bundle block adjustment with 3d natural cubic splines

5.3 Recovery of EOPs and spline parametersThe object space knowledge about splines is available to recover the exterior orientationparameters in bundle block adjustment.Control spline and partial controlspline are applied to verify the feasibility of control information with splines.In both cases, equations of the arc-length parameterization are not necessary if wehave enough equations to solve the system since spline parameters are independentof each other. In the experiment of full control spline, the total number of equationsare 2 × 6(the number of images)×4(the number of points) +3(the number ofarc-length)×6(the number of images) = 66 and the total number of unknowns are36(the number of EOPs) +24(the number of spline location parameters) = 60. Theredundancy is 6.In the case of the partial control spline with one spline segment, the total numberof equations are 2 × 6(the number of images)×4(the number of points) +3(the numberof arc-length)×6(the number of images) = 66 and the total number of unknownsare 36(the number of EOPs)+9(the number of partial spline parameters)+24(thenumber of spline location parameters) = 69. Thus one more segment is required tosolve the underdetermined system. The total number of equations using two splinesegments are 2 × 6(the number of images)×4(the number of points)×2(the numberof spline segment) +3(the number of arc-length)×6(the number of images)×2(thenumber of spline segment) = 132 and the total number of unknowns are 36(the numberof EOPs)+9(the number of partial spline parameters)×2(the number of splinesegment)+24(the number of spline location parameters)×2(the number of spline segment)= 102. The redundancy is 30. A convergence of EOPs of an image block andspline parameters have been achieved in both experiments.85