Skip to Main content Skip to Navigation
Conference papers

Self-duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images

Abstract : In digital topology, the use of a pair of connectivities is required 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.
Document type :
Conference papers
Complete list of metadata

Cited literature [23 references]  Display  Hide  Download

https://hal.inria.fr/hal-01476218
Contributor : Thierry Géraud <>
Submitted on : Friday, February 24, 2017 - 4:21:55 PM
Last modification on : Wednesday, June 9, 2021 - 5:28:03 PM
Long-term archiving on: : Thursday, May 25, 2017 - 1:51:46 PM

File

article.pdf
Files produced by the author(s)

Identifiers

Citation

Thierry Géraud, Edwin Carlinet, Sébastien Crozet. Self-duality and Digital Topology: Links Between the Morphological Tree of Shapes and Well-Composed Gray-Level Images. 12th International Symposium on Mathematical Morphology (ISMM, May 2017, Reykjavik, Iceland. pp.573 - 584, ⟨10.1007/978-3-319-18720-4_48⟩. ⟨hal-01476218⟩

Share

Metrics

Record views

267

Files downloads

423