq. (2.6) is obtained. The equation still models a valid thin plate. Variousapproximations to the stabilizing term were discussed to overcome the computationalcomplexity. A two-stage reconstruction algorithm that would form an approximatelyinvariant surface was proposed. The first stage forms a piecewise planar approximationto the surface that is invariant to the coordinate system. The piecewise planar surfaceis then used to construct an approximate parameterization of the reconstructed surfacethat can be used to make a valid approximation to the invariant functional. The minimizationproblem was solved using finite element methods. The experiment only showedthe reconstruction of surfaces with simple shapes. The method involves computing thesecond order derivatives on the surface, which are sensitive to the surface noise.Yi and Chelberg [107] proposed a simple first order smoothing term because first13
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: two-dimensional (2D) image, 2D lowp
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
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
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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
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images.4.3 Candidate Point Selectio
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(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
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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
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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
Page 138 and 139:
(a) (b) (c) (d)(e) (f) (g) (h)(i)(j
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(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
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(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
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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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