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.