Geometric primitive feature extraction - concepts, algorithms, and applications

TL;DR

This thesis introduces new algorithms and theoretical insights for extracting geometric primitives like polygons, tangents, and ellipses from digital images, improving accuracy and efficiency over existing methods.

Contribution

It presents a non-heuristic framework for polygonal approximation, a superior tangent estimation method, and a stable ellipse fitting and detection approach for digital curves.

Findings

Proposed a generic error bound for digitized line segments.

Demonstrated superior tangent estimation accuracy on conic and non-conic curves.

Developed an ellipse detection method with high true positive rate and low false positives.

Abstract

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.