Module: Curvature Integrals ()

Description:

For an introduction, see section Analysis.

This module computes the integral of mean curvature and integral of total curvature of objects in a binary image. Intuitively, "curvature" is the amount by which a geometric object deviates from being "flat".

This module computes a local measure. It is obtained as the sum of measures in local 2x2x2 neighborhoods (a cube), for 13 planes associated with different normal directions and hitting three or four vertices of the cells (in the cubical lattice).

In the case of very elongated objects (needles or fibers) the integral of mean curvature can be used to measure the length of the object :

For convex object, the integral of mean curvature is (up to a constant) equivalent to the mean diameter, i.e.

The Euler number and the Integral of Total Curvature carry the same information about the object. They differ by the constant factor . If we consider a set X of the 3-dimensional space and being its Euler number then the integral total curvature of X will be : .

See Also : Euler Number

For more information on Integral Curvatures you can refer to
C .Lang, J. Ohser, R.Hilfer (1999) On the Analysis of Spatial Binary Images

See also: Area 3D, Euler Number 3D, Fractal Dimension, Moments of Inertia 3D, Volume Fraction.

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. The port is grayed if alternate interpretation is not available.