PHOTOGRAMMETRIC TRIANGULATION OF 3D CUBIC SPLINES

A common application in Photogrammetry is the 3D reconstruction of objects. Many objects are composed of curved features which are difficult to model using only point-based matching. We present an intersection method for the triangulation of 3D cubic splines from a series of measurements in several images. The method stems from the basic observation equation of a point on a 3D cubic spline; it minimizes the measurement residuals by adjusting the parameters of the spline, and the ratio of each measurement along the spline. As such, the method is flexible and can easily handle multiple projections (perspective and orthogonal) and widely varying fields-of-view. Also, the triangulation only requires that the measurements of the ends of the spline are matched between images. The intermediate measurements can be located at any point along the spline and need not match between images. We discuss the 3D natural cubic spline and the Hermite spline. The method is demonstrated with several features on a vessel imaged with a long lens in a surveillance setting.