bundle block adjustment with 3d natural cubic splines

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(a) Known EOPs with tie splines(b) Known EOPs with partial control splines(c) Known EOPs with full control splines(d) Unknown EOPs with partial control splines(e) Unknown EOPs with full control splines(Red: Unknown parameters, Green: Partially fixed parameters,Blue: Fixed parameters)Figure 5.1: Different examples72
cubic spline in the image and the object space. More than four point observations onan image spline segment increase the redundancy related with the accuracy but donot decrease the overall rank deficiency of the proposed adjustment system. In thesame fashion, the case using a polynomial of degree 2 can be implemented. Threepoints on a quadratic polynomial curve in one image are the only independent sets soadditional points on the same curve segment are a dependent observation. More thanindependent point observations on a polynomial increase the redundancy related withthe accuracy but do not provide the non-redundant information. Depending on theorder of a polynomial, the number of independent points for bundle block adjustmentis limited as table 5.2.Polynomial Number of independent pointsConstant polynomial 1Linear polynomial 2Quadratic polynomial 3Cubic polynomial 4Table 5.2: Number of independent points for bundle block adjustmentThe amount of information carried by a natural cubic spline can be calculatedwith the redundancy budget. Every spline segment has twelve parameters and everypoint measured on a spline segment increases one additional parameter. Let n bethe number of points measured on one spline segment in the image space and m bethe number of images which contain a tie spline.2nm collinearity equations andm(n-1) the arc-length parameterizations are equations and 12 (the number of onespline segment parameters) + nm (the number of spline location parameters) are73
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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
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: about splines, their relationships,
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 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
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bundle block adjustment with 3d natural cubic splines

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