DegreeOfAnisotropy

Computes an anisotropy indicator of a binary image with a mean intercept length method.

Access to parameter description

For an introduction:

• section Image Analysis
• section Moment And Orientation

This algorithm computes a measurement of anisotropy. It is a good indicator to detect structural alignments along particular directional axis. The measurement is based on an eigenvalue analysis of the mean intercept length at different angles.

Mean intercept length proceeds by sending a set of oriented rays through the binary input image. A set of discreet angles are processed with a pitch angle fixed at 10 degrees. For each orientation, a regularly spaced grid of rays is shot. The length of the intersection of each ray with the objects encountered is measured, and averaged over the grid of rays. The spacing of this grid is controlled by the interceptDistance parameter, which represents the distance between two intercept lines.

The distribution of the mean intercept length, as a function of the angle, is analyzed using an eigenvalue decomposition. This analysis allows one to extract $\lambda_1$ and $\lambda_2$, respectively, the maximum and minimum eigenvalues. The closer these values are, the less the structural anisotropy is. Indeed, $\lambda_1=\lambda_2$ means that there is no privileged structural direction. $$ DA = \left( 1-\left|\frac{\lambda_2}{\lambda_1}\right| \right) $$ Degree of anisotropy is 0 for total isotropy, and 1 for total anisotropy.

Reference:
A.Odgaard. "Three-Dimensional Methods for Quantification of Cancellous Bone Architecture". Bone, vol. 20, no. 4, pp. 315-328, 1997.

See also

• MomentsOfInertia2d
• MomentsOfInertia3d
• Eccentricity2d

// Function prototype
AnisotropyDegreeMsr::Ptr
degreeOfAnisotropy( std::shared_ptr< iolink::ImageView > inputBinaryImage,
                    int32_t interceptDistance,
                    AnisotropyDegreeMsr::Ptr outputMeasurement = NULL );

// Function prototype.
degree_of_anisotropy( input_binary_image, intercept_distance = 3, output_measurement = None )

// Function prototype.
public static AnisotropyDegreeMsr
DegreeOfAnisotropy( IOLink.ImageView inputBinaryImage,
                    Int32 interceptDistance = 3,
                    AnisotropyDegreeMsr outputMeasurement = null );

// Command constructor.
DegreeOfAnisotropy();

/// Gets the inputBinaryImage parameter.
/// The input binary image.
std::shared_ptr< iolink::ImageView > inputBinaryImage() const;
/// Sets the inputBinaryImage parameter.
/// The input binary image.
void setInputBinaryImage( std::shared_ptr< iolink::ImageView > inputBinaryImage );

/// Gets the interceptDistance parameter.
/// The distance in pixels between two intercept lines.
int32_t interceptDistance() const;
/// Sets the interceptDistance parameter.
/// The distance in pixels between two intercept lines.
void setInterceptDistance( const int32_t& interceptDistance );

/// Gets the outputMeasurement parameter.
/// The output measurement result.
AnisotropyDegreeMsr::Ptr outputMeasurement() const;


// Method to launch the command.
void execute();

# Property of the inputBinaryImage parameter.
DegreeOfAnisotropy.input_binary_image
# Property of the interceptDistance parameter.
DegreeOfAnisotropy.intercept_distance
# Property of the outputMeasurement parameter.
DegreeOfAnisotropy.output_measurement

// Method to launch the command.
execute()

// Command constructor.
DegreeOfAnisotropy()

// Property of the inputBinaryImage parameter.
DegreeOfAnisotropy.inputBinaryImage
// Property of the interceptDistance parameter.
DegreeOfAnisotropy.interceptDistance
// Property of the outputMeasurement parameter.
DegreeOfAnisotropy.outputMeasurement

// Method to launch the command.
Execute()

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

DegreeOfAnisotropy degreeOfAnisotropyAlgo;
degreeOfAnisotropyAlgo.setInputBinaryImage( polystyrene_sep );
degreeOfAnisotropyAlgo.setInterceptDistance( 3 );
degreeOfAnisotropyAlgo.execute();

std::cout << "anisotropy: " << degreeOfAnisotropyAlgo.outputMeasurement()->anisotropy( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

degree_of_anisotropy_algo = imagedev.DegreeOfAnisotropy()
degree_of_anisotropy_algo.input_binary_image = polystyrene_sep
degree_of_anisotropy_algo.intercept_distance = 3
degree_of_anisotropy_algo.execute()

print( "anisotropy: ", str( degree_of_anisotropy_algo.output_measurement.anisotropy( 0 ) ) )

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

DegreeOfAnisotropy degreeOfAnisotropyAlgo = new DegreeOfAnisotropy
{
    inputBinaryImage = polystyrene_sep,
    interceptDistance = 3
};
degreeOfAnisotropyAlgo.Execute();

Console.WriteLine( "anisotropy: " + degreeOfAnisotropyAlgo.outputMeasurement.anisotropy( 0 ) );

auto polystyrene_sep = readVipImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene_sep.vip" );

auto result = degreeOfAnisotropy( polystyrene_sep, 3 );

std::cout << "anisotropy: " << result->anisotropy( 0 ) ;

polystyrene_sep = imagedev.read_vip_image(imagedev_data.get_image_path("polystyrene_sep.vip"))

result = imagedev.degree_of_anisotropy( polystyrene_sep, 3 )

print( "anisotropy: ", str( result.anisotropy( 0 ) )  )

ImageView polystyrene_sep = Data.ReadVipImage( @"Data/images/polystyrene_sep.vip" );

AnisotropyDegreeMsr result = Processing.DegreeOfAnisotropy( polystyrene_sep, 3 );

Console.WriteLine(  "anisotropy: " + result.anisotropy( 0 )  );