# ImGeodesics

The imGeodesics module containes functions for computing distance functions in binary images, and computing related geodesic parameters.

## Contents

## Description

The base function is 'imChamferDistance'. It propagates distances from a set of markers, using a mask to constrain the propagation. Chamfer distances are used as approximation of euclidean distances. The function 'imChamferDistance3d' is its extension for 3D images.

Using Chamfer distance propagation, it is possible to compute geodesic distances and geodesic path between two markers in a particle.

It is also possible to compute morphological parameters, such as the geodesic length or the geodesic radius. For some parameters, an exhaustive search is performed, making the computation time rather high.

Some functions are defined for 2D and 3D images. Some other exist in two different forms. The computation of geodesic path is not defined for 3D images.

## Functions

### Distance propagation

imChamferDistance - Compute chamfer distance using scanning algorithm imChamferDistance3d - Compute chamfer distance in 3D images imGeodesicPath - Compute a geodesic path between two markers in an image imMaxGeodesicPath - Find a path in a region with maximal geodesic length imGeodesicDistance - Compute geodesic distance between 2 markers

### Geodesic parameters

imGeodesicDiameter - Compute geodesic diameter of particles imGeodesicDiameter3d - Compute geodesic diameter of 3D particles imGeodesicCenter - Compute geodesic center of a binary particle imGeodesicExtremities - Compute geodesic extremities of a binary particle imGeodesicRadius - Compute the geodesic radius of a binary particle imGeodesicPropagation - Compute geodesic propagation for each foreground pixel

### Validation

chamferDistanceError - Compute relative error of chamfer distance with euclidean

## References

- Lantuéjoul, C. & Beucher, S. On the use of geodesic metric in image analysis. J. Miscrosc., 1981, 121, 39-40
- Borgefors, G. Distance transformations in digital images. Comp. Vis. Graph. Im. Proc., 1986, 34, 344-371
- Legland, D. & Beaugrand, J. Automated clustering of lignocellulosic fibres based on morphometric features and using clustering of variables. Industrial Crops and Products, 2013, 45, 253 - 261