bundle block adjustment with 3d natural cubic splines

about splines, their relationships, and the orientation information of images can beconsidered as control information.Spline parameters in partial control spline ororientation parameters can be considered as stochastic constraints in the integratedadjustment model. The starting point of a spline is considered as a known parameterin the partial control spline which a 0 , b 0 and c 0 of X, Y and Z coordinates of a splineare known. The number of unknowns is described in table 5.1 and figure 5.1 wheren is the number of points in the object space, t shows the number of spline locationparameters and m represents the number of overlapped images in the target area.EOP Spline Number of unkonwnsTie spline12(n − 1) + tKnown EOP Partial control spline 9(n − 1) + tFull control splinetUnknown EOP Partial control spline 6m + 9(n − 1) + tFull control spline 6m + tTable 5.1: Number of unknownsFour points on a spline segment in one image are the only independent observationsso additional points on the same spline segment do not provide non-redundantinformation to reduce the overall deficiency of the EOP and spline parameter recovery.To prove the information content of an image spline, we demonstrate that anyfive points on a spline segment generates a dependent set of the extended collinearityequations. Any combinations of four points yielding eight collinearity equations areindependent observations but five points bearing ten collinearity equations producea dependent set of observations related with the correspondence between a natural71