I am happy to announce that the following paper has been accepted at the 12th International Symposium on Mathematical Morphology (ISMM'15), to be held on May 27-29 2015 in Reykjavik, Iceland. Self-Duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images Thierry Géraud¹, Edwin Carlinet¹², Sébastien Crozet¹, ¹ EPITA Research and Development Laboratory (LRDE) ² Université Paris-Est, LIGM, Équipe A3SI, ESIEE Paris https://www.lrde.epita.fr/wiki/Publications/geraud.15.ismm Abstract: In digital topology, the use of a pair of connectivities is re- quired to avoid topological paradoxes. In mathematical morphology, self-dual operators and methods also rely on such a pair of connectivities. There are several major issues: self-duality is impure, the image graph structure depends on the image values, it impacts the way small objects and texture are processed, and so on. A sub-class of images defined on the cubical grid, well-composed images, has been proposed, where all connectivities are equivalent, thus avoiding many topological problems. In this paper we unveil the link existing between the notion of well-composed images and the morphological tree of shapes. We prove that a well-composed image has a well-defined tree of shapes. We also prove that the only self-dual well-composed interpolation of a 2D image is obtained by the median operator. What follows from our results is that we can have a purely self-dual representation of images, and consequently, purely self-dual operators.