<p>Edge detection is important in image processing. Extracting edge features is the main and necessary process in edge detection. Since features in edge detection are implicit, most of the existing edge features only work well on specific images. Using a moving window has a trade-off between noise rejection and localisation accuracy. Genetic Programming (GP) has been widely applied to image processing, and GP has potential for extracting edge features, although there is little work in GP for edge detection. The overall goal of this thesis is to investigate GP for automatic edge feature extraction using different amounts of existing knowledge from only using raw pixel intensities and ground truth to more advanced domain knowledge such as Gaussian filters. First of all, this thesis conducts an investigation on fundamental low-level edge detector construction with very little prior edge knowledge. Search operators based on a single raw pixel, a block of pixels, and two blocks of pixels are proposed to construct edge detectors. Unlike most existing methods, this GP system automatically searches neighbours and avoids manually predefining a window size. The results show that the evolved edge detectors outperform some existing edge detectors, such as the Sobel edge detector. Secondly, from the pixel and image views, localisation of detected edges, and observations of GP programs, new fitness functions are suggested in this thesis. It is found that the pixel view is better than the image view to design fitness functions without allowing a distance from predictions to ground truth. However, in terms of edge localisation, the pixel view is worse than the image view to design fitness functions. A new fitness function combining detection accuracy and localisation effectively improves the performance of evolved edge detectors. When utilising observations of GP programs to construct soft edge maps, two new fitness functions including a restriction on the range of observations are proposed to evolve edge detectors with good soft edge maps on test images. Thirdly, pixels implicitly selected by the GP system based on full images are analysed. A set of pixels are extracted from the evolved programs and used to construct edge filters. A merge operation is proposed to extract six pixels to construct second-order edge filters. The results show that a rich but compact set of pixels can be extracted from the evolved edge detectors. Fourthly, GP is utilised to evolve edge detectors based on the Gaussian-based technique. These GP evolved edge detectors are significantly better than the Gaussian gradient and the surround suppression technique. An efficient and effective sampling technique is proposed for evolving Gaussian-based edge detectors. From the results, there are no significant differences between the Gaussian-based edge detectors evolved by a full set of images and by the sampling technique on the training set. Fifthly, GP is employed to construct features using an existing set of basic features. The distribution of observations of GP programs is estimated. Evolved composite features are proposed using known distribution models to indicate the probability of pixels being discriminated as edge points. It is found that the composite features effectively combine advantages of basic features and can richly indicate edge responses. Finally, a Bayesian-based GP system is proposed to construct high-level edge features via employing two general algebraic operators and a function developed from a simple Bayesian model. The simple Bayesian model utilises a general multivariate normal density to combine basic features. Experiments show that the GP evolved programs perform better than the simple Bayesian model to obtain composite features. Overall, this thesis shows that GP has the capability to effectively extract edge features using different degrees of prior knowledge about edges.</p>
Comparison of Gradient-Based Edge Detectors Applied on Mammograms
