Quality Control Methodologies for 3D Geometric Primitives Derived from LiDAR Data

The purpose of this study is to develop algorithms with a computational ability to reliably establish with precision and accuracy the critical parameters of a solid object in space. Utilizing a least-squares adjustment method and laser scanned data, a three-dimensional computer assisted drawing (3D CAD) model of an object (e.g., machinery component) may be then used in the redesign, retrofitting, and updating of technical drawings. This thesis presents a unique approach to point cloud data modeling and visualization as well as numerical analysis based on stability criteria. Several statistical techniques from the literature are reviewed and implemented dealing with numerical methods using the stability of matrices as a criterion. The thesis discusses topics ranging from basic statistical analysis to advanced topics such as Singular Value Decomposition (SVD) and condition numbers. Various theories and techniques of obtaining stability criteria are described and analyzed. Test of point cloud data revealed that combining standard numerical analysis with Condition Numbers allows for quantifying the goodness-of-fit of the results and for predicting the behavior of the algorithms.