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Chapter 2BackgroundThis work makes contributions in surface smoothing, registration, integration, and segmentation.The literature reviews of the related research are presented in Section 2.1to 2.4.2.1 Surface SmoothingAs explained in the Appendix A, raw data acquired by range scanners are always corruptedby noise. Smoothing the corrupted surfaces is essential to build a robust surfacemodeling framework. The technique also applies to surfaces digitized using other techniquessuch as stereo vision. Successful surface smoothing can greatly improve the visualappearance of a 3D object, and at the same time, can feed improved data to successiveprocesses, such as matching, surface segmentation, and mesh simplification.If a range value of a range image is considered equivalent to an intensity value of a10
two-dimensional (2D) image, 2D lowpass filtering can serve as a simple surface smoothingmethod. For an arbitrary surface, 2D image processing algorithms such as spatialor frequency domain lowpass filterings, however, cannot provide promising results becausethey do not take 3D parameters into consideration. For this reason, the surfacesmoothing problem has been tackled in the literature using different approaches, includingregularization, surface fairing, and surface evolution using the level set method.The approach proposed in this research is based on regularization.Regularization has been used for surface interpolation from sparse range data and forrestoring noisy surfaces. Regularization performs smoothing operations by minimizingan energy functionf(x) =g(x)+λh(x) x ∈ R 3 (2.1)that includes data compatibility term g(x) and smoothing term h(x). Minimization ofg(x) involves the compatibility of the solution to the original observation, and minimizationof h(x) incorporates prior knowledge. λ is called the regularization parameterwhich determines the weight of minimization between g(x) andh(x). The result of minimizationis a trade-off between remaining close to the given observed data and avoidinga bumpy, coarse surface.Most existing regularization works consider the surface as a height map. For a height11
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: scending path, and region merging.L
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
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
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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
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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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