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

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AbstractThis dissertation presents a framework for 3D reconstruction and scene analysis,using a set of range images. The motivation for developing this framework came fromthe needs to reconstruct the surfaces of small mechanical parts in reverse engineeringtasks, build a virtual environment of indoor and outdoor scenes, and understand 3Dimages.The input of the framework is a set of range images of an object or a scene capturedby range scanners. The output is a triangulated surface that can be segmentedinto meaningful parts.A textured surface can be reconstructed if color images areprovided. The framework consists of surface smoothing, registration, integration, andsegmentation.Surface smoothing eliminates the noise present in raw measurements from rangescanners. This research proposes area-decreasing flow that is theoretically identical tothe mean curvature flow. Using area-decreasing flow, there is no need to estimate thecurvature value and an optimal step size of the flow can be obtained. Crease edges andsharp corners are preserved by an adaptive scheme.Surface registration aligns measurements from different viewpoints in a commoncoordinate system. This research proposes a new surface representation scheme namedpoint fingerprint.Surfaces are registered by finding corresponding point pairs in anoverlapping region based on fingerprint comparison.Surface integration merges registered surface patches into a whole surface. This rev
search employs an implicit surface-based integration technique. The proposed algorithmcan generate watertight models by space carving or filling the holes based on volumetricinterpolation. Textures from different views are integrated inside a volumetric grid.Surface segmentation is useful to decompose CAD models in reverse engineeringtasks and help object recognition in a 3D scene. This research proposes a watershedbasedsurface mesh segmentation approach. The new algorithm accurately segmentsthe plateaus by geodesic erosion using fast marching method.The performance of the framework is presented using both synthetic and real worlddata from different range scanners.The dissertation concludes by summarizing thedevelopment of the framework and then suggests future research topics.vi
Page 1 and 2: To the Graduate Council:I am submit
Page 3 and 4: Copyright c○ Yiyong Sun, 2002All
Page 5: AcknowledgmentsFirst and foremost,
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 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
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y minimizing the following energy f
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tions were used:r α = r i,j+1 −
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where κ represents a parameter tha
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inequality, such asI∑I∑S i ≤
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n ′ in iT ipqn ipw in ′ i−→
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The singular value decomposition is
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a limit on sharp edges. This limit
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of the smoothing.Surface smoothing
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fingerprint are presented. Section
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erroneously includes surface patch
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(ρ, θ)ρθT p (S)expSexp p (ρ,
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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
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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
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Bibliography[1] E. L. Allgower and
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[26] G. Dziuk and J. E. Hutchinson.
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[54] W. E. Lorensen and H. E. Cline
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[81] M. Soucy and D. Laurendeau. A
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[106] S. M. Yamany, A. A. Farag, an
Page 178 and 179:
Appendix ALaser Range ScannersLaser
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(a)(b)Transmitter LensTargetDiodeLa
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A.2 Scanners Based on Laser Triangu
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LaserBaseline B-s0saOpticalCenter(a
Page 186 and 187:
Appendix BSimplification of theArea
Page 188:
VitaYiyong Sun was born in Beijing,
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