bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines
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+Du ′ (t 2 )r 11 X i ′′ (t 2 ) + Dv ′ (t 2 )r 23 Y i ′′ (t 2 ) + Dw ′ (t 2 )r 33 Z i ′′ (t 2 )}( ) t1 + t −12+2f2+Dw( t 1 + t 222 { Du( t 1 + t 22)r 33 Z i( ′ t 1 + t 2)2)r 11 X ′ i( t 1 + t 22) + Dv( t 1 + t 2)r 23 Y ′2+Du ′ ( t 1 + t 2)r 13 X i ′′ ( t 1 + t 2) + Dv ′ ( t 1 + t 2)r 23 Y i ′′ ( t 1 + t 2)2222+Dw ′ ( t 1 + t 2)r 33 Z i ′′ ( t }]1 + t 2)}22i ( t 1 + t 2)2A.3 Derivation of the tangent of a splineThe partial derivatives of symbolic representation of the tangent of the splinebetween image and object space are illustrated as follows.L 1 = − w′ (v ′ w − w ′ v)(u ′ w − w ′ u) r w ′2 11 +(u ′ w − w ′ u) r 21 − w′ (u ′ v − v ′ u)(u ′ w − w ′ u) r 2 31L 2 = − w′ (v ′ w − w ′ v)(u ′ w − w ′ u) r w ′2 12 +(u ′ w − w ′ u) r 22 − w′ (u ′ v − v ′ u)(u ′ w − w ′ u) r 2 32L 3 = − w′ (v ′ w − w ′ v)(u ′ w − w ′ u) r w ′2 13 +(u ′ w − w ′ u) r 23 − w′ (u ′ v − v ′ u)(u ′ w − w ′ u) r 2 33L 4 = (v′ w − w ′ v)(u ′ w − w ′ u) 2 {w′ [r 12 (Z i (t) − Z C ) − r 13 (Y i (t) − Y C )]−w[r 12 (Z ′ i(t)) − r 13 (Y ′i (t))]}1−u ′ w − w ′ u {w′ [r 22 (Z i (t) − Z C ) − r 23 (Y i (t) − Y C )]−w[r 22 (Z ′ i(t)) − r 23 (Y ′i (t))]}1+(u ′ w − w ′ u) {[v′ − u′ (v ′ w − v ′ w)u ′ w − w ′ u ][r 32(Z i (t) − Z C ) − r 33 (Y i (t) − Y C )]−[v − u(v′ w − v ′ w)u ′ w − w ′ u ][r 32(Z ′ i(t) − r 33 (Y ′i (t)]}L 5 = (v′ w − w ′ v)(u ′ w − w ′ u) 2 {w′ [s 11 (X i (t) − X C ) + s 12 (Y i (t) − Y C ) + s 13 (Z i (t) − Z C )]−w[s 11 (X ′ i(t)) + s 12 (Y i (t)) + s 13 (Z i (t))]}110