Segmentation and analysis of oriented flow patterns.

Abstract

This dissertation presents a computational system for extracting both qualitative and quantitative descriptions from a planar orientation field containing multiple critical points. We model the orientation field, a special kind of vector field with $\pm\pi$ ambiguity in its phase angle, using the relative parameters of differential equations. Two equivalent classification schemes are designed to define the flow pattern types of orientation fields. One is eigenvalue-based and the other is based on the quantitative measurements of curl, divergence, and deformation of orientation fields. We proved a fundamental theorem showing that using only the phase angle of an orientation field to identify the flow pattern type is sufficient. We first designed an isotangent-based estimator to approximate a measured orientation field. It separates the estimation of the critical point position from the estimation of the characteristic parameters for determining flow pattern type. By designing a direct estimator that considers both the critical point position and the characteristic parameters of an objective function, we significantly improve the orientation field approximation. We carried out Error analysis on the estimated parameters. Qualitative error analysis of the estimated flow pattern type is performed by utilizing the classification space spanned by the curl, divergence, and deformation of the corresponding vector field. We designed a closed-form condition number to measure the vulnerability of an estimated critical point position to noise perturbation. After combining the results for all of our previous analysis, we develop a segmentation system for a planar orientation field containing multiple critical points. This system performs local parameter estimation first using the direct estimator. Dynamic critical point detection and region growing were designed to integrate the information from the parameter estimation. Three principles were used to design the detection algorithm: attention focusing, hypothesis testing, and lateral inhibition. Region growing was implemented using an isotangent property and a proximity principle.