bundle block adjustment with 3d natural cubic splines

3D natural cubic spline parameters are expected to recover correctly since extendedcollinearity equations with 3D natural cubic splines increase redundancy.3.3 Arc-length parameterization of 3D natural cubic splinesThe assumption in bundle block adjustment by the Gauss-Markov model is thatall estimated parameters are uncorrelated. Hence design matrix of bundle block adjustmentmust be of full rank, the non-singular normal matrix. However, since splineparameters are not independent to spline location parameters, additional observationsare required to obtain the estimations of parameters. In point-based approaches thepoint location relationship between image and object space is established to determinepose estimation including positions and orientations of a camera, which is afundamental application in photogrammetry, the remote sensing and the computervision. The coordinates of a point is the only piece of possible information to obtainthe solutions of the space intersection and the space resection. To remove the rankdeficiency which is caused by datum defects, constraints are adopted to estimate unknownparameters in point-based photogrammetry. The most common constraintsare coplanarity, symmetry, perpendicularity, and parallelism. The minimum numberof constraints is equal to the rank deficiency of the system. Inner constraints areoften used in the photogrammetric network, which can be applied both the objectfeatures and the camera orientation parameters. Angle or distance condition equationsprovide the relative information between observations in the object space andpoints in the image space. The absolute information can be obtained from the fixedcontrol points.44