Topological Structure For The Space Consisting Of Images And Its Properties

The theory of Mathematical Morphology is developed for image management and pattern analysis. In actual management , the image under consideration is always considered as a set in Rn. Because we can not discern a set from its convex closure , we can consider the image as a closed set . However , the image for management usually comprise some "noisy data" , in another word , we always get some sets with error in practice. Therefore, the insensitive to those errors is important in image transformation and a relevant concept is continuity. In order to understand the continuity, we must set up an accurate geometrical and topological structure to process those sets .In the present paper , we shall discuss another more crucial topological structure on the base of HM topology which has been set up in Mathematical Morphology . Because the transformations in Mathematical Morphology are defined by means of geometry , the properties of these transformations are bound to relevant to geometry. Exactly , the geometry plays an important role in solving Mathematical Morphology problems. It is not only the tool , but the goal. In the paper , algebraical properties of morphology operation together with topological and geometrical properties are discussed : the properties of skeletons ; the operation properties of convex set and convex closure ; Minkowski function for convex set and its properties ; Steiner formulae and its developing.