Vision sensors observe 3D objects in a dynamic environment. Objects consist of several connected 3D part and these parts can be connected in different ways: rigidly, articulated, smoothly deformable. In most cases objects move independently and smoothly. This scene topology is projected into the image topology where noise and occlusions and the enormous amount of data introduce further difficulties. We plan to elaborate the concept of the topological pyramid from the classical, regular image pyramids by means of examples. At the transition to the irregular pyramids was the idea to consider the treatment of the hierarchical structure and the content separately but in a synchronous way. We will discuss in detail the basic concept of dual graph pyramids and show results for connected component analysis and segmentation. We finally discuss their main properties among which the preservation of the image topology,