# How to Make n-D Plain Maps Alexandrov-Well-Composed in a Self-dual Way

### From LRDE

- Authors
- Nicolas Boutry, Thierry Géraud, Laurent Najman
- Journal
- Journal of Mathematical Imaging and Vision
- Type
- article
- Projects
- Olena
- Keywords
- Image
- Date
- 2019-02-04

## Abstract

In 2013, Najman and Géraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.

## Documents

## Bibtex (lrde.bib)

@Article{ boutry.19.jmiv, author = {Nicolas Boutry and Thierry G\'eraud and Laurent Najman}, title = {How to Make {$n$-D} Plain Maps {A}lexandrov-Well-Composed in a Self-dual Way}, journal = {Journal of Mathematical Imaging and Vision}, volume = {61}, number = {6}, pages = {849--873}, year = {2019}, month = jul, doi = {10.1007/s10851-019-00873-4}, abstract = {In 2013, Najman and G\'eraud proved that by working on a well-composed discrete representation of a gray-level image, we can compute what is called its tree of shapes, a hierarchical representation of the shapes in this image. This way, we can proceed to morphological filtering and to image segmentation. However, the authors did not provide such a representation for the non-cubical case. We propose in this paper a way to compute a well-composed representation of any gray-level image defined on a discrete surface, which is a more general framework than the usual cubical grid. Furthermore, the proposed representation is self-dual in the sense that it treats bright and dark components in the image the same way. This paper can be seen as an extension to gray-level images of the works of Daragon et al. on discrete surfaces.} }