ImageDev

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: 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

Parameters

Class Name EigenvaluesToStructureness2d

Parameter Name Description Type Supported Values Default Value
input
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
input
lightness
The type of structure lightness to extract.
BRIGHT Extracts bright structures from dark background.
DARK Extracts dark structures from bright background.
Enumeration BRIGHT
input
structureType
The type of structure shapes to extract.
ROD Extracts rod-like (tubular) structures.
BALL Extracts blob-like (spherical) structures.
Enumeration ROD
input
beta
The blobness sensitivity threshold. It corresponds to the beta term of the score equation. Float64 >0 0.75
input
noiseCutoff
The noise scale factor. It is used for computing the c term of the score equation. Float64 >0 0.5
output
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() );