ABSTRACT
Irregular pyramids overcome these negative properties while keeping the main advantages of their regular ancestors. Such pyramids are defined as a stack of successively reduced graphs. The construction of such pyramids raises two questions: How to build efficiently each level of the pyramid from the one below? Which properties of the plane are captured at each level? This chapter provides answers to both questions together with an overview of hierarchical models. It presents the regular pyramid framework and the main parallel construction schemes of irregular pyramids. These construction schemes determine an important "vertical" property of an irregular pyramid: the speed at which the size of graphs decreases between the different levels of the pyramid. The chapter also presents the main graph encodings used within the irregular pyramid framework together with image properties captured by such models. Image properties captured by a given graph model may be considered as horizontal's properties of a pyramid.
