Images encoding angular information are common in image analysis. Examples include the hue band of color images, or images encoding directional texture information. Applying mathematical morphology to image data distributed on the unit circle is not immediately possible, as the unit circle is not a lattice. Three approaches to solving this problem are presented. First, difference-based operators are studied (e.g., gradient, top-hat). Second, a definition of grouped circular data is suggested, and "pseudo" morphological operators, which operate only on grouped data, are introduced. Finally, processing using pixel labeling is presented, leading to the development of a cyclic opening operator. Applications for treating the hue band of color images and for finding perturbations in wood texture are given.