Analytic Hough transform for conic curve detection

In this dissertation, an analytic approach to the solution of the digital conic curve detection problem has been studied. This approach will accurately determine which set of curves may be represented by a group of pixels in a discrete image.; The Analytic Hough Transform (AHT) has been employed as the key tool in this research. As the first step in this research, we have improved the data structure used to implement the AHT for straight lines resulting in increased efficiency. A complete study of the AHT for straight lines has been performed in this dissertation. Both synthetic and real images have been used to test our improved data structure.; The primary goal of this work was the development of an extension of the AHT theory for the detection and exact parameter bounding of discrete parabolic curves. A data structure that parallels that developed for the straight line AHT has been obtained. An entire system has been implemented and tested with synthetic and real images. Results were also obtained regarding computational complexity and memory requirements.; Based on the studies of the AHT for straight lines and parabolas, this dissertation also discusses extending the AHT theory for detection of general digital conic curves.