EigenvaluesToStructureness2d

Computes a structure score image from the eigenvalues of a two-dimensional tensor image.

Access to parameter description

This algorithm allows extracting tubular or blob-like structures from dark or bright background.

The computation is based on eigenvalues

$\lambda_{1}$ and

$\lambda_{2}$ where

$\mid \lambda_{1} \mid \geq \mid \lambda_{2} \mid$ .

The structure score for bright tubular structures corresponds to:

$score = \left\{ \begin{array}{l l} 0 & \quad \text{if $\lambda_{1} > 0$, }\\ exp(- \frac{ \big( \frac{\lambda_{2}}{\lambda_{1}} \big) ^{2} }{2 \beta^{2} } ) \big(1-exp \big(- \frac{S^{2}}{2c^{2}} \big) \big) \\ \end{array} \right.$

The score for bright blob-like structures is computed as follows:

$score = \left\{ \begin{array}{l l} 0 & \quad \text{if $\lambda_{1} > 0$ or $\lambda_{2} > 0$, }\\ \big(1-exp(- \frac{ \big( \frac{\lambda_{2}}{\lambda_{1}} \big) ^{2} }{2 \beta^{2} } )\big) \big(1-exp \big(- \frac{S^{2}}{2c^{2}} \big) \big) \\ \end{array} \right.$

Where:

$S$ is the Hessian norm $S = \sqrt{\lambda_{1}^{2}\lambda_{2}^{2}}$
$\beta$ is a threshold which controls the blobness sensitivity,
c is a sensitivity threshold wich controls the noise influence.

$c = noiseCutoff \cdot S_{max}$

$S_{max}$

For dark objects the conditions on

$\lambda_{1}$ and

$\lambda_{2}$ are reversed.

This algorithm outputs a float grayscale image where each pixel intensity represents a structure score between 0 and 1.

The method for tubular structures is referenced by Alejandro Frangi publication:
A.F.Frangi, W.J.Niessen, K.L.Vincken, M.A.Viergever. "Multiscale vessel enhancement filtering". Lecture Notes in Computer Science(MICCAI), vol. 1496, pp. 130-137, 1998.

See also

Function Syntax

This function returns the outputImage output parameter.

// Function prototype.
std::shared_ptr< iolink::ImageView >
eigenvaluesToStructureness2d( std::shared_ptr< iolink::ImageView > inputEigenvaluesImage,
                              EigenvaluesToStructureness2d::Lightness lightness,
                              EigenvaluesToStructureness2d::StructureType structureType,
                              double beta,
                              double noiseCutoff,
                              std::shared_ptr< iolink::ImageView > outputImage = NULL );

This function returns the outputImage output parameter.

// Function prototype.
eigenvalues_to_structureness_2d( input_eigenvalues_image,
                                 lightness = EigenvaluesToStructureness2d.Lightness.BRIGHT,
                                 structure_type = EigenvaluesToStructureness2d.StructureType.ROD,
                                 beta = 0.75,
                                 noise_cutoff = 0.5,
                                 output_image = None )

This function returns the outputImage output parameter.

// Function prototype.
public static IOLink.ImageView
EigenvaluesToStructureness2d( IOLink.ImageView inputEigenvaluesImage,
                              EigenvaluesToStructureness2d.Lightness lightness = ImageDev.EigenvaluesToStructureness2d.Lightness.BRIGHT,
                              EigenvaluesToStructureness2d.StructureType structureType = ImageDev.EigenvaluesToStructureness2d.StructureType.ROD,
                              double beta = 0.75,
                              double noiseCutoff = 0.5,
                              IOLink.ImageView outputImage = null );

Class Syntax

// Command constructor.
EigenvaluesToStructureness2d();

// Get method of the inputEigenvaluesImage parameter.
std::shared_ptr< iolink::ImageView > inputEigenvaluesImage() const;
// Set method of the inputEigenvaluesImage parameter.
void setInputEigenvaluesImage( std::shared_ptr< iolink::ImageView > inputEigenvaluesImage );

// Get method of the lightness parameter.
EigenvaluesToStructureness2d::Lightness lightness() const;
// Set method of the lightness parameter.
void setLightness( const EigenvaluesToStructureness2d::Lightness& lightness );

// Get method of the structureType parameter.
EigenvaluesToStructureness2d::StructureType structureType() const;
// Set method of the structureType parameter.
void setStructureType( const EigenvaluesToStructureness2d::StructureType& structureType );

// Get method of the beta parameter.
double beta() const;
// Set method of the beta parameter.
void setBeta( const double& beta );

// Get method of the noiseCutoff parameter.
double noiseCutoff() const;
// Set method of the noiseCutoff parameter.
void setNoiseCutoff( const double& noiseCutoff );

// Get method of the outputImage parameter.
std::shared_ptr< iolink::ImageView > outputImage() const;
// Set method of the outputImage parameter.
void setOutputImage( std::shared_ptr< iolink::ImageView > outputImage );

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

// Property of the inputEigenvaluesImage parameter.
EigenvaluesToStructureness2d.input_eigenvalues_image
// Property of the lightness parameter.
EigenvaluesToStructureness2d.lightness
// Property of the structureType parameter.
EigenvaluesToStructureness2d.structure_type
// Property of the beta parameter.
EigenvaluesToStructureness2d.beta
// Property of the noiseCutoff parameter.
EigenvaluesToStructureness2d.noise_cutoff
// Property of the outputImage parameter.
EigenvaluesToStructureness2d.output_image

// Method to launch the command.
execute()

// Command constructor.
EigenvaluesToStructureness2d()

// Property of the inputEigenvaluesImage parameter.
EigenvaluesToStructureness2d.inputEigenvaluesImage
// Property of the lightness parameter.
EigenvaluesToStructureness2d.lightness
// Property of the structureType parameter.
EigenvaluesToStructureness2d.structureType
// Property of the beta parameter.
EigenvaluesToStructureness2d.beta
// Property of the noiseCutoff parameter.
EigenvaluesToStructureness2d.noiseCutoff
// Property of the outputImage parameter.
EigenvaluesToStructureness2d.outputImage

// Method to launch the command.
Execute()

Parameters

Class Name	EigenvaluesToStructureness2d

Parameter Name

Description

Type

Supported Values

Default Value

inputEigenvaluesImage

The input image containing the eigenvalues field. Type must be float. Spectral series size is 2 (channel 0 = largest eigenvalue, channel 1 = smallest eigenvalue).

Image

Multispectral

nullptr

lightness

The type of structure lightness to extract.

BRIGHT	Extracts bright structures from dark background.
DARK	Extracts dark structures from bright background.

Enumeration

BRIGHT

structureType

The type of structure shapes to extract.

ROD	Extracts rod-like (tubular) structures.
BALL	Extracts blob-like (spherical) structures.

Enumeration

ROD

beta

The blobness sensitivity threshold. It corresponds to the beta term of the score equation.

Float64

0.75

noiseCutoff

The noise scale factor. It is used for computing the c term of the score equation.

Float64

0.5

outputImage

The score output image. X and Y dimensions, calibration and interpretation of the output image are forced to the same values as the input. The spectral dimension is forced to 1. Type is forced to float and all values are between 0 and 1.

Image

nullptr

Object Examples

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

EigenvaluesToStructureness2d eigenvaluesToStructureness2dAlgo;
eigenvaluesToStructureness2dAlgo.setInputEigenvaluesImage( retina_eigenvalues );
eigenvaluesToStructureness2dAlgo.setLightness( EigenvaluesToStructureness2d::Lightness::BRIGHT );
eigenvaluesToStructureness2dAlgo.setStructureType( EigenvaluesToStructureness2d::StructureType::ROD );
eigenvaluesToStructureness2dAlgo.setBeta( 0.75 );
eigenvaluesToStructureness2dAlgo.setNoiseCutoff( 0.5 );
eigenvaluesToStructureness2dAlgo.execute();

std::cout << "outputImage:" << eigenvaluesToStructureness2dAlgo.outputImage()->toString();

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

eigenvalues_to_structureness_2d_algo = imagedev.EigenvaluesToStructureness2d()
eigenvalues_to_structureness_2d_algo.input_eigenvalues_image = retina_eigenvalues
eigenvalues_to_structureness_2d_algo.lightness = imagedev.EigenvaluesToStructureness2d.BRIGHT
eigenvalues_to_structureness_2d_algo.structure_type = imagedev.EigenvaluesToStructureness2d.ROD
eigenvalues_to_structureness_2d_algo.beta = 0.75
eigenvalues_to_structureness_2d_algo.noise_cutoff = 0.5
eigenvalues_to_structureness_2d_algo.execute()

print( "output_image:", str( eigenvalues_to_structureness_2d_algo.output_image ) );

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

EigenvaluesToStructureness2d eigenvaluesToStructureness2dAlgo = new EigenvaluesToStructureness2d
{
    inputEigenvaluesImage = retina_eigenvalues,
    lightness = EigenvaluesToStructureness2d.Lightness.BRIGHT,
    structureType = EigenvaluesToStructureness2d.StructureType.ROD,
    beta = 0.75,
    noiseCutoff = 0.5
};
eigenvaluesToStructureness2dAlgo.Execute();

Console.WriteLine( "outputImage:" + eigenvaluesToStructureness2dAlgo.outputImage.ToString() );

Function Examples

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

auto result = eigenvaluesToStructureness2d( retina_eigenvalues, EigenvaluesToStructureness2d::Lightness::BRIGHT, EigenvaluesToStructureness2d::StructureType::ROD, 0.75, 0.5 );

std::cout << "outputImage:" << result->toString();

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

result = imagedev.eigenvalues_to_structureness_2d( retina_eigenvalues, imagedev.EigenvaluesToStructureness2d.BRIGHT, imagedev.EigenvaluesToStructureness2d.ROD, 0.75, 0.5 )

print( "output_image:", str( result ) );

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

IOLink.ImageView result = Processing.EigenvaluesToStructureness2d( retina_eigenvalues, EigenvaluesToStructureness2d.Lightness.BRIGHT, EigenvaluesToStructureness2d.StructureType.ROD, 0.75, 0.5 );

Console.WriteLine( "outputImage:" + result.ToString() );

EigenvaluesToStructureness2d

- Function Syntax

+ Class Syntax

Parameters

Object Examples

Function Examples

Function Syntax

Class Syntax