bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines bundle block adjustment with 3d natural cubic splines
The stereo model consisting of two images with twelve EOPs is a common orientationunit. The mechanism of object reconstruction from stereo model is the samewith the animal and human visual system. The principle aspects of the human visionsystem including neurophysiology, anatomy and visual perception is well describedin Digital Photogrammetry (Schenk, 1999 [57]). The classical orientation model isimplemented in two steps with relative orientation and absolute orientation to solvetwelve orientation parameters for a model of two images. Five unknowns are solvedfrom relative orientation for a stereoscopic view to the model, and seven unknownsthree shifts, three rotations, and one scale factor are determined from absolute orientation.At least three vertical and two horizontal control points are required to obtainseven parameters of absolute orientation. In traditional photogrammetry, all orientationprocedures are performed manually by a photogrammetric operator. Fiducialmarks which define the photo coordinate system while they define the pixel coordinatesystem in digital photogrammetry are used in interior orientation which is imagereconstruction with respect to perspective center.The matching of conjugate entities plays an important role in relative orientation,and ground control points (GCPs) are adopted in absolute orientation to calculatethe object space coordinate system. Matching techniques can be divided into twocategories, area-based matching and feature-based matching. Area-based matchingmethods employ a similarity property between a small image patch in a templatewindow and an image patch in a matching window.Two well known area-basedmatching methods are cross-correlation and least squares matching, also gray levelsplay an important role in area-based matching. Feature-based matching uses featuresfor conjugate entities such as points, edges, linear features and volume features and the4
similarity of geometric properties are compared to find conjugate entities. Featurebasedmatching is more invariant to radiometric changes and the implementation timeof feature-based matching is faster than that of area-based matching. Extracting andmatching conjugate points are the first step for the autonomous space resection butthe general procedure of the autonomous space resection has not been developed yetas no matching algorithm can guarantee consistent accuracy.Conjugate entities correspond to the same point in the object space using collinearityequation that all a point on the image, a perspective center and the correspondingpoint in the object space are on the same straight line. For stereo model, thecoplanarity condition which is established by the equation for the volume of the parallelepipedcan be adopted with a mathematical formula. The volume of the parallelepipedis decided by the three vectors which are a vector between a left perspectivecenter and an image point on the left image, a vector between a right perspectivecenter and an image point on the right image and a vector between two perspectivecenters. That means that two perspective centers and two conjugate image rays liein the one plane and vectors are the object space vectors.The coplanarity equation is used for the relative orientation in the stereo model.Seven of twelve exterior parameters are fixed and the remaining five parameters areobtained by five or more coplanarity equations since one coplanarity equation eliminatesone degree of freedom. Adding more coplanarity equations increases the possibilityof the detection of the incorrect observation and the obtainment of a moreprecise result. However, the relative orientation of more than two images using coplanarityequations has a problem since, in general, all rays from each images do not5
- 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: y an intersection employing more th
- 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
similarity of geometric properties are compared to find conjugate entities. Featurebasedmatching is more invariant to radiometric changes and the implementation timeof feature-based matching is faster than that of area-based matching. Extracting andmatching conjugate points are the first step for the autonomous space resection butthe general procedure of the autonomous space resection has not been developed yetas no matching algorithm can guarantee consistent accuracy.Conjugate entities correspond to the same point in the object space using collinearityequation that all a point on the image, a perspective center and the correspondingpoint in the object space are on the same straight line. For stereo model, thecoplanarity condition which is established by the equation for the volume of the parallelepipedcan be adopted <strong>with</strong> a mathematical formula. The volume of the parallelepipedis decided by the three vectors which are a vector between a left perspectivecenter and an image point on the left image, a vector between a right perspectivecenter and an image point on the right image and a vector between two perspectivecenters. That means that two perspective centers and two conjugate image rays liein the one plane and vectors are the object space vectors.The coplanarity equation is used for the relative orientation in the stereo model.Seven of twelve exterior parameters are fixed and the remaining five parameters areobtained by five or more coplanarity equations since one coplanarity equation eliminatesone degree of freedom. Adding more coplanarity equations increases the possibilityof the detection of the incorrect observation and the obtainment of a moreprecise result. However, the relative orientation of more than two images using coplanarityequations has a problem since, in general, all rays from each images do not5
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