Arc-length parameterization of linear features for photogrammetric tasks

While in traditional photogrammetry, photogrammetric tasks are solved by point-to-point correspondences, in the advanced computer technology environment higher-level linear features may be used to develop more robust, general, and accurate techniques. Employing high-level features increases the prospect that geometric information can provide suitable solutions and that prior knowledge of correspondence between individual points, consisting of features in object space and in image space, is not required. Three-dimensional natural cubic splines are employed as mathematical models of linear features in the object space and their counterparts in the projected image space. To solve overparameterization of 3D natural cubic splines, arc-length parameterization using Simpson's rule is used, and tangents of the splines provide additional constraints to the overparameterized system. Traditional collinearity equations are expanded to allow employment of the 3D curve. In this work, the integrated model of the extended collinearity equation utilizing 3D natural cubic splines, tangents of splines, and arc-length parameterization is derived to recover the exterior orientation parameters, 3D natural cubic spline parameters, and spline location parameters.