A Gray-level Morphological Operation Method Based on the Umbra Notion

Mathematical morphology as a nonlinear image processing theory has been used in various aspects of image processing. However, with the emergence of morphological networks and the increasing resolution of images, the demand for the speed of morphological image processing is increasing. In this paper, we propose an implementation method of binary operations for gray-level morphology based on the umbra notion. In this method, firstly, the gray-level image to be calculated and the structural element image are converted into the corresponding binary umbra image according to the umbra notion. Then, dilation, erosion, opening and closing operations are performed on the umbra of the structural element image and the image to be processed to obtain the corresponding umbra result image. Finally, the umbra result image is converted into its top surface based on the linkage of the binary image with the pixel value of the gray-level image to obtain the corresponding gray-level image dilation, erosion, opening and closing operational results. The experimental results on one-dimensional and two-dimensional images demonstrate the effectiveness of the method, which can lay a foundation for the fast calculation of gray-level morphological images.