Single View Coplanar Photogrammetry and Uncertainty Analysis for Traffic Accident Reconstruction
Photogrammetry is defined as the science of measuring distances and objects by using photographs. Rapid advances in computer technology and digital photography in recent years have resulted in growing applications of digital photogrammetry. Although various aspects of photogrammetry have been investigated; the question of uncertainties in measurement, which is important for forensic applications, such as traffic accident reconstruction, has not been widely explored. This study attempted to develop an applicable comprehensive mathematical model to perform coplanar photogrammetry and provide a measure of uncertainty for its measurements. Photogrammetry requires information about the interior and exterior orientation of the camera. Process maximum likelihood estimation (MLE) of the interior parameters of the camera or camera calibration and methods to provide uncertainty for those parameters are discussed. To find the maximum likelihood estimation of the exterior orientation of the camera, a new pose estimation algorithm has been developed that requires only information about the length of three or more lines in the scene while taking into account nonlinearities due to lens distortion. Formulation to find the maximum likelihood estimation of back projection of individual points to world frame considering uncertainties in interior and exterior orientation has been provided. Finally, all uncertain models have been compiled into an uncertain comprehensive model for photogrammetric measurement on a coplanar scene. A computer application equipped with a simulation tool has been developed for the Windows operating system to implement the model. A simulation has been performed to investigate the effect of various parameters on photogrammetry measurement and it was found that the error in the length of reference lines has the most significant effect. Aerial photos of a mock accident scene were used for the experimental study. Experiment results showed that the proposed method can provide distance measurement with an average error of 1%, while the uncertainty for its measurements follows the three-sigma rule.
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Faculty of Graduate Studies and Research, University of Regina