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

Seedahmed, Gamal H
http://rave.ohiolink.edu/etdc/view?acc_num=osu1073186865

Abstract Details

2004, Doctor of Philosophy, Ohio State University, Geodetic Science and Surveying.
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. In particular, the CCA outperformed the PTFA, the collinearity, and a mixed algorithm that combined the CCA and the collinearity model. Moreover, the mixed algorithm outperformed the other two algorithms. From this finding we can infer that the CCA gives highly accurate single-photo resection parameters with very small dispersions and minimum correlation among the parameters compared to the other three algorithms. In general, these experiments confirmed that there is a strong element of global precision that can be obtained from the use of conics. Thus, applications that require highly accurate estimates, such as tolerance checking, may benefit from the CCA to derive reliable parameters. Moreover, the CCA is highly resistant to the deficiencies in the network design. As expected, a direct relationship between the conic size and the precision was found. Simulated examples show that improvement by an order of magnitude in the precision can be achieved by increasing the size of the conic by an order of magnitude. A successful camera calibration algorithm was developed based on the CCA. This algorithm behaves very satisfactorily in simulated and real examples. An over-optimistic accuracy performance was attainted for the estimated principle point. A solely conics-based photogrammetric triangulation was demonstrated using the CCA. To the best of our knowledge, this is the first successful demonstration of the conics as suitable tie and control features to replace control and tie points in the classical point-based triangulation. A geometric configuration with tilted images that have different depths is rather suitable to minimize the existing dependency between the exterior orientation parameters and the plane parameters. Partially extracted conics did not impact the precision of the estimated parameters. It is very important to stress that there are no manual measurements involved in any of the developed algorithms. In particular, an autonomous solution was achieved for the single-photo resection. The set of the developed algorithms could be used to build a close range photogrammetric measurement system for industrial applications. Although the current use of the algorithms is restricted to circles and ellipses for practical reasons, these algorithms are general enough to handle the full class of conic sections, even the degenerate ones such as straight lines.
Anton Schenk (Advisor)
138 p.
Geodesy
Autonomous Photogrammetry; Feature-Based Photogrammetry; Point-Based Photogrammetry; Conic Sections; Hough Transform; RANSAC; Conic Fitting; Single-Photo Resection; Exterior Orientation; Camera Calibration; Photogrammetric Triangulation

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Citations

  • Seedahmed, G. H. (2004). On the suitability of conic sections in a single-photo resection, camera calibration, and photogrammetric triangulation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1073186865

    APA Style (7th edition)

  • Seedahmed, Gamal. On the suitability of conic sections in a single-photo resection, camera calibration, and photogrammetric triangulation. 2004. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1073186865.

    MLA Style (8th edition)

  • Seedahmed, Gamal. "On the suitability of conic sections in a single-photo resection, camera calibration, and photogrammetric triangulation." Doctoral dissertation, Ohio State University, 2004. http://rave.ohiolink.edu/etdc/view?acc_num=osu1073186865

    Chicago Manual of Style (17th edition)

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This open access ETD is published by The Ohio State University and OhioLINK.