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

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area. The optimal, unique magnitude of the adjustment can be obtained. Crease edgesare preserved by adaptive smoothing according to the edge strength of each vertex on atriangle mesh, which is computed by fusing the tensor voting and the orientation checkof the normal vector field inside a geodesic window.2.2 Surface RegistrationSurface matching has two direct important applications in the area of computer vision.The first is three-dimensional (3D) image registration [33, 45, 94, 105, 110], which is alsoknown as pose estimation. When 3D images are taken at different viewpoints and datafusion is necessary, the rigid transformation between each view needs to be computed.Horn [41] showed that, given three or more pairs of non-coplanar corresponding 3Dpoints, the rigid transformation between the point pairs has a closed form solution.Thus the pose estimation problem becomes a surface point matching problem.Theother application is object recognition [16, 20, 25, 82, 109]. The model library storesthe surface features of each object, and the corresponding scene object is found bycomparing those features.Discrete surface matching is difficult because two surfaces may have self occlusions,different sampling resolutions, and are only partly overlapped, which makes statisticallybased features such as moments [67] difficult to apply. Because the local surfacegeometry characteristic is insensitive to the sampling resolution, previous works in thisarea tried to use this information in the encoded form for point matching, especially16
with different surface representation schemes which convert the problem of 3D pointmatching into 1D or 2D feature matching [20, 45, 82, 105, 110].More specifically, previous works encoded the point’s local surface geometry characteristicsusing either a contour on the surface or a 2D image of neighborhood nearthe encoded point. Stein and Medioni [82] used the notion of Splash to represent thenormals along a geodesic circle of a center point, which is the local Gauss map, for 3Dobject recognition tasks. The geodesic circle is parameterized by the angle θ from 0to 2π. On each point, a local orthogonal coordinate system is defined on the tangentplane with the normal n as the z axis. Each point on the geodesic circle is encodedby three angles θ, φ θ and ψ θ . For the point p on the geodesic circle, φ θ and ψ θ aredefined as φ θ = arccos(n · n θ )andψ θ = arccos(x · n θ(z=0) ), where x is a vector alongthe x axis and n θ is the normal vector at p. In the coordinate system created by θ,φ θ and ψ θ , the geodesic circle is encoded by another 3D curve and approximated bypolygons. For every polygonal approximation, a 3D super segment is computed. Thestarting point of a 3D super segment is defined as the point with the maximal distancefrom the θ axis. The 3D super segment is also encoded using various attributes. All 3Dsuper segments serve as keys into a database. Models containing similar codes as theSplashes appearing in the scene are extracted.Chua and Jarvis [20] proposed a point feature named Point Signature (PS) for 3Dobject recognition. For a given point p, a sphere of radius r centered at p is intersectedwith the surface and creates a 3D space curve C. The curve’s orientation is defined by17
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: smoothing on the surface mesh. Shri
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 −
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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
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If the singular-value decomposition
Page 96 and 97:
Chapter 5Surface Reconstruction fro
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Figure 5.2: Two registered and over
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Figure 5.4: Intersecting triangles.
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Figure 5.7: Gap between surfaces af
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5.2 Volume-Based Surface Integratio
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2D texture coordinate of x is set t
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ABFigure 5.9: Hole filling illustra
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are presented in Section 7.4.6.1 A
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6.3 Applying the Fast Marching Wate
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Algorithm 6.2 (Fast Marching Waters
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15: end if16: if v i.h
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6.3.2 Geodesic ErosionThis step ass
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(a)(b)(c)(d)Figure 6.3: Segmenting
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Chapter 7Experimental ResultsThis c
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no discernible improvement. For fai
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(a)(b)(c)(d)Figure 7.4: Surface smo
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(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
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(a)(b)(c)(d)(e)(f)Figure 7.12: Matc
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(a) (b) (c) (d)(e) (f) (g) (h)(i)(j
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(a)(b)ICP Registration Error (mm)21
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(a)(b)(c)(d)(e)(f)Figure 7.17: Surf
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Table 7.1: Small parts 3D reconstru
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(a)(b)(c)(d)Figure 7.21: Surface mo
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(a)(b)Figure 7.23: Automatic hole f
Page 150 and 151:
(a)(b)(c)(d)(e)(f)(g)(h)Figure 7.25
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(a)(b)(c)(d)Figure 7.27: Four-view
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(a)(b)(c)(d)Figure 7.28: Segmentati
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(a)(b)(c)(d)Figure 7.30: Surface se
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Table 7.2: Performance of the fast
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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
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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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