bundle block adjustment with 3d natural cubic splines

In the case of straight lines and conic sections, tangents are the additional observationsin the integrated model. Conic sections which, like points, are good mathematicalconstraints since conic sections are non-singular curves of degree 2. Second-degreeequations provide the information for reconstruction and transformation and conicsections are divided by the eccentricity e as shown in table 4.1. Since conic sectionscan adopt more constraints than points and straight line features, conic sections areuseful for close range photogrammetric applications. In addition, conic sections havethe strength in the correspondence establishment between 3D conic sections in theobject space and their counterpart features in the 2D projected image space.Eccentricity Conic forme=0 Circle0 < e < 1 Ellipsee = 1 Parabolae > 1 HyperbolaTable 4.1: Relationship between the eccentricity and the conic formJi et al.(2000) [36] employed conic sections for the recovery of EOPs andHeikkila(2000) [33] used them for camera calibration. Hough transformation reducesthe time complexity of the conic section extraction using five parameter spaces for asingle-photo resection, camera calibration and triangulation [63].x p + f u0w 0 = M 1 dX C + M 2 dY C + M 3 dZ C + M 4 dω + M 5 dϕ + M 6 dκ + M 7 da i0+M 8 da i1 + M 9 da i2 + M 10 da i3 + M 11 db i0 + M 12 db i1 + M 13 db i258