bundle block adjustment with 3d natural cubic splines

Recommendations

Info

slope and distance observations are dependent on the extended collinearity equationsusing splines, other constraints such as slope and arc-length increase non-redundantinformation in adjustment to reduce the overall rank deficiency of the system.The coplanarity approach is another mathematical model of the perspective relationshipbetween the image and the object space features. The projection planedefined by the perspective center in the image space and the plane including thestraight line in the object space are identical. Since the coplanarity condition is foronly straight lines, the coplanarity approach can not be extended to curves.Object space knowledge about a starting point of a spline can be employed tobundle block adjustment. Since control information about a starting point is availablefor only three parameters of total twelve unknown parameters of a spline, a splinewith control information about a starting point is called a partial control spline.Three spline parameters related to a starting point of a spline are set to stochasticconstraints and the result is in table 5.5.The total number of equations is 2 × 6(the number of images)×2(the number ofpoints) +6(the number of the arc-length) = 30 and the total number of unknownsis 9(the number of partial spline parameters)+12(the number of spline location parameters)= 21 so the redundancy is 9. A convergence of a partial spline and splinelocation parameters has been archived with a partial control spline.In the next experiment, spline location parameters are estimated with knownEOPs and a full control spline. Since spline parameters and spline location parametersare dependent with respect to other parameters, the unknowns can be obtained withthe model of an observation equation with stochastic constraints. In this experimentspline parameters are set to stochastic constraints and the result is in table 5.6. The82
Spline location parametersImage 1 Image 2 Image 3t 1 t 7 t 2 t 8 t 3 t 9ξ 0 0.04 0.36 0.09 0.40 0.14 0.45ˆξ 0.0525 0.3547 0.1128 0.4158 0.1575 0.4543±0.0067 ±0.0020 ±0.0047 ±0.0091 ±0.0028 ±0.0083Image 4 Image 5 Image 6t 4 t 10 t 5 t 11 t 6 t 12ξ 0 0.21 0.50 0.27 0.54 0.31 0.61ˆξ 0.1916 0.5128 0.2563 0.5319 0.2961 0.6239±0.0037 ±0.0087 ±0.0044 ±0.0056 ±0.0139 ±0.1115Spline parametersa 11 a 12 a 13 b 11 b 12 b 13ξ 0 75.14 -52.87 30.71 70.05 -40.33 10.98ˆξ 71.7099 -47.2220 -15.8814 62.3703 -28.7260 7.1137±0.0795 ±0.6872 ±2.6439 ±0.0579 ±0.6473 ±1.7699c 11 c 12 c 13ξ 0 0.82 -30.72 10.51ˆξ 7.1198 -35.3841 8.1557±0.9483 ±1.3403 ±3.5852Table 5.5: Partial spline parameter and spline location parameter recovery83
Page 2:
c○ Copyright byWon Hee Lee2008
Page 7 and 8:
ACKNOWLEDGMENTSThanks be to God, my
Page 10 and 11:
3. BUNDLE BLOCK ADJUSTMENTWITH 3D N
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
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: 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 and 106: All locations are assumed as on the
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
show all

bundle block adjustment with 3d natural cubic splines

Create successful ePaper yourself

Delete template?

Save as template?