bundle block adjustment with 3d natural cubic splines

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Spline location parametersImage 762 Image 764t 1 t 4 t 7 t 2 t 5 t 8ξ 0 0.08 0.38 0.72 0.22 0.53 0.82ˆξ 0.0844 0.4258 0.6934 0.2224 0.5170 0.8272±0.0046 ±0.0058 ±0.0072 ±0.0175 ±0.0104 ±0.0156Image 766t 3 t 6 t 9ξ 0 0.32 0.59 0.88ˆξ 0.3075 0.6176 0.9158±0.0097 ±0.0148 ±0.0080Spline parametersa 10 a 11 a 12 a 13ξ 0 535000.00 830.00 -150.00 50.00ˆξ 535394.1732 867.6307 -173.1357 24.3213±0.1273 ±0.7142 ±7.6540 ±21.3379b 10 b 11 b 12 b 13ξ 0 7671000.00 150.00 140.00 -300.00ˆξ 7672048.3173 143.1734 130.8147 -290.1270±0.2237 ±1.6149 ±10.9058 ±26.7324c 10 c 11 c 12 c 13ξ 0 0.00 -10.00 -50.00 50.00ˆξ 2.1913 -3.7669 -39.8003 27.7922±0.0547 ±0.1576 ±9.1572 ±19.6787Table 5.10: Spline parameter and spline location parameter recovery92
All locations are assumed as on the second spline segment and the second splinesegment calculated from softcopy workstation is used as control information.Spline location parametersImage 762 Image 764 Image 766t 1 t 4 t 2 t 5 t 3 t 6ξ 0 0.15 0.60 0.30 0.75 0.45 0.90ˆξ 0.1647 0.6177 0.2872 0.7481 0.4362 0.9249±0.0084 ±0.0091 ±0.0034 ±0.0093 ±0.0155 ±0.0087Table 5.11: Spline location parameter recoveryThe next experiment is the recovery of EOPs with control spline. Spline controlpoints are (534415.91, 767199305, -18.97), (535394.52, 7672045.02, 2.127), (536110.66,7672024.29, -13.897), and (536654.04, 7671016.20, -2.51). Even though the edgedetectors are often used in digital photogrammetry and remote sensing software,the control points are extracted manually since edge detection is not our main goal.Among three segments, the second spline segment is used for the EOP recovery.The information of control spline is obtained by manual operation using softcopyworkstation with an estimated accuracy of ±1 pixel. The convergence radius of theproposed iterative algorithm is proportional to the estimated accuracy level.Theimage coordinate system is converted into the photo coordinate system using theinterior orientation parameters from KMS. The association between a point on a 3Dspline segment and a point on a 2D image is not established in this study. Of course3D spline measurement in the stereo model using softcopy workstation can not be93
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c○ Copyright byWon Hee Lee2008
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ACKNOWLEDGMENTSThanks be to God, my
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3. BUNDLE BLOCK ADJUSTMENTWITH 3D N
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CHAPTER 1INTRODUCTION1.1 OverviewOn
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y an intersection employing more th
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similarity of geometric properties
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straight linear features or formula
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• Bundle block adjustment by the
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Hessian. Interest point operators w
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[60], Ebner and Ohlhof(1994) [16],
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a complicated problem. The developm
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⎡⎢⎣x i − x py i − y p−f
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x p = −f (X A + t · a − X C )r
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surfaces and terrain models in 2D a
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f(u) − e(u) = g(u)f(u) − e(u) =
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Tankovich[69] used linear features
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(a) 0th order continuity (b) 1st or
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Cardinal splineA Cardinal spline is
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2.3.2 Fourier transformFourier seri
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For other polyline expressions, Aya
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Each segment of a natural cubic spl
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⎡⎢⎣2 11 4 11 4 1· · ·1 4 1
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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
Page 65 and 66: 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
Page 75 and 76: [ ] [ ] [ ]N11 N 12 ˆξ1 c1N12T =N
Page 77 and 78: systematic errors in the image spac
Page 79 and 80: interval based on the normal distri
Page 81 and 82: 1 ∂Φ2 ∂l= (X C + d 1 l − a i
Page 83 and 84: about splines, their relationships,
Page 85 and 86: cubic spline in the image and the o
Page 87 and 88: The redundancy budget of a tie poin
Page 89 and 90: of bundle block adjustment is requi
Page 91 and 92: ξ kiSP = [ da i0 da i1 da i2 da i3
Page 93 and 94: Spline location parametersImage 1 I
Page 95 and 96: Spline location parametersImage 1 I
Page 97 and 98: 5.3 Recovery of EOPs and spline par
Page 99 and 100: Table 5.7 expressed the convergence
Page 101 and 102: Iteration with an incorrect spline
Page 103: Vertical aerial photographData 9 Ju
Page 107 and 108: of the Gauss-Markov model correspon
Page 109 and 110: estimation is obstacled by the corr
Page 111 and 112: Interior orientation defines a tran
Page 113 and 114: + fu ( w2 31 (X i (t) − X C ) + s
Page 115 and 116: A.2 Derivation of arc-length parame
Page 117 and 118: +2f( t [1 + t 2) − 1 22s 12 (Y i
Page 119 and 120: +Du ′ ( t 1 + t 22)2r 11 t + Dv
Page 121 and 122: A 17 = t [2 − t 1 16 2 f(t 1) −
Page 123 and 124: 1−u ′ w − w ′ u {w′ [s 21
Page 125 and 126: BIBLIOGRAPHY[1] Ackerman, F., and V
Page 127 and 128: [24] Haala, N., and G. Vosselman. 1
Page 129 and 130: [49] Parian, J.A., and A. Gruen. 20
Page 131: [73] Vosselman, G., and H. Veldhuis
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bundle block adjustment with 3d natural cubic splines

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