bundle block adjustment with 3d natural cubic splines

Recommendations

Info

a lot in man-made structures and mobile mapping system in reality, they have focusedon implementation with straight linear features with geometric constraints.Since many man-made environments including buildings often have straight edgesand planar faces, it is advantageous to employ line photogrammetry instead of pointphotogrammetry when mapping polyhedral model objects.Mikhail[43] and Habib et al.[27] accomplished the geometrical modeling and theperspective transformation of linear features within a triangulation process. Linearfeatures were used to recover relative orientation parameters. Habib et al. proposeda free-form line in object space by a sequence of 3D points along the object spaceline.Lee and Bethel[38] proposed employing both points and linear features were moreaccurate than using only points in ortho-rectification of airborne hyperspectral imagery.EOPs were recovered accurately and serious distortions were removed by thecontribution of linear features.Schenk[59] extended the concept of aerial triangulation from point features tolinear features. The line equation of six dependent parameters replaced the pointbased collinearity equation.X = X A + t · aY = Y A + t · bZ = Z A + t · c(2.9)where a real variable t, the start point (X A , Y A , Z A ) and direction vector (a, b, c).Traditional point-based collinearity equation was extended to line features18
x p = −f (X A + t · a − X C )r 11 + (Y A + t · b − Y C )r 12 + (Z A + t · c − Z C )r 13(X A + t · a − X C )r 31 + (Y A + t · b − Y C )r 32 + (Z A + t · c − Z C )r 33y p = −f (X A + t · a − X C )r 21 + (Y A + t · b − Y C )r 22 + (Z A + t · c − Z C )r 23(X A + t · a − X C )r 31 + (Y A + t · b − Y C )r 32 + (Z A + t · c − Z C )r 33(2.10)with x p , y p photo coordinates, f the focal length, X C , Y C , Z C camera perspectivecenter, and r ij the elements of the 3D orthogonal rotation matrix. The extendedcollinearity equation with six parameters was derived as the line expression of fourparameters (φ, θ, x o , y o ) since a 3D straight line has only four independent parameters.Two constrains are required to solve a common form of the 3D straight equations usingsix parameters determined by two vectors.⎡⎢⎣XYZ⎤⎥⎦ =⎡⎢⎣cos θ cos φ · x o − sin φ · y o + sin θ cos φ · zcos θ sin φ · x o + cos φ · y o + sin θ sin φ · z− sin θ · x o + cos θ · z⎤⎥⎦ (2.11)where z is a real variable. The advantage of the 3D straight line using four independentparameters is that it reduces the computation and time complexity in theadjustment processes such as a bundle block adjustment. The collinearity equationas the straight line function of four parameters was developed.x p = −f (X − X C)r 11 + (Y − Y C )r 12 + (Z − Z C )r 13(X − X C )r 31 + (Y − Y C )r 32 + (Z − Z C )r 33y p = −f (X − X (2.12)C)r 21 + (Y − Y C )r 22 + (Z − Z C )r 23(X − X C )r 31 + (Y − Y C )r 32 + (Z − Z C )r 33where X, Y, and Z were defined in (2.11).The solution of the bundle block adjustment with linear features was implemented sothat the line-based aerial triangulation can provide a more robust and autonomousenvironment than the traditional point-based bundle block adjustment.Anothermathematical model of the perspective relationship between the image and the object19
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: ⎡⎢⎣x i − x py i − y p−f
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 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
show all

bundle block adjustment with 3d natural cubic splines

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?