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is cheaper than 2D image representation-based schemes. Since the projection on thetangent plane is not a one-to-one mapping, some projections of geodesic circles arepossibly overlapped. Each geodesic circle projection can, however, be traced back to thecorresponding geodesic circle, and therefore, the method can have the same advantage ofthe one-to-one mapping. The above mentioned representation schemes are summarizedin Table. 2.1 in chronological order, identifying whether the mapping is using localgeometry, computing geodesic distance and being able to carry features. This table isan updated version of the summary published in [109].2.3 Surface IntegrationSurface reconstruction is a step that extracts a surface from 3D measurements. Themeasurements are from multiple views of range images that have been registered together.For a calibrated range scanner, each range image can be converted to a surfacepatch. The registered surface patches may overlap in the 3D space and may not coverthe whole object due to incomplete scans. The surface reconstruction algorithm has todeal with the partly redundant and partly incomplete data, surface sampling noise, andregistration error.Previous works in surface reconstruction from multi-view range images can be classifiedinto three groups: reconstruction from unorganized points [2, 3, 6, 13, 28, 40],mesh integration [66, 74, 75, 81, 85, 96], and implicit surface integration [21, 36, 101].22
Reconstruction from Unorganized PointsSurface Reconstruction algorithms using unorganized points are flexible because onlya cloud of points are needed. These approaches estimate the neighborhood relationsbetween points. The Euclidean distance between measurements is used as the basis forestablishing the adjacency on the surface. Neighborhood relations enable approximationof surface topology and continuity. Boissonnat [13] describes a method for Delaunaytriangulation of a set of points in 3D space. Edelsbrunner and Mucke [28] proposed theα-shape which is a parameterized construction that associates a polyhedral shape withan organized set of points. For α = ∞, the α-shape is identical to the convex hull. As αdecreases, the α-shape shrinks by gradually developing cavities. α-shapes were appliedfor surface reconstruction.Hoppe et al. [40] developed an algorithm to reconstruct surfaces from unorganizedpoints using the concept of the implicit surface. A signed distance field is estimatedfrom the point cloud. The isosurface is then extracted using a variation of the marchingcubes algorithm [1]. The key ingredient in defining the signed distance function is toassociate a tangent plane with each of the data points. These tangent planes serve aslocal linear approximations to the surface and are used to define the signed distancefunction to the surface.Amenta et al. [2] proposed an algorithm that reconstructs surfaces with provableguarantees. The output is guaranteed to be topologically correct and convergent to theoriginal surface as the sampling density increases. The algorithm is based on the 3D23
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: Table 2.1: Comparison of different
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
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
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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
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(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
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[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
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(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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