bundle block adjustment with 3d natural cubic splines

slope and distance observations are dependent on the extended collinearity equationsusing splines, other constraints such as slope and arc-length increase non-redundantinformation in adjustment to reduce the overall rank deficiency of the system.The coplanarity approach is another mathematical model of the perspective relationshipbetween the image and the object space features. The projection planedefined by the perspective center in the image space and the plane including thestraight line in the object space are identical. Since the coplanarity condition is foronly straight lines, the coplanarity approach can not be extended to curves.Object space knowledge about a starting point of a spline can be employed tobundle block adjustment. Since control information about a starting point is availablefor only three parameters of total twelve unknown parameters of a spline, a splinewith control information about a starting point is called a partial control spline.Three spline parameters related to a starting point of a spline are set to stochasticconstraints and the result is in table 5.5.The total number of equations is 2 × 6(the number of images)×2(the number ofpoints) +6(the number of the arc-length) = 30 and the total number of unknownsis 9(the number of partial spline parameters)+12(the number of spline location parameters)= 21 so the redundancy is 9. A convergence of a partial spline and splinelocation parameters has been archived with a partial control spline.In the next experiment, spline location parameters are estimated with knownEOPs and a full control spline. Since spline parameters and spline location parametersare dependent with respect to other parameters, the unknowns can be obtained withthe model of an observation equation with stochastic constraints. In this experimentspline parameters are set to stochastic constraints and the result is in table 5.6. The82