bundle block adjustment with 3d natural cubic splines

cubic spline in the image and the object space. More than four point observations onan image spline segment increase the redundancy related with the accuracy but donot decrease the overall rank deficiency of the proposed adjustment system. In thesame fashion, the case using a polynomial of degree 2 can be implemented. Threepoints on a quadratic polynomial curve in one image are the only independent sets soadditional points on the same curve segment are a dependent observation. More thanindependent point observations on a polynomial increase the redundancy related withthe accuracy but do not provide the non-redundant information. Depending on theorder of a polynomial, the number of independent points for bundle block adjustmentis limited as table 5.2.Polynomial Number of independent pointsConstant polynomial 1Linear polynomial 2Quadratic polynomial 3Cubic polynomial 4Table 5.2: Number of independent points for bundle block adjustmentThe amount of information carried by a natural cubic spline can be calculatedwith the redundancy budget. Every spline segment has twelve parameters and everypoint measured on a spline segment increases one additional parameter. Let n bethe number of points measured on one spline segment in the image space and m bethe number of images which contain a tie spline.2nm collinearity equations andm(n-1) the arc-length parameterizations are equations and 12 (the number of onespline segment parameters) + nm (the number of spline location parameters) are73