A framework for digital label images

International audienceDigital label images - partitions of a discrete space - need a specific topological model to take into account not only the topologies of the regions but also the topology of the partition. In this article, we propose a topological framework for label images in which all the regions of the initial partition and of any coarser partition of the space can be explicitly represented accordingly to any classical adjacency relation. Moreover, we define a notion of simple point which enables atomic changes in the partition without breaking any topology. Finally, we discuss about the implementation of the framework