bundle block adjustment with 3d natural cubic splines

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3. BUNDLE BLOCK ADJUSTMENTWITH 3D NATURAL CUBIC SPLINES . . . . . . . . . . . . . . . . . . 343.1 3D natural cubic splines . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Extended collinearity equation model for splines . . . . . . . . . . . 393.3 Arc-length parameterization of 3D natural cubic splines . . . . . . 443.4 Tangents of spline between image and object space . . . . . . . . . 524. MODEL INTEGRATION . . . . . . . . . . . . . . . . . . . . . . . . . . 564.1 Bundle block adjustment . . . . . . . . . . . . . . . . . . . . . . . . 564.2 Evaluation of bundle block adjustment . . . . . . . . . . . . . . . . 644.3 Pose estimation with ICP algorithm . . . . . . . . . . . . . . . . . 675. EXPERIMENTS AND RESULTS . . . . . . . . . . . . . . . . . . . . . . 705.1 Synthetic data description . . . . . . . . . . . . . . . . . . . . . . . 755.2 Experiments with error free EOPs . . . . . . . . . . . . . . . . . . 785.3 Recovery of EOPs and spline parameters . . . . . . . . . . . . . . . 855.4 Tests with real data . . . . . . . . . . . . . . . . . . . . . . . . . . 896. CONCLUSIONS AND FUTURE WORK . . . . . . . . . . . . . . . . . . 96APPENDICES:A. DERIVATION OF THE PROPOSED MODEL . . . . . . . . . . . . . . 100A.1 Derivation of extended collinearity equation . . . . . . . . . . . . . 100A.2 Derivation of arc-length parameterization . . . . . . . . . . . . . . 103A.3 Derivation of the tangent of a spline . . . . . . . . . . . . . . . . . 110BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113ix
LIST OF TABLESTablePage4.1 Relationship between the eccentricity and the conic form . . . . . . . 585.1 Number of unknowns . . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Number of independent points for bundle block adjustment . . . . . . 735.3 EOPs of six bundle block images for simulation . . . . . . . . . . . . 765.4 Spline parameter and spline location parameter recovery . . . . . . . 815.5 Partial spline parameter and spline location parameter recovery . . . 835.6 Spline location parameter recovery . . . . . . . . . . . . . . . . . . . 845.7 EOP and spline location parameter recovery . . . . . . . . . . . . . . 865.8 EOP, control and tie spline parameter recovery . . . . . . . . . . . . 885.9 Information about aerial images used in this study . . . . . . . . . . . 915.10 Spline parameter and spline location parameter recovery . . . . . . . 925.11 Spline location parameter recovery . . . . . . . . . . . . . . . . . . . 935.12 EOP and spline location parameter recovery . . . . . . . . . . . . . . 94x
Page 2: c○ Copyright byWon Hee Lee2008
Page 7 and 8: ACKNOWLEDGMENTSThanks be to God, my
Page 13 and 14: CHAPTER 1INTRODUCTION1.1 OverviewOn
Page 15 and 16: y an intersection employing more th
Page 17 and 18: similarity of geometric properties
Page 19 and 20: straight linear features or formula
Page 21 and 22: • Bundle block adjustment by the
Page 23 and 24: Hessian. Interest point operators w
Page 25 and 26: [60], Ebner and Ohlhof(1994) [16],
Page 27 and 28: a complicated problem. The developm
Page 29 and 30: ⎡⎢⎣x i − x py i − y p−f
Page 31 and 32: x p = −f (X A + t · a − X C )r
Page 33 and 34: surfaces and terrain models in 2D a
Page 35 and 36: f(u) − e(u) = g(u)f(u) − e(u) =
Page 37 and 38: Tankovich[69] used linear features
Page 39 and 40: (a) 0th order continuity (b) 1st or
Page 41 and 42: Cardinal splineA Cardinal spline is
Page 43 and 44: 2.3.2 Fourier transformFourier seri
Page 45 and 46: For other polyline expressions, Aya
Page 47 and 48: Each segment of a natural cubic spl
Page 49 and 50: ⎡⎢⎣2 11 4 11 4 1· · ·1 4 1
Page 51 and 52: 3.2 Extended collinearity equation
Page 53 and 54: R −1 = R T . The matrix R T (= R
Page 55 and 56: dx p = M 1 dX C + M 2 dY C + M 3 dZ
Page 57 and 58: In this research, the arc-length pa
Page 59 and 60:
=√∫ √√√ ()ti+1−f u′ (
Page 61 and 62:
This equation can be replaced with
Page 63 and 64:
order polynomial using Newton’s d
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y collinearity equations, tangents
Page 67 and 68:
d tan(θ t ) = w′ (v ′ w − w
Page 69 and 70:
y each two points, which are four e
Page 71 and 72:
+M 14 db i3 + M 15 dc i0 + M 16 dc
Page 73 and 74:
collinearity model are described in
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[ ] [ ] [ ]N11 N 12 ˆξ1 c1N12T =N
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systematic errors in the image spac
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interval based on the normal distri
Page 81 and 82:
1 ∂Φ2 ∂l= (X C + d 1 l − a i
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about splines, their relationships,
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cubic spline in the image and the o
Page 87 and 88:
The redundancy budget of a tie poin
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of bundle block adjustment is requi
Page 91 and 92:
ξ kiSP = [ da i0 da i1 da i2 da i3
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Spline location parametersImage 1 I
Page 95 and 96:
Spline location parametersImage 1 I
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5.3 Recovery of EOPs and spline par
Page 99 and 100:
Table 5.7 expressed the convergence
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Iteration with an incorrect spline
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Vertical aerial photographData 9 Ju
Page 105 and 106:
All locations are assumed as on the
Page 107 and 108:
of the Gauss-Markov model correspon
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estimation is obstacled by the corr
Page 111 and 112:
Interior orientation defines a tran
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+ fu ( w2 31 (X i (t) − X C ) + s
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A.2 Derivation of arc-length parame
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+2f( t [1 + t 2) − 1 22s 12 (Y i
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+Du ′ ( t 1 + t 22)2r 11 t + Dv
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A 17 = t [2 − t 1 16 2 f(t 1) −
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1−u ′ w − w ′ u {w′ [s 21
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BIBLIOGRAPHY[1] Ackerman, F., and V
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[24] Haala, N., and G. Vosselman. 1
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[49] Parian, J.A., and A. Gruen. 20
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[73] Vosselman, G., and H. Veldhuis
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bundle block adjustment with 3d natural cubic splines

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