SoCurvatureIntegralsQuantification3d Class Reference
[Global Measures]

SoCurvatureIntegralsQuantification3d engine computes the integral of mean curvature and integral of total curvature. More...

#include <ImageViz/Engines/ImageAnalysis/GlobalMeasures/SoCurvatureIntegralsQuantification3d.h>

Inheritance diagram for SoCurvatureIntegralsQuantification3d:

List of all members.

Classes
class	SbCurvatureIntegralsDetail
	Results details of curvature integrals. More...
Public Member Functions
	SoCurvatureIntegralsQuantification3d ()
Public Attributes
SoSFImageDataAdapter	inImage
SoImageVizEngineAnalysisOutput < SbCurvatureIntegralsDetail >	outResult

Detailed Description

SoCurvatureIntegralsQuantification3d engine computes the integral of mean curvature and integral of total curvature.

For an introduction, see section Analysis.

This engine 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 engine 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 $M$ can be used to measure the length $L$ of the object : $L=M/$

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

$M=2\pi d ~~\mbox{where} ~~ d=\frac{1}{13}\left(\sum_{i=0}^13 d_i\right)$

The Euler number and the Integral of Total Curvature carry the same information about the object. They differ by the constant factor $4\pi$ . If we consider a set X of the 3-dimensional space and $(X)$ being its Euler number then the integral total curvature of X will be : $K(X)=4(X)$ .