DIPlib Documentation - ©1995-2013 Quantitative Imaging Group, Delft University of Technology.

# FeatureAnisotropy2D

Measure the anisotropy in a labeled region

## SYNOPSIS

`#include "dip_measurement.h"`

dip_int dip_FeatureAnisotropy2DID ( void )

## OUTPUT DATA TYPE

`dip_float`

## FUNCTION

`dip_FeatureAnisotropy2DID` returns the ID value of this measurement function, that is registered by `Initialise`.

The grey value input image should contain an orientation field. For each labeled region, a tensor is constructed at each of the region's pixels. This tensor is as follow:

      cos^2(phi)         cos(phi)sin(phi)
    [                                     ]
      cos(phi)sin(phi)   sin^2(phi)

The next step is to compute a new tensor, each element computed by averaging the corresponding elements of all the individual tensors. This average tensor represents the orientation information of the region as a whole. Eigenvalue analysis of this tensor yields two eigenvalues, the largest `l0`, the smallest `l1`. The anisotropy measure is:

    ( l0 - l1 ) / ( l0 + l1 )

which is zero for a fully isotropic regions (i.e. one where there is no preferred orientation), and one for a fully anisotropic region (i.e. when there is a single orientation).

## NOTE

This function ignores any physical dimensions passed through the `Measure` function.

## SEE ALSO

`Measure`

`FeatureAnisotropy2D`, `FeatureBendingEnergy`, `FeatureCenter`, `FeatureChainCodeBendingEnergy`, `FeatureConvexArea`, `FeatureConvexPerimeter`, `FeatureConvexity`, `FeatureDimension`, `FeatureExcessKurtosis`, `FeatureFeret`, `FeatureGinertia`, `FeatureGmu`, `FeatureGravity`, `FeatureInertia`, `FeatureLongestChaincodeRun`, `FeatureMass`, `FeatureMaxVal`, `FeatureMaximum`, `FeatureMean`, `FeatureMinVal`, `FeatureMinimum`, `FeatureMu`, `FeatureOrientation2D`, `FeatureP2A`, `FeaturePerimeter`, `FeatureRadius`, `FeatureShape`, `FeatureSize`, `FeatureSkewness`, `FeatureStdDev`, `FeatureSum`, `FeatureSurfaceArea`