(Dr. Thomas Kurfess, advisor)

"Initial Guessing of Primitives for Minimization"

Abstract

Developments in manufacturing techniques have been heavily dependent on the ability to characterize the process through measuring and analyzing the produced part. This is especially important for new manufacturing processes that are still in the early stages of development such as MEMS fabrication. Metrology techniques (i.e. tomography, interferometry) are used to gather measurement data from the surfaces of the part.

The data (in the form a of a 3D point cloud) must be processed and analyzed in order to compare the original design or CAD file to the parameters of the part. Many engineered components can be analyzed by fitting primitives (i.e. planes, spheres, torus etc…) to the point cloud using nonlinear least squares minimization. The problem is that the minimizer requires a starting point (initial guess) that does not lead to a local minimum. This can result in a primitive fit that is offset in rotational orientation by 90 degrees. Previous initial guessing techniques assumed that the primitive was principally aligned, which can lead to spurious results. Computation time is also a function of how close the initial guess is to the actual parameters.

This thesis will outline strategies for obtaining initial estimates for the iterative fitting of analytic primitives to point cloud data. The primitives discussed will be the plane, torus, and the specific quadrics of sphere, right circular cone, and right circular cylinder. Depending on the primitive, a varying number of approaches are discussed. The main strategies for obtaining initial estimates of parameters include analytic methods and numerical methods such as bounding boxes. For each primitive, the approach(s) is explained, outlined and then any pitfalls or limitations are discussed. The methods are presented in the context of speed of execution, robustness in the presence of partial clouds or noise, accuracy of fit, and ease of implementation.