On the suitability of conic sections in a single-photo resection, camera calibration, and photogrammetric triangulation

At the present time, the algorithms involved in photogrammetric activities are changing substantially. Photogrammetric activities are expanding to accommodate features other than points, such as straight-line, in the photogrammetric solution. Along this line of expansion, in this study, conic sections (circles and ellipses) were formulated as computational entities for the solution of single photo resection, camera calibration, and photogrammetric triangulation.; Feature extraction is the entry point for the use of conics. In this research, an integrated and robust algorithm for the extraction of multiple conic was developed. This algorithm addresses the extraction of conics at three stages. The first two stages are based on parametric data extraction under the general framework of Hough Transform. A crucial contribution in this algorithm is the notion of the directional attribute, which facilitates the best use of the information provided by the parametric extraction. The third stage takes the form of a probabilistic inference rule. Successful performance was demonstrated on simulated and real data.; Analytical representation of conic sections was required in this study. To this end, a least-squares conic fitting algorithm was developed. This algorithm minimizes the distance between the observed points and a modified conic along the normal to its tangent for every observed point. This algorithm neglects second order terms induced by the quadratic nature of the conic equation at each step and, therefore, requires some iterations. Experimental finding based on simulated and real data confirmed the good performance of this algorithm.; Two non-linear conics-based algorithms for a single-photo resection were developed (CCA and PTFA). The CCA is very robust to the selection of the initial approximations. Slightly different from zero and exactly zero approximations are sufficient to initialize the camera position and the rotation angles, respectively. On the other hand, the PTFA is very sensitive to the initial approximations, and even the hierarchical initialization through the CCA could not facilitate its use in a practical camera calibration that suffered from severe distortions. The CCA and the PTFA show different sensitivity to random noise. Small variances were encountered in the CCA, and relatively large ones are induced by the PTFA. Most likely the developed target function for the PTFA does not explain the complete relationship between an image point and its associated conic in the object space.; One of the most striking and interesting findings was revealed by the variance-covariance comparison metric. This metric showed that the use of CCA in a single-photo resection gives the best global accuracy among three other algorithms. (Abstract shortened by UMI.)...