Geometric primitive feature extraction - concepts, algorithms, and applications
This work solves problems in computer vision for applications like image analysis, but it is incremental as it builds on existing methods with specific improvements.
The thesis tackles the extraction of geometric primitives from digital image edges by addressing polygonal approximation, tangent estimation, and ellipse fitting/detection, resulting in a non-heuristic framework, a tangent method outperforming 72 existing ones, and an ellipse detection method with high selectivity.
This thesis presents important insights and concepts related to the topic of the extraction of geometric primitives from the edge contours of digital images. Three specific problems related to this topic have been studied, viz., polygonal approximation of digital curves, tangent estimation of digital curves, and ellipse fitting anddetection from digital curves. For the problem of polygonal approximation, two fundamental problems have been addressed. First, the nature of the performance evaluation metrics in relation to the local and global fitting characteristics has been studied. Second, an explicit error bound of the error introduced by digitizing a continuous line segment has been derived and used to propose a generic non-heuristic parameter independent framework which can be used in several dominant point detection methods. For the problem of tangent estimation for digital curves, a simple method of tangent estimation has been proposed. It is shown that the method has a definite upper bound of the error for conic digital curves. It has been shown that the method performs better than almost all (seventy two) existing tangent estimation methods for conic as well as several non-conic digital curves. For the problem of fitting ellipses on digital curves, a geometric distance minimization model has been considered. An unconstrained, linear, non-iterative, and numerically stable ellipse fitting method has been proposed and it has been shown that the proposed method has better selectivity for elliptic digital curves (high true positive and low false positive) as compared to several other ellipse fitting methods. For the problem of detecting ellipses in a set of digital curves, several innovative and fast pre-processing, grouping, and hypotheses evaluation concepts applicable for digital curves have been proposed and combined to form an ellipse detection method.