bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines bundle block adjustment with 3d natural cubic splines
+Du ′ (t 1 ){r 12 (Z ′ i(t 1 )) − r 13 (Y ′i (t 1 ))} + Dv(t 1 ){r 22 (Z i (t 1 ) − Z C )−r 23 (Y i (t 1 ) − Y C )} + Dv ′ (t 1 ){r 22 (Z ′ i(t 1 )) − r 23 (Y ′i (t 1 ))}+Dw(t 1 ){r 32 (Z i (t 1 ) − Z C ) − r 33 (Y i (t 1 ) − Y C )}+Dw ′ (t 1 ){r 32 (Z i(t ′ 1 )) − r 33 (Y i ′ (t 1 ))}+2f( t [1 + t 2) − 1 2 Du( t 1 + t 2){r 12 (Z i ( t 1 + t 2) − Z C )222−r 13 (Y i ( t 1 + t 22+Dv(t 1 ){r 22 (Z i ( t 1 + t 22+Dv ′ ( t 1 + t 22+Dw( t 1 + t 22+Dw ′ ( t 1 + t 22) − Y C )} + Du ′ ( t 1 + t 22){r 12 (Z i( ′ t 1 + t 2)) − r 13 (Y ′2) − Z C ) − r 23 (Y i ( t 1 + t 2) − Y C )}2){r 22 (Z i( ′ t 1 + t 2)) − r 23 (Y ′2){r 32 (Z i ( t 1 + t 22){r 32 (Z i( ′ t 1 + t 2)) − r 33 (Y ′2i ( t 1 + t 2))}2) − Z C ) − r 33 (Y i ( t 1 + t 2) − Y C )}2i ( t ]1 + t 2))}2+ 1 2 f(t 2) − 1 2 {Du(t2 ){r 12 (Z i (t 2 ) − Z C ) − r 13 (Y i (t 2 ) − Y C )}+Du ′ (t 2 ){r 12 (Z ′ i(t 2 )) − r 13 (Y ′i (t 2 ))} + Dv(t 2 ){r 22 (Z i (t 2 ) − Z C )−r 23 (Y i (t 2 ) − Y C )} + Dv ′ (t 2 ){r 22 (Z ′ i(t 2 )) − r 23 (Y ′i (t 2 ))}+Dw(t 2 ){r 32 (Z i (t 2 ) − Z C ) − r 33 (Y i (t 2 ) − Y C )}+Dw ′ (t 2 ){r 32 (Z i(t ′ 2 )) − r 33 (Y i ′ (t 2 ))}]A 5 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 ){s 11 (X i (t 1 ) − X C )) + s 12 (Y i (t 1 ) − Y C )i ( t 1 + t 2))}2+s 13 (Z i (t 1 ) − Z C )} + Du ′ (t 1 ){s 11 (X ′ i(t 1 )) + s 12 (Y ′i (t 1 )) + s 13 (Z ′ i(t 1 ))}+Dv(t 1 ){s 21 (X i (t 1 ) − X C )) + s 22 (Y i (t 1 ) − Y C ) + s 23 (Z i (t 1 ) − Z C )}+Dv ′ (t 1 ){s 21 (X ′ i(t 1 )) + s 22 (Y ′i (t 1 )) + s 23 (Z ′ i(t 1 ))}+Dw(t 1 ){s 31 (X i (t 1 ) − X C )) + s 32 (Y i (t 1 ) − Y C ) + s 33 (Z i (t 1 ) − Z C )}+Dw ′ (t 1 ){s 31 (X ′ i(t 1 )) + s 32 (Y ′i (t 1 )) + s 33 (Z ′ i(t 1 ))}104
+2f( t [1 + t 2) − 1 22s 12 (Y i ( t 1 + t 22+Du ′ ( t 1 + t 22+Dv( t 1 + t 22s 22 (Y i ( t 1 + t 22+Dv ′ ( t 1 + t 22+Dw( t 1 + t 22+s 32 (Y i ( t 1 + t 22Du( t 1 + t 22){s 11 (X i ( t 1 + t 2) − X C ))+2) − Y C ) + s 13 (Z i ( t 1 + t 2) − Z C ))2){s 11 (X i( ′ t 1 + t 2)) + s 12 (Y ′2){s 21 (X i ( t 1 + t 2) − X C )) +2i ( t 1 + t 22) − Y C ) + s 23 (Z i ( t 1 + t 2) − Z C ))2){s 12 (X i( ′ t 1 + t 2)) + s 22 (Y ′2){s 31 (X i ( t 1 + t 2) − X C ))2i ( t 1 + t 22) − Y C ) + s 33 (Z i ( t 1 + t 2) − Z C ))2)) + s 13 (Z i( ′ t 1 + t 2)))2)) + s 23 (Z i( ′ t 1 + t 2)))2+Dw ′ ( t 1 + t 2){s 31 (X ′2i( t 1 + t 2)) + s 32 (Y i ′ ( t 1 + t 2)) + s 33 (Z ′22i( t 1 + t 2)))212 f(t 2) − 1 2 {Du(t2 ){s 11 (X i (t 2 ) − X C )) + s 12 (Y i (t 2 ) − Y C )+s 13 (Z i (t 2 ) − Z C )} + Du ′ (t 2 ){s 11 (X ′ i(t 2 )) + s 12 (Y ′i (t 2 )) + s 13 (Z ′ i(t 1 ))}+Dv(t 2 ){s 21 (X i (t 2 ) − X C )) + s 22 (Y i (t 2 ) − Y C ) + s 23 (Z i (t 2 ) − Z C )}+Dv ′ (t 2 ){s 21 (X ′ i(t 2 )) + s 22 (Y ′i (t 2 )) + s 23 (Z ′ i(t 2 ))}+Dw(t 2 ){s 31 (X i (t 2 ) − X C )) + s 32 (Y i (t 2 ) − Y C ) + s 33 (Z i (t 2 ) − Z C )}+Dw ′ (t 2 ){s 31 (X i(t ′ 2 )) + s 32 (Y i ′ (t 2 )) + s 33 (Z i(t ′ 2 ))}A 6 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 ){r 21 (X i (t 1 ) − X C )) + r 22 (Y i (t 1 ) − Y C )+r 23 (Z i (t 1 ) − Z C )} + Du ′ (t 1 ){r 21 (X ′ i(t 1 )) + r 22 (Y ′i (t 1 )) + r 23 (Z ′ i(t 1 ))}+Dv(t 1 ){−r 11 (X i (t 1 ) − X C )) − r 12 (Y i (t 1 ) − Y C ) − r 13 (Z i (t 1 ) − Z C )}+Dv ′ (t 1 ){−r 11 (X i(t ′ 1 )) − r 12 (Y i ′ (t 1 )) − r 13 (Z i(t ′ 1 ))}+2f( t [1 + t 2) − 1 2 Du( t 1 + t 2){r 21 (X i ( t 1 + t 2) − X C ))+222r 22 (Y i ( t 1 + t 22) − Y C ) + r 23 (Z i ( t 1 + t 2) − Z C ))2105
- 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 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: A.2 Derivation of arc-length parame
- 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
+Du ′ (t 1 ){r 12 (Z ′ i(t 1 )) − r 13 (Y ′i (t 1 ))} + Dv(t 1 ){r 22 (Z i (t 1 ) − Z C )−r 23 (Y i (t 1 ) − Y C )} + Dv ′ (t 1 ){r 22 (Z ′ i(t 1 )) − r 23 (Y ′i (t 1 ))}+Dw(t 1 ){r 32 (Z i (t 1 ) − Z C ) − r 33 (Y i (t 1 ) − Y C )}+Dw ′ (t 1 ){r 32 (Z i(t ′ 1 )) − r 33 (Y i ′ (t 1 ))}+2f( t [1 + t 2) − 1 2 Du( t 1 + t 2){r 12 (Z i ( t 1 + t 2) − Z C )222−r 13 (Y i ( t 1 + t 22+Dv(t 1 ){r 22 (Z i ( t 1 + t 22+Dv ′ ( t 1 + t 22+Dw( t 1 + t 22+Dw ′ ( t 1 + t 22) − Y C )} + Du ′ ( t 1 + t 22){r 12 (Z i( ′ t 1 + t 2)) − r 13 (Y ′2) − Z C ) − r 23 (Y i ( t 1 + t 2) − Y C )}2){r 22 (Z i( ′ t 1 + t 2)) − r 23 (Y ′2){r 32 (Z i ( t 1 + t 22){r 32 (Z i( ′ t 1 + t 2)) − r 33 (Y ′2i ( t 1 + t 2))}2) − Z C ) − r 33 (Y i ( t 1 + t 2) − Y C )}2i ( t ]1 + t 2))}2+ 1 2 f(t 2) − 1 2 {Du(t2 ){r 12 (Z i (t 2 ) − Z C ) − r 13 (Y i (t 2 ) − Y C )}+Du ′ (t 2 ){r 12 (Z ′ i(t 2 )) − r 13 (Y ′i (t 2 ))} + Dv(t 2 ){r 22 (Z i (t 2 ) − Z C )−r 23 (Y i (t 2 ) − Y C )} + Dv ′ (t 2 ){r 22 (Z ′ i(t 2 )) − r 23 (Y ′i (t 2 ))}+Dw(t 2 ){r 32 (Z i (t 2 ) − Z C ) − r 33 (Y i (t 2 ) − Y C )}+Dw ′ (t 2 ){r 32 (Z i(t ′ 2 )) − r 33 (Y i ′ (t 2 ))}]A 5 = t [2 − t 1 16 2 f(t 1) − 1 2 {Du(t1 ){s 11 (X i (t 1 ) − X C )) + s 12 (Y i (t 1 ) − Y C )i ( t 1 + t 2))}2+s 13 (Z i (t 1 ) − Z C )} + Du ′ (t 1 ){s 11 (X ′ i(t 1 )) + s 12 (Y ′i (t 1 )) + s 13 (Z ′ i(t 1 ))}+Dv(t 1 ){s 21 (X i (t 1 ) − X C )) + s 22 (Y i (t 1 ) − Y C ) + s 23 (Z i (t 1 ) − Z C )}+Dv ′ (t 1 ){s 21 (X ′ i(t 1 )) + s 22 (Y ′i (t 1 )) + s 23 (Z ′ i(t 1 ))}+Dw(t 1 ){s 31 (X i (t 1 ) − X C )) + s 32 (Y i (t 1 ) − Y C ) + s 33 (Z i (t 1 ) − Z C )}+Dw ′ (t 1 ){s 31 (X ′ i(t 1 )) + s 32 (Y ′i (t 1 )) + s 33 (Z ′ i(t 1 ))}104
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