EigenDecomposition3d

Performs the singular value decomposition (SVD) of a 3D tensor field image.

Access to parameter description

This algorithm creates one or several output images containing the eigenvectors and/or eigenvalues of the input matrix image $I$ (or 3D tensor field). The input image must have six channels, where each channel contains one of the unique components of a 3x3 symmetric matrix. The redundant components are not contained in the input image.

Let $A(P)$ be the 3x3 symmetric matrix at position $P=(x,y,z)$.
The input image $I$ has 6 spectral component values $s$ at the spatial position $P$:

$I(P,0)=A(P)_{1,1}$
$I(P,1)=A(P)_{1,2}$
$I(P,2)=A(P)_{1,3}$
$I(P,3)=A(P)_{2,2}$
$I(P,4)=A(P)_{2,3}$
$I(P,5)=A(P)_{3,3}$

Where $I(P,s)$ is the spectral component value $s$ at the spatial position $P$.

See also

Function Syntax

This function returns a EigenDecomposition3dOutput structure containing the outputVectorImage1, outputVectorImage2, outputVectorImage3 and outputEigenvaluesImage output parameters.

// Output structure.
struct EigenDecomposition3dOutput
{
    std::shared_ptr< iolink::ImageView > outputVectorImage1;
    std::shared_ptr< iolink::ImageView > outputVectorImage2;
    std::shared_ptr< iolink::ImageView > outputVectorImage3;
    std::shared_ptr< iolink::ImageView > outputEigenvaluesImage;
};

// Function prototype.
EigenDecomposition3dOutput
eigenDecomposition3d( std::shared_ptr< iolink::ImageView > inputTensorImage,
                      int32_t outputSelection,
                      std::shared_ptr< iolink::ImageView > outputVectorImage1 = NULL,
                      std::shared_ptr< iolink::ImageView > outputVectorImage2 = NULL,
                      std::shared_ptr< iolink::ImageView > outputVectorImage3 = NULL,
                      std::shared_ptr< iolink::ImageView > outputEigenvaluesImage = NULL );

This function returns a tuple containing the output_vector_image1, output_vector_image2, output_vector_image3 and output_eigenvalues_image output parameters.

// Function prototype.
eigen_decomposition_3d( input_tensor_image,
                        output_selection = 11,
                        output_vector_image1 = None,
                        output_vector_image2 = None,
                        output_vector_image3 = None,
                        output_eigenvalues_image = None )

This function returns a EigenDecomposition3dOutput structure containing the outputVectorImage1, outputVectorImage2, outputVectorImage3 and outputEigenvaluesImage output parameters.

/// Output structure of the EigenDecomposition3d function.
public struct EigenDecomposition3dOutput
{
    public IOLink.ImageView outputVectorImage1;
    public IOLink.ImageView outputVectorImage2;
    public IOLink.ImageView outputVectorImage3;
    public IOLink.ImageView outputEigenvaluesImage;
};

// Function prototype.
public static EigenDecomposition3dOutput
EigenDecomposition3d( IOLink.ImageView inputTensorImage,
                      Int32 outputSelection = 11,
                      IOLink.ImageView outputVectorImage1 = null,
                      IOLink.ImageView outputVectorImage2 = null,
                      IOLink.ImageView outputVectorImage3 = null,
                      IOLink.ImageView outputEigenvaluesImage = null );

Class Syntax

// Command constructor.
EigenDecomposition3d();

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

// Get method of the outputSelection parameter.
int32_t outputSelection() const;
// Set method of the outputSelection parameter.
void setOutputSelection( const int32_t& outputSelection );

// Get method of the outputVectorImage1 parameter.
std::shared_ptr< iolink::ImageView > outputVectorImage1() const;
// Set method of the outputVectorImage1 parameter.
void setOutputVectorImage1( std::shared_ptr< iolink::ImageView > outputVectorImage1 );

// Get method of the outputVectorImage2 parameter.
std::shared_ptr< iolink::ImageView > outputVectorImage2() const;
// Set method of the outputVectorImage2 parameter.
void setOutputVectorImage2( std::shared_ptr< iolink::ImageView > outputVectorImage2 );

// Get method of the outputVectorImage3 parameter.
std::shared_ptr< iolink::ImageView > outputVectorImage3() const;
// Set method of the outputVectorImage3 parameter.
void setOutputVectorImage3( std::shared_ptr< iolink::ImageView > outputVectorImage3 );

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

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

// Property of the inputTensorImage parameter.
EigenDecomposition3d.input_tensor_image
// Property of the outputSelection parameter.
EigenDecomposition3d.output_selection
// Property of the outputVectorImage1 parameter.
EigenDecomposition3d.output_vector_image1
// Property of the outputVectorImage2 parameter.
EigenDecomposition3d.output_vector_image2
// Property of the outputVectorImage3 parameter.
EigenDecomposition3d.output_vector_image3
// Property of the outputEigenvaluesImage parameter.
EigenDecomposition3d.output_eigenvalues_image

// Method to launch the command.
execute()

// Command constructor.
EigenDecomposition3d()

// Property of the inputTensorImage parameter.
EigenDecomposition3d.inputTensorImage
// Property of the outputSelection parameter.
EigenDecomposition3d.outputSelection
// Property of the outputVectorImage1 parameter.
EigenDecomposition3d.outputVectorImage1
// Property of the outputVectorImage2 parameter.
EigenDecomposition3d.outputVectorImage2
// Property of the outputVectorImage3 parameter.
EigenDecomposition3d.outputVectorImage3
// Property of the outputEigenvaluesImage parameter.
EigenDecomposition3d.outputEigenvaluesImage

// Method to launch the command.
Execute()

Parameters

Class Name	EigenDecomposition3d

Parameter Name

Description

Type

Supported Values

Default Value

inputTensorImage

The input image of which each voxel represents a 3x3 symmetric matrix. This image must have the float data type and contain 6 channels.
The 6 channels must be in the following order: $(A_{11}, A_{12}, A_{13}, A_{22}, A_{23}, A_{33})$ where $A$ is a symmetric 3x3 matrix (or 3D tensor).

Image

Binary, Label or Multispectral

nullptr

outputSelection

The output images to be computed. Several outputs can be generated by combining the associated enumerated values.

EIGEN_VECTOR_1	Enable the computation of the first eigenvector, corresponding to the largest eigenvalue. Associated value = 1.
EIGEN_VECTOR_2	Enable the computation of the second eigenvector, corresponding to the medium eigenvalue. Associated value = 2.
EIGEN_VECTOR_3	Enable the computation of the third eigenvector, corresponding to the smallest eigenvalue. Associated value = 4.
EIGEN_VALUES	Enable the computation of the eigenvalues. Associated value = 8.

MultipleChoice

EIGEN_VECTOR_1 | EIGEN_VECTOR_2 | EIGEN_VALUES

outputVectorImage1

The first eigenvector output image containing the largest eigenvalue.
The X, Y and Z dimensions of this output image are the same as the input but the number of channels is three (channel 0: X component, channel 1: Y component, channel 2: Z component). The calibration (voxel size, origin, orientation) is the same as the input image. The output data type is forced to float.

Image

nullptr

outputVectorImage2

The second eigenvector image containing the medium eigenvalue.
The X, Y and Z dimensions of this output image are the same as the input but the number of channels is three (channel 0: X component, channel 1: Y component, channel 2: Z component). The calibration (voxel size, origin, orientation) is the same as the input image. The output data type is forced to float.

Image

nullptr

outputVectorImage3

The third eigenvector image containing the smallest eigenvalue.
The X, Y and Z dimensions of this output image are the same as the input but the number of channels is three (channel 0: X component, channel 1: Y component, channel 2: Z component). The calibration (voxel size, origin, orientation) is the same as the input image. The output data type is forced to float.

Image

nullptr

outputEigenvaluesImage

The eigenvalues output image. Each channel corresponds to an eigenvalue, from the largest to the smallest.
The X, Y and Z dimensions of this output image are the same as the input but the number of channels is three (channel 0: largest eigenvalue, channel 1: medium eigenvalue, channel 2: smallest eigenvalue). The calibration (voxel size, origin, orientation) is the same values as the input image. The output data type is forced to float.

Image

nullptr

Object Examples

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

EigenDecomposition3d eigenDecomposition3dAlgo;
eigenDecomposition3dAlgo.setInputTensorImage( neuron_hessian );
eigenDecomposition3dAlgo.setOutputSelection( 15 );
eigenDecomposition3dAlgo.execute();

std::cout << "outputVectorImage1:" << eigenDecomposition3dAlgo.outputVectorImage1()->toString();
std::cout << "outputVectorImage2:" << eigenDecomposition3dAlgo.outputVectorImage2()->toString();
std::cout << "outputVectorImage3:" << eigenDecomposition3dAlgo.outputVectorImage3()->toString();
std::cout << "outputEigenvaluesImage:" << eigenDecomposition3dAlgo.outputEigenvaluesImage()->toString();

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

eigen_decomposition_3d_algo = imagedev.EigenDecomposition3d()
eigen_decomposition_3d_algo.input_tensor_image = neuron_hessian
eigen_decomposition_3d_algo.output_selection = 15
eigen_decomposition_3d_algo.execute()

print( "output_vector_image1:", str( eigen_decomposition_3d_algo.output_vector_image1 ) );
print( "output_vector_image2:", str( eigen_decomposition_3d_algo.output_vector_image2 ) );
print( "output_vector_image3:", str( eigen_decomposition_3d_algo.output_vector_image3 ) );
print( "output_eigenvalues_image:", str( eigen_decomposition_3d_algo.output_eigenvalues_image ) );

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

EigenDecomposition3d eigenDecomposition3dAlgo = new EigenDecomposition3d
{
    inputTensorImage = neuron_hessian,
    outputSelection = 15
};
eigenDecomposition3dAlgo.Execute();

Console.WriteLine( "outputVectorImage1:" + eigenDecomposition3dAlgo.outputVectorImage1.ToString() );
Console.WriteLine( "outputVectorImage2:" + eigenDecomposition3dAlgo.outputVectorImage2.ToString() );
Console.WriteLine( "outputVectorImage3:" + eigenDecomposition3dAlgo.outputVectorImage3.ToString() );
Console.WriteLine( "outputEigenvaluesImage:" + eigenDecomposition3dAlgo.outputEigenvaluesImage.ToString() );

Function Examples

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

auto result = eigenDecomposition3d( neuron_hessian, 15 );

std::cout << "outputVectorImage1:" << result.outputVectorImage1->toString();
std::cout << "outputVectorImage2:" << result.outputVectorImage2->toString();
std::cout << "outputVectorImage3:" << result.outputVectorImage3->toString();
std::cout << "outputEigenvaluesImage:" << result.outputEigenvaluesImage->toString();

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

result_output_vector_image1, result_output_vector_image2, result_output_vector_image3, result_output_eigenvalues_image = imagedev.eigen_decomposition_3d( neuron_hessian, 15 )

print( "output_vector_image1:", str( result_output_vector_image1 ) );
print( "output_vector_image2:", str( result_output_vector_image2 ) );
print( "output_vector_image3:", str( result_output_vector_image3 ) );
print( "output_eigenvalues_image:", str( result_output_eigenvalues_image ) );

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

Processing.EigenDecomposition3dOutput result = Processing.EigenDecomposition3d( neuron_hessian, 15 );

Console.WriteLine( "outputVectorImage1:" + result.outputVectorImage1.ToString() );
Console.WriteLine( "outputVectorImage2:" + result.outputVectorImage2.ToString() );
Console.WriteLine( "outputVectorImage3:" + result.outputVectorImage3.ToString() );
Console.WriteLine( "outputEigenvaluesImage:" + result.outputEigenvaluesImage.ToString() );

EigenDecomposition3d

- Function Syntax

+ Class Syntax

Parameters

Object Examples

Function Examples

Function Syntax

Class Syntax