Directional morphological gradient edge detector

In this thesis, the limitations of the conventional morphological gradient (MG) as an edge detector are theoretically analyzed, and three new methods with improved performance are developed. The new methods are analyzed theoretically and demonstrated with both synthetic and real image data. The basic issues regarding edge detection, linear and nonlinear filtering, especially in morphological filtering, are overviewed. By thoroughly studying the behavior of morphological gradient with the order statistic method, the thesis proves theoretically that conventional MG has higher noise sensitivity than other gradient operators. This is the first comprehensive theoretical analysis for MG noise sensitivity reported in image processing literature.; The MG does not provide edge orientation information, which is available from other gradient operators such as the Sobel operator. Directional morphological gradient operators are proposed to overcome this drawback and also reduce the noise response. One dimensional MGs for different orientations (horizontal, vertical and diagonal directions) are used to calculate directional morphological gradient components. Basic MG and Blurred-minimum-operator (BMO) methods are augmented for the calculation of directional morphological gradients, which are called DMG and DBMO. With those directional gradients, edge angles can be estimated from horizontal/vertical (HV) and diagonal components. To reduce noise, inconsistent angle checking methods are developed in the DMG and DBMO, which compare the HV gradient components to the diagonal gradient components. It is a novel approach to remove noise with consistency of angle estimates instead of solely depending on edge magnitude threshold. With prefiltering and the use of a post processing method of combining non-maximum suppression in terms of edge orientations, another operator, called DMGF, is introduced and analyzed as well.; The performance of the DMG, DBMO and DMGF are evaluated with respect to the accuracy of the gradient magnitude, the accuracy of the angle estimation, and the sensitivity to noise for a constant gradient image, a step edge model and a synthetic image. Proposed operators are compared with similar complexity operators, such as the Sobel operator, in noiseless images for angle and magnitude estimation. To study noise sensitivity, Gaussian and impulsive noise are added to an ideal step edge and a synthetic image that has complex image corners and different curvatures. The false edge detection rate is designed to measure the performance for noisy images from different operators. Furthermore, using a set of natural images from different applications with typical contents, the performance of proposed operators are compared with Laplacian of Gaussian (LOG), Canny, BMO and Graduated-Non-Convex (GNC) operators.; The theoretical and experimental results show that proposed operators have better or competitive results in angle and magnitude estimation than Sobel in the noiseless case. The maximum error for angle estimation is down about 50% compared to Sobel. Using table lookup techniques not only speeds up angle estimation, but also significantly improves the accuracy of angle estimation. With inconsistent angle checking and combining filtering, DBMO and DMGF significantly reduce noise sensitivity compared to the Sobel. The false edge detection rate is reduced by 10–40%. With application to a variety of natural images, Chapter 7 shows that the proposed operator demonstrates promising results compared with other popular linear and nonlinear operators.