Functional Modeling of Structured Images

摘要

Functional Graphical Models (FGM) describe functional dependence between variables by means of implicit equations. They offer a convenient way to represent, code, and analyze many problems in computer vision. By explicitly modeling functional dependences by a hypergraph, we obtain a structure well-adapted to information retrieval and processing. Thanks to the functional dependences, we show how all the variables involved in a functional graphical model can be stored efficiently. We derive from that result a description length of general FGMs which can be used to achieve model selection for example. We demonstrate their relevance for capturing regularities in data by giving examples of functional models coding 1D signals and 2D images.