bundle block adjustment with 3d natural cubic splines

space features is the coplanarity approach. Projection plane defined by the perspectivecenter in the image space and the plane including the straight line in the objectspace are identical. The extended collinearity model using linear features comparingwith the coplanarity method was proposed. Zielinski[80] described another straightline expression with independent parameters.Zalmanson and Schenk[79] extended their algorithm to relative orientation usingline parameters. Epipolar lines were employed to adopt linear features in relativeorientation with the extended collinearity equations (2.10).Gauss-Markov modelwas partitioned into orientation parameters and line parameters as (2.13).y = [ A R A L] [ ξ Rξ L]+ e (2.13)where ξ R relative orientation parameters, ξ L line parameters, A R the partial derivativesof extended collinearity equations with respect to relative orientation parameters,A L the partial derivatives of extended collinearity equations with respect to lineparameters, and e the error vector. They demonstrated that parallel lines to epipolarlines contributed to relative orientation totally and vertical lines to epipolar linesrendered only surface reconstruction. In addition, they introduced a regularizationscheme with soft constraints for the general cases.Zalmanson[78] updated EOPs using the correspondence between the parametriccontrol free-form line in object space and the projected 2D free-form line in imagespace. The hierarchical approach, the modified iteratively close point (ICP) method,was developed to estimate curve parameters. The ray lies on the free-form line whoseparametric equation represented with l parameter is as following. Besl and McKay[7]employed the ICP algorithm to solve matching problem of point sets, free-form curves,20