bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines bundle block adjustment with 3d natural cubic splines
without error so the accuracy of control spline is propagated into the recovery ofEOPs. The result is described in table 5.12.EOPsImage X c [m] Y c [m] Z c [m] ω [deg] ϕ [deg] κ [deg]ξ 0 547000.00 7659000.00 14000.00 3.8471 2.1248 91.8101762 ˆξ 547465.37 7658235.41 13700.25 0.3622 0.5124 91.5124±15.0911 ±13.0278 ±5.4714 ±0.8148 ±0.1784 ±0.1717ξ 0 546500.00 7670000.00 13500.00 0.1125 0.6128 90.7015764 ˆξ 546963.22 7672016.87 13708.82 -0.3258 -0.5217 91.1612±12.5460 ±17.1472 ±7.1872 ±0.6913 ±0.8632 ±1.1004ξ 0 546000.00 7680000 13700 1.4871 5.9052 92.0975766 ˆξ 546547.58 7685836.75 13712.20 1.2785 0.5469 92.9796±13.8104 ±12.1486 ±8.4854 ±1.4218 ±1.1957 ±0.6557Spline location parametersImage 762 Image 764t 1 t 4 t 7 t 10 t 2 t 5ξ 0 0.08 0.32 0.56 0.80 0.16 0.40ˆξ 0.0865 0.3192 0.5701 0.8167 0.1759 0.4167±0.0097 ±0.0159 ±0.0072 ±0.0088 ±0.0067 ±0.0085Image 764 Image 766t 8 t 11 t 3 t 6 t 9 t 12ξ 0 0.64 0.88 0.24 0.48 0.72 0.96ˆξ 0.6557 0.8685 0.2471 0.4683 0.7251 0.9713±0.0131 ±0.0092 ±0.0086 ±0.0069 ±0.0141 ±0.0089Table 5.12: EOP and spline location parameter recoveryThe control information about spline is utilized as stochastic constraints in theadjustment model. Since adding stochastic constraints removes the rank deficiency94
of the Gauss-Markov model corresponding to spline parameters which spline parametersare dependent to spline location parameters, bundle block adjustment can beimplemented using only the extended collinearity equations for natural cubic splines.95
- 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 and 104: Vertical aerial photographData 9 Ju
- Page 105: All locations are assumed as on the
- 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
of the Gauss-Markov model corresponding to spline parameters which spline parametersare dependent to spline location parameters, <strong>bundle</strong> <strong>block</strong> <strong>adjustment</strong> can beimplemented using only the extended collinearity equations for <strong>natural</strong> <strong>cubic</strong> <strong>splines</strong>.95
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