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Geometric measures in discrete images

french version


The package imMinkowski is a set of functions for measuring geometrical and topological parameters (area, perimeter, surface area, mean breadth, euler number...) in discrete 2D and 3D images. Available parameters are:

  • in 2D, Euler-Poincaré characteristic, perimeter, area
  • in 3D, Euler-Poincaré characteristic, surface area, mean breath
  • These parameters can be encompassed within the formalism of Minkowski functionals, or intrinsic volumes.

Parameters can be obtained via several ways:

  • global measure of the parameter within the whole image
  • computation of parameter density with respect to the image size
  • local contribution of individual pixel or voxel to the whole measure
  • computation of profiles along one of the main directions

The method uses a discretisation of the Crofton formula. It is possible to choose between several adjacencies or number of directions, and to use grids with various resolutions.

Installation instructions

imMinkowski (Matlab)

This function library make it possible to measure most of the described parameters. Simply download and uncompress the archive (version 2011.11.09), then add the library to the path using the "addpath" command. A detailed summary describes the functions included into the package.

Crofton Perimeter (ImageJ)

The ImageJ plugin allows the measurement of particle perimeter in label images. Installation is made by downloading and uncompressing the archive (version 20/07/2011), and copying the file "Crofton_Perimeter.class" into the "plugins" directory of ImageJ. It is necessary either to restart ImageJ, or to refresh the plugins menu via "Help>Refresh Menus".


  • Target : Matlab, ImageJ
  • Type: function library, plugin
  • Author(s) : David Legland
  • Licence : BSD


  • Legland, D.; Kiêu, K. & Devaux, M.-F. (2007) Computation of Minkowski measures on 2D and 3D binary images Image Anal. Stereol., 26, 83-92 (link, pdf)
  • Lehmann G., Legland D. (2012) Efficient N-Dimensional surface estimation using Crofton formula and run-length encoding. The Insight Journal, January-June (link, pdf).