Primitive extraction via gathering evidence of global parameterised models
The extraction of geometric primitives from images is a fundamental task in computer vision. The objective of shape extraction is to find the position and recognise descriptive features of objects (such as size and rotation) for scene analysis and interpretation. The Hough transform is an established technique for extracting geometric shapes based on the duality definition of the points on a curve and their parameters. This technique has been developed for extracting simple geometric shapes such as lines, circles and ellipses as well as arbitrary shapes represented in a non-analytically tabular form. The main drawback of the Hough transform technique is the computational requirement which has an exponential growth of memory space and processing time as the number of parameters used to represent a primitive increases. For this reason most of the research on the Hough transform has focused on reducing the computational burden for extracting simple geometric shapes. This thesis presents two novel techniques based on the Hough transform approach, one for ellipse extraction and the other for arbitrary shape extraction. The ellipse extraction technique confronts the primary problems of the Hough transform, namely the storage and computational load, by considering the angular changes in the position vector function of the points in an ellipse. These changes are expressed in terms of sets of points and gradient direction to obtain simplified mappings which split the five-dimensional parameter space required for ellipse extraction into two two-dimensional and one one-dimensional spaces. The new technique for arbitrary shape extraction uses an analytic representation of arbitrary shapes. This representation extends the applicability of the Hough transform from lines and quadratic forms, such as circles and ellipses, to arbitrary shapes avoiding the discretisation problems inherent in current (tabular) approaches. The analytic representation of shapes is based on the Fourier expansion of a curve and the extraction process is formulated by including this representation in a general novel definition of the Hough transform. In the development of this technique some strategies of parameter reduction are implemented and evaluated.