bundle block adjustment with 3d natural cubic splines
bundle block adjustment with 3d natural cubic splines bundle block adjustment with 3d natural cubic splines
straight features and conic sections. In this work the integrated model of the extendedcollinearity equation utilizing 3D natural cubic spline and arc-length parameterizationis derived to recover the exterior orientation parameters, 3D natural cubic splineparameters and spline location parameters. The research topics in this dissertationare sketched below bullet items.• 3D natural cubic spline is adopted for the 3D line expression in the objectspace to represent 3D features as parametric form. The result of this algorithmare the tie and control features for bundle block adjustment.This is a keyconcept of the mathematical model of linear features in the object space andits counterpart in the projected image space for line photogrammetry.• Arc-length parameterization of 3D natural cubic splines using Simpson’s rule isdeveloped to solve over-parameterization of 3D natural cubic splines. Additionalequation to the extended collinearity equation expands bundle block adjustmentfrom limited conditions such as straight lines or conic sections (circles, ellipses,parabolas and hyperbolas) to general cases.• Tangents of splines which are additional equations to solve the overparameterizationof 3D natural cubic splines are established in case linear features in theobject space are straight lines or conic sections.• To establish the correspondence between 3D natural cubic splines in the objectspace and their associated features in the 2D projected image space, the extendedcollinearity equation employing the projection ray which intersects the3D natural cubic splines is developed and linearized for least squares method.8
• Bundle block adjustment by the proposed method including the extended collinearityequation and arc-length parameterization equation is developed to show thefeasibility of tie splines and control splines for the estimation of exterior orientationof multiple images, spline parameters and t spline location parameterswith simulated and real data.1.3 Organization of dissertationThis dissertation is divided into six chapters. The next chapter presents a reviewof line photogrammetry including mathematical representations of 3D curves.Chapter 3 provides the extended collinearity model and formulation using 3D naturalcubic splines and presents arc-length parameterization of 3D natural cubic splines.The non-linear integrated model is followed to recover EOPs, spline parameters andspline location parameters by tie and control features of 3D natural cubic splinesin chapter 4. Detailed derivations of the extended collinearity equations, arc-lengthparameterization and tangents of splines are provided in the appendix. Chapter 5introduces experimental results to demonstrate the feasibility of bundle block adjustmentwith 3D natural cubic splines with synthetic and real data. Finally, a summaryof experience and recommended future research are included in chapter 6.9
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• Bundle <strong>block</strong> <strong>adjustment</strong> by the proposed method including the extended collinearityequation and arc-length parameterization equation is developed to show thefeasibility of tie <strong>splines</strong> and control <strong>splines</strong> for the estimation of exterior orientationof multiple images, spline parameters and t spline location parameters<strong>with</strong> simulated and real data.1.3 Organization of dissertationThis dissertation is divided into six chapters. The next chapter presents a reviewof line photogrammetry including mathematical representations of 3D curves.Chapter 3 provides the extended collinearity model and formulation using 3D <strong>natural</strong><strong>cubic</strong> <strong>splines</strong> and presents arc-length parameterization of 3D <strong>natural</strong> <strong>cubic</strong> <strong>splines</strong>.The non-linear integrated model is followed to recover EOPs, spline parameters andspline location parameters by tie and control features of 3D <strong>natural</strong> <strong>cubic</strong> <strong>splines</strong>in chapter 4. Detailed derivations of the extended collinearity equations, arc-lengthparameterization and tangents of <strong>splines</strong> are provided in the appendix. Chapter 5introduces experimental results to demonstrate the feasibility of <strong>bundle</strong> <strong>block</strong> <strong>adjustment</strong><strong>with</strong> 3D <strong>natural</strong> <strong>cubic</strong> <strong>splines</strong> <strong>with</strong> synthetic and real data. Finally, a summaryof experience and recommended future research are included in chapter 6.9
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