== Measurements ==
[[MorphoLibJ]] contains several tools for quantifying the size, the shape, or the spatial organization, from '''binary or label''' 2D and 3D images. The aim is to facilitate the management of label images, contrary to the built-in “Analyze Particles...” function that operates directly on a grayscale image.
=== Particle Region analysis ===This section describes the methods implemented in MorphoLibJ for describing individual particlesregions, represented as label images (one label for each particleregion). We first define and describe the implemented features, then we present the plugins that integrate them.
==== Intrinsic volumes ====
[[Image:MorphoLibJ-Euler-number.png|thumb|400px|Illustration of Euler Number definition. Left: three particles with Euler numbers equal to 1, 0 and -1, respectively. Right: example of a 3D particle with an Euler number equal to -1, corresponding to the subtraction of 1 connected components minus two handles.]]The intrinsic volumes are a set of features with interesting mathematical properties that are commonly used for describing individual particles as well as binary microstructrues. In the planar case, they correspond to the area, the perimeter and the Euler number. The Euler number is a topological characteristic that equals the number of connected components minus the number of holes.
* '''x2, y2''': coordinates of another geodesic extremity of the particle.
===== Particle Region Analysis 3D =====The plugin calculating these measurements is found under {{bc | Plugins | MorphoLibJ | Analyze | Particle Region Analysis 3D}}. The results are provided in an ImageJ Results table, whose name contains the name of the original image.
* '''Label''': the label of the particle measured on the current line (it can be different from the row number if some labels do no exist in original image).