Date of Award


Degree Type


Degree Name

Doctor of Philosophy



First Advisor


Committee Members

Yi HU, Jun ZHANG, Ethan MUNSON, Jugal Ghorai


3D Camera Calibration Tool, Camera Calibration, Image Metrology, Robust Statistics, Singularity of Representation, Spherical Coordinate System


This thesis demonstrates theenhancement to camera calibrationin three aspects: representation of pose, robust statistics and 3D calibration tool. Camera calibration is the reconstruction of digital camera information based on digital images of an object in 3D space, since the digital images are 2D projections of a 3D object onto the camera sensor. Camera calibration is the estimation of the interior orientation (IO) parameters and exterior orientation (EO) parameters of a digital camera. Camera calibration is an essential part of image metrology. If the quality of camera calibration cannot be guaranteed, neither can the reliability of the subsequent analysis and applications based on digital images.

The first enhancement of camera calibration is in representation of pose. A formal definition of "singularity of representation" is given mathematically. An example is offered to show how singularity can lead to difficulty or failure in optimization. The spherical coordinate system is introduced as a representation method instead of other widely-used representations. Thespherical coordinate systemrepresents camera poses according to camera calibration tool images in digital image processing. With the introduction of the v frame in digital images, the singularities of spherical coordinate system are demonstrated mathematically.

The application ofrobust statisticsin optimization is the second enhancement of camera calibration. In photogrammetry, it is typical to collect thousands of observed data points for bundle adjustment. Unexpected outliers in observed data are unavoidable, and thus, the algorithm accuracy may not reach our goal. The least squares estimator is a widely used estimation method in camera calibration, but its sensitivity to outliers makes the algorithm unreliable, and it can even fail to fit the observations. By closely analyzing and comparing the characteristics of the least squares estimator, robust estimators with alternative assumptions are shown to detect and de-weight outliers that are not well processed with the classical assumptions, and provide a reliable fit to the observations. Among all possible robust estimators, two robust estimators from M-estimator family are applied to optimization in existing camera calibration algorithm. The robustified method can considerably improve accuracy for camera calibration estimation.

Anew metric \bar{D}is introduced, which is the distance between two camera calibrations considering all of the estimated camera IO parameters. \bar{D} can be used to evaluate the performance among various estimators. After applying the robust estimator, the system improves the accuracy and performance in camera calibration up to 25\%. The influence of a robustified estimator modification is also considered. It is established that the modification has impact on the estimation accuracy.

The third enhancement is the design and application of a3D calibration toolfor data collection. An all-new 3D calibration tool is designed to improve camera calibration accuracy over the 2D calibration tool. The comparison of the 3D and 2D calibration tools is conducted experimentally and theoretically. The experimental analysis is based on camera calibration results and the corresponding \bar{D} matrix, which shows that the 3D calibration tool improves accuracy. The mathematical analysis is based on the calculated covariance matrix of camera calibration without other impact factors. The experimental and theoretical analyses show that the 3D calibration tool can obtain more accurate calibration results compared with the 2D calibration tool, establishing that a carefully designed 3D calibration tool will yield better estimates than a 2D calibration tool.