bundle block adjustment with 3d natural cubic splines

estimation is obstacled by the correspondence problem, but employing splines is oneway to overcome the occlusion and ambiguity problems. The manual identificationof corresponding entities in two images is crucial in the automation of photogrammetrictasks.Another problem of point-based approaches is the weak geometricconstraints compared to feature-based methods so the accurate initial values for theunknown parameters are required. Feature-based aerial triangulation can be implementedwithout conjugate points since the measured points in each image are notthe conjugate points in this proposed adjustment model. Thus tie spline which doesnot appear in all overlapped images together can be employed in feature-based aerialtriangulation. Another advantage of employing splines is that adopting high levelfeatures increases the feasibility of geometric information and provides an analyticaland suitable solution to increase the redundancy of aerial triangulation.3D linear features expressed by 3D natural cubic splines are employed as themathematical model of linear features in the object space and its counterpart in theprojected image space for bundle block adjustment. To solve over-parameterizationof 3D natural cubic splines, arc-length parameterization using Simpson’s rule is developedand in case of straight lines and conic sections, tangents of spline can be additionalequations to the overparameterized system. Photogrammetric triangulationby the proposed model including the extended collinearity equation and arc-lengthparameterization equation is developed to show the feasibility of tie splines and controlsplines for the estimation of exterior orientation of multiple images, spline andspline location parameters.A useful stochastic constraint for a spline segment is examined to become a fullor partial control spline such as known EOPs with a tie, partial control, and full97