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