### Table of Contents

# Chamfer distances and Geodesic diameters

## Introduction

A plugin for computing geodesic distances within binary images, and to compute geodesic diameters (or geodesic lengths) of labeled particles. Both functions uses chamfer distances (approximations of euclidean distance around pixels).

## Author

David Legland email : david dot legland (at) grignon dot inra dot fr

## Features

The plugin includes two functions, available in menu “Plugins>Geodesics”:

**Geodesic Diameter**: this function computes the geodesic diameter of particles in a label image**Chamfer Distance**: this function propagates geodesic distances from a marker image within a mask image.

## Description

### Geodesic Length

Geodesic Diameter of a particle is the length of the longest geodesic path within a particle. A geodesic path is the shortest path (series of neighbor pixels within particle) that connects two points in the particle. The geodesic diameter is a good alternative to other shape descriptors such as perimeter.

The functions use a label image as input. It computes for each particule/label the following parameters:

**Geodesic Diam.**: as explained above**radius**: radius of the greatest enclosed circle**Geod elong**: ratio of the geodesic length over the inscribed circle radius**xi, yi**: center of the greatest enclosed circle (not necessarily unique)**x1, y1, x2, y2**: coordinates of the two geodesic extremities detected by the algorithm

Note that current implementation computes only an approximation of the real geodesic diameter. For most particles, it seems to give the same result as the real chamfer geodesic diameter (computed from Matlab).

If the checkbox “Overlay results” is checked, a line joining geodesic extremities is shown, as well as the inscribed circle.

### Chamfer Distance

Chamfer distances are used by used for computing geodesic diameters. The principle is to propagate chamfer distances from a binary image (the marker), constrained to another binary image (the mask). Result is something like this:

## Installation

Copy the file “ij_Geodesics.jar” into the “plugins” subfolder of ImageJ. Under Windows, this is typically “C:\Program Files\ImageJ\plugins”. You can then restart ImageJ.

## Download

First you need to download the following files:

Then copy the jar file into the “plugins” folder of ImageJ, and restart ImageJ. A new “Geodesics” menu is available in the plugin menu.

You can also download one of the following files:

- ijGeodesicsManuel.pdf a short manual (for the moment only in french…)
- ijGeodesics.zip the archive that contains the jar, the manuel, and some test images.

## License

This plugin follows the terms of the LGPL licence.

If you find the plugin usefull, please make a citation to the paper it was developed for:

**Legland, D. & Beaugrand, J. (2013)**Automated clustering of lignocellulosic fibres based on morphometric features and using clustering of variables.*Industrial Crops and Products*,**45**, 253 - 261 (url)

## Changelog

* 2014.02.21 add support for chessknight distances, and for computation of tortuosity maps

* 2011.07.25 First release on this wiki. It includes “plugins.config” file.

## Known bugs

None yet…