Module: Euler Number 3D ()

Description:

For an introduction, see:

This module computes the Euler-Poincaré number of the object. It is an indicator of the connectivity of a 3D complex structure. The Euler number is a characteristic of a three-dimensional structure which is topologically invariant (it remains unchanged by elastic transformations of the structure). It measures what might be called "redundant connectivity" - the degree to which parts of the object are multiply connected (Odgaard et al. 1993). It is a measure of how many connections in a structure can be severed before the structure falls into two separate pieces. The components of the Euler number are the three Betti numbers: is the number of objects (that is to say the number of connected components), the connectivity, and the number of enclosed cavities. The Euler-Poincare formula for a 3D object is given:



See also: Average Object Area Per Slice, Volume Fraction, Object Boundary Area, Total Image Boundary Area, Average Object Number Per Slice.

Connections:

Input Image [required]
The image to be analyzed. Supported types include: binary images (Uniform Label Field with 2 labels).

Ports:

Interpretation

This port specifies whether the input will be interpreted as a 3D volume or a stack of 2D images for processing.