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 outputVectorImage1, outputVectorImage2, outputVectorImage3 and outputEigenvaluesImage.

// Output structure of the eigenDecomposition3d function.
struct EigenDecomposition3dOutput
{
    /// The first eigenvector output image containing the largest eigenvalue.
    std::shared_ptr< iolink::ImageView > outputVectorImage1;
    /// The second eigenvector image containing the medium eigenvalue.
    std::shared_ptr< iolink::ImageView > outputVectorImage2;
    /// The third eigenvector image containing the smallest eigenvalue.
    std::shared_ptr< iolink::ImageView > outputVectorImage3;
    /// The eigenvalues output image. Each channel corresponds to an eigenvalue, from the largest to the smallest.
    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 output_vector_image1, output_vector_image2, output_vector_image3 and output_eigenvalues_image.

// 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 outputVectorImage1, outputVectorImage2, outputVectorImage3 and outputEigenvaluesImage.

/// Output structure of the EigenDecomposition3d function.
public struct EigenDecomposition3dOutput
{
    /// The first eigenvector output image containing the largest eigenvalue.
    public IOLink.ImageView outputVectorImage1;
    /// The second eigenvector image containing the medium eigenvalue.
    public IOLink.ImageView outputVectorImage2;
    /// The third eigenvector image containing the smallest eigenvalue.
    public IOLink.ImageView outputVectorImage3;
    /// 
    /// The eigenvalues output image. Each channel corresponds to an eigenvalue, from the largest to the smallest.
    /// 
    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();

/// Gets the inputTensorImage parameter.
/// The input image of which each voxel represents a 3x3 symmetric matrix. This image must have the float data type and contain 6 channels.
std::shared_ptr< iolink::ImageView > inputTensorImage() const;
/// Sets the inputTensorImage parameter.
/// The input image of which each voxel represents a 3x3 symmetric matrix. This image must have the float data type and contain 6 channels.
void setInputTensorImage( std::shared_ptr< iolink::ImageView > inputTensorImage );

/// Gets the outputSelection parameter.
/// The output images to be computed. Several outputs can be generated by combining the associated enumerated values.
int32_t outputSelection() const;
/// Sets the outputSelection parameter.
/// The output images to be computed. Several outputs can be generated by combining the associated enumerated values.
void setOutputSelection( const int32_t& outputSelection );

/// Gets the outputVectorImage1 parameter.
/// The first eigenvector output image containing the largest eigenvalue.
std::shared_ptr< iolink::ImageView > outputVectorImage1() const;
/// Sets the outputVectorImage1 parameter.
/// The first eigenvector output image containing the largest eigenvalue.
void setOutputVectorImage1( std::shared_ptr< iolink::ImageView > outputVectorImage1 );

/// Gets the outputVectorImage2 parameter.
/// The second eigenvector image containing the medium eigenvalue.
std::shared_ptr< iolink::ImageView > outputVectorImage2() const;
/// Sets the outputVectorImage2 parameter.
/// The second eigenvector image containing the medium eigenvalue.
void setOutputVectorImage2( std::shared_ptr< iolink::ImageView > outputVectorImage2 );

/// Gets the outputVectorImage3 parameter.
/// The third eigenvector image containing the smallest eigenvalue.
std::shared_ptr< iolink::ImageView > outputVectorImage3() const;
/// Sets the outputVectorImage3 parameter.
/// The third eigenvector image containing the smallest eigenvalue.
void setOutputVectorImage3( std::shared_ptr< iolink::ImageView > outputVectorImage3 );

/// Gets the outputEigenvaluesImage parameter.
/// The eigenvalues output image. Each channel corresponds to an eigenvalue, from the largest to the smallest.
std::shared_ptr< iolink::ImageView > outputEigenvaluesImage() const;
/// Sets the outputEigenvaluesImage parameter.
/// The eigenvalues output image. Each channel corresponds to an eigenvalue, from the largest to the smallest.
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

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

Parameter Name

Description

Type

Supported Values

Default Value

input_tensor_image

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

None

output_selection

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.

multiple_choice

EIGEN_VECTOR_1 | EIGEN_VECTOR_2 | EIGEN_VALUES

output_vector_image1

image

None

output_vector_image2

image

None

output_vector_image3

image

None

output_eigenvalues_image

image

None

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

null

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

Image

null

outputVectorImage2

Image

null

outputVectorImage3

Image

null

outputEigenvaluesImage

Image

null

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