# Tesselations by Connection in Orders

@inproceedings{Couprie2000TesselationsBC, title={Tesselations by Connection in Orders}, author={Michel Couprie and Gilles Bertrand}, booktitle={DGCI}, year={2000} }

The watershed transformation is a powerful tool for segmenting images, but its precise definition in discrete spaces raises difficult problems. We propose a new approach in the framework of orders. We introduce the tesselation by connection, which is a transformation that preserves the connectivity, andcan be implementedb y a parallel algorithm. We prove that this transformation possesses goodg eometrical properties. The extension of this transformation to weighted orders may be seen as a…

## 6 Citations

### Some properties of topological grayscale watersheds

- MathematicsIS&T/SPIE Electronic Imaging
- 2004

In this paper, we investigate topological watersheds. For that purpose we introduce a notion of “separation between two points” of an image. One of our main results is a necessary and sufficient…

### Watersheds, extension maps, and the emergence paradigm

- Mathematics
- 2004

In this paper, we investigate the links between the flooding paradigm and the topological watershed. Guided by the analysis of a classical flooding algorithm, we introduce several notions that help…

### Geodesy on label images, and applications to video sequence processing

- MathematicsJ. Vis. Commun. Image Represent.
- 2008

### On Topological Watersheds

- MathematicsJournal of Mathematical Imaging and Vision
- 2005

A necessary and sufficient condition for a map G to be a watershed of a map F, this condition is based on a notion of extension and is derived from the framework of topological watersheds.

### Advances in the Analysis of Topographic Features on Discrete Images

- Environmental ScienceDGCI
- 2002

This paper presents some advances related to the imposition of minima, the lower complete transformation, the hit-or-miss transform, and the extraction of crest lines by a skeletonisation procedure.

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