The accuracy with which a computer vision system is able to identify objects in an image is heavily dependent upon the accuracy of the low level processes that identify which points lie on the edges of an object. In order to remove noise and fine texture from an image, it is usually smoothed before edge detection is performed. This smoothing causes edges to be displaced from their actual location in the image. Knowledge about the changes that occur with different degrees of smoothing (scales) and the physical conditions that cause these changes is essential to proper interpretation of the results obtained. In this work the amount of delocalization and the magnitude of the response to the Normalized Gradient of Gaussian operator are analyzed as a function of σ, the standard deviation of the Gaussian. As a result of this analysis it was determined that edge points could be characterized as to slope, contrast, and proximity to other edges. The analysis is also used to define the size that the neighborhood of an edge point must be in order to assure its containing the delocalized edge point at another scale when σ is known.
Given this theoretical background, an algorithm was developed to obtain sequential lists of edge points. This used multiple scales in order to achieve the superior localization and detection of weak edges possible with smaller scales combined with the noise suppression of the larger scales. The edge contours obtained with this method are significantly better than those achieved with a single scale. A second algorithm was developed to allow sets of edge contour points to be represented as active contours so that interaction with a higher level process is possible. This higher level process could do such things as determine where corners or discontinuities could appear. The algorithm developed here allows hard constraints and represents a significant improvement in speed over previous algorithms allowing hard constraints, being linear rather than cubic.
Doctor of Philosophy (Ph.D.)
College of Arts and Sciences
Department of Computer Science
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Doctoral Dissertation (Open Access)
Williams, Donna J., "Edge Contours" (1989). Retrospective Theses and Dissertations. 4246.