# Introducing the Dahu Pseudo-Distance

### From LRDE

- Authors
- Thierry Géraud, Yongchao Xu, Edwin Carlinet, Nicolas Boutry
- Where
- Mathematical Morphology and Its Application to Signal and Image Processing – Proceedings of the 13th International Symposium on Mathematical Morphology (ISMM)
- Place
- Fontainebleau, France
- Type
- inproceedings
- Publisher
- Springer
- Projects
- Olena
- Keywords
- Image
- Date
- 2017-02-23

## Abstract

The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapeswhich in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.

## Documents

(some materials will be published here soon...)

## Bibtex (lrde.bib)

@InProceedings{ geraud.17.ismm, author = {Thierry G\'eraud and Yongchao Xu and Edwin Carlinet and Nicolas Boutry}, title = {Introducing the {D}ahu Pseudo-Distance}, booktitle = {Mathematical Morphology and Its Application to Signal and Image Processing -- Proceedings of the 13th International Symposium on Mathematical Morphology (ISMM)}, year = {2017}, editor = {J. Angulo and S. Velasco-Forero and F. Meyer}, volume = {10225}, series = {Lecture Notes in Computer Science}, pages = {55--67}, month = may, address = {Fontainebleau, France}, publisher = {Springer}, abstract = {The minimum barrier (MB) distance is defined as the minimal interval of gray-level values in an image along a path between two points, where the image is considered as a vertex-valued graph. Yet this definition does not fit with the interpretation of an image as an elevation map, i.e. a somehow continuous landscape. In this paper, based on the discrete set-valued continuity setting, we present a new discrete definition for this distance, which is compatible with this interpretation, while being free from digital topology issues. Amazingly, we show that the proposed distance is related to the morphological tree of shapes, which in addition allows for a fast and exact computation of this distance. That contrasts with the classical definition of the MB distance, where its fast computation is only an approximation.} }