GaussianGradientTensor3d

Computes a pointwise structure tensor on a three-dimensional image.

Access to parameter description

This algorithm computes the local structure tensor

$\begin{pmatrix} I_x.I_x & I_x.I_y & I_x.I_z\\ I_x.I_y & I_y.I_y & I_y.I_z\\ I_x.I_z & I_y.I_z & I_z.I_z \end{pmatrix} = \begin{pmatrix} I_x\\ I_y\\ I_z \end{pmatrix} \cdot \begin{pmatrix} I_x & I_y & I_z\end{pmatrix}$ by convolving the input image with the square first order derivatives of a Gaussian kernel.

Each element of the structure tensor represents a product of two partial derivatives
For instance,

$I_x.I_x = \frac{\partial I}{\partial x}\cdot\frac{\partial I}{\partial x}$ ,

$I_x.I_y = \frac{\partial I}{\partial x}\cdot\frac{\partial I}{\partial y}$ .
The partial derivatives are computed as explained in the GaussianDerivative3d documentation.

This filter provides a spectral image output where each channel represents a tensor element; for instance, a product of two partial derivatives, set in the following order:

$I_x.I_x$ ,

$I_x.I_y$ ,

$I_x.I_z$ ,

$I_y.I_y$ ,

$I_y.I_z$ ,

$I_z.I_z$ .
To extract the eigenvalues or vectors of the tensor image the EigenDecomposition3d can be applied on this output image.

See also

Function Syntax

This function returns outputTensorImage.

// Function prototype
std::shared_ptr< iolink::ImageView >
gaussianGradientTensor3d( std::shared_ptr< iolink::ImageView > inputImage,
                          iolink::Vector3d standardDeviation,
                          std::shared_ptr< iolink::ImageView > outputTensorImage = NULL );

This function returns outputTensorImage.

// Function prototype.
gaussian_gradient_tensor_3d( input_image, standard_deviation = [1, 1, 1], output_tensor_image = None )

This function returns outputTensorImage.

// Function prototype.
public static IOLink.ImageView
GaussianGradientTensor3d( IOLink.ImageView inputImage,
                          double[] standardDeviation = null,
                          IOLink.ImageView outputTensorImage = null );

Class Syntax

// Command constructor.
GaussianGradientTensor3d();

/// Gets the inputImage parameter.
/// The input image. The image type can be integer or float.
std::shared_ptr< iolink::ImageView > inputImage() const;
/// Sets the inputImage parameter.
/// The input image. The image type can be integer or float.
void setInputImage( std::shared_ptr< iolink::ImageView > inputImage );

/// Gets the standardDeviation parameter.
/// The sigma value of the Gaussian filter for each direction X, Y, and Z. Each value must be greater than or equal to 0.1.
iolink::Vector3d standardDeviation() const;
/// Sets the standardDeviation parameter.
/// The sigma value of the Gaussian filter for each direction X, Y, and Z. Each value must be greater than or equal to 0.1.
void setStandardDeviation( const iolink::Vector3d& standardDeviation );

/// Gets the outputTensorImage parameter.
/// The output image. Its spatial dimensions, calibration and interpretation are forced to the same values as the input image. Its type is forced to float.
std::shared_ptr< iolink::ImageView > outputTensorImage() const;
/// Sets the outputTensorImage parameter.
/// The output image. Its spatial dimensions, calibration and interpretation are forced to the same values as the input image. Its type is forced to float.
void setOutputTensorImage( std::shared_ptr< iolink::ImageView > outputTensorImage );


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

# Property of the inputImage parameter.
GaussianGradientTensor3d.input_image
# Property of the standardDeviation parameter.
GaussianGradientTensor3d.standard_deviation
# Property of the outputTensorImage parameter.
GaussianGradientTensor3d.output_tensor_image

// Method to launch the command.
execute()

// Command constructor.
GaussianGradientTensor3d()

// Property of the inputImage parameter.
GaussianGradientTensor3d.inputImage
// Property of the standardDeviation parameter.
GaussianGradientTensor3d.standardDeviation
// Property of the outputTensorImage parameter.
GaussianGradientTensor3d.outputTensorImage

// Method to launch the command.
Execute()

Parameters

	Description	Type	Supported Values	Default Value
inputImage	The input image. The image type can be integer or float.	Image	Binary, Label or Grayscale	nullptr
standardDeviation	The sigma value of the Gaussian filter for each direction X, Y, and Z. Each value must be greater than or equal to 0.1.	Vector3d	>=0.1	{1.f, 1.f, 1.f}
outputTensorImage	The output image. Its spatial dimensions, calibration and interpretation are forced to the same values as the input image. Its type is forced to float.	Image		nullptr

Description	Type	Supported Values	Default Value
input_image	The input image. The image type can be integer or float.	image	Binary, Label or Grayscale	None
standard_deviation	The sigma value of the Gaussian filter for each direction X, Y, and Z. Each value must be greater than or equal to 0.1.	vector3d	>=0.1	[1, 1, 1]
output_tensor_image	The output image. Its spatial dimensions, calibration and interpretation are forced to the same values as the input image. Its type is forced to float.	image		None

Description	Type	Supported Values	Default Value
inputImage	The input image. The image type can be integer or float.	Image	Binary, Label or Grayscale	null
standardDeviation	The sigma value of the Gaussian filter for each direction X, Y, and Z. Each value must be greater than or equal to 0.1.	Vector3d	>=0.1	{1f, 1f, 1f}
outputTensorImage	The output image. Its spatial dimensions, calibration and interpretation are forced to the same values as the input image. Its type is forced to float.	Image		null

Object Examples

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

GaussianGradientTensor3d gaussianGradientTensor3dAlgo;
gaussianGradientTensor3dAlgo.setInputImage( foam );
gaussianGradientTensor3dAlgo.setStandardDeviation( {1, 1, 1} );
gaussianGradientTensor3dAlgo.execute();

std::cout << "outputTensorImage:" << gaussianGradientTensor3dAlgo.outputTensorImage()->toString();

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

gaussian_gradient_tensor_3d_algo = imagedev.GaussianGradientTensor3d()
gaussian_gradient_tensor_3d_algo.input_image = foam
gaussian_gradient_tensor_3d_algo.standard_deviation = [1, 1, 1]
gaussian_gradient_tensor_3d_algo.execute()

print( "output_tensor_image:", str( gaussian_gradient_tensor_3d_algo.output_tensor_image ) )

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

GaussianGradientTensor3d gaussianGradientTensor3dAlgo = new GaussianGradientTensor3d
{
    inputImage = foam,
    standardDeviation = new double[]{1, 1, 1}
};
gaussianGradientTensor3dAlgo.Execute();

Console.WriteLine( "outputTensorImage:" + gaussianGradientTensor3dAlgo.outputTensorImage.ToString() );

Function Examples

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

auto result = gaussianGradientTensor3d( foam, {1, 1, 1} );

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

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

result = imagedev.gaussian_gradient_tensor_3d( foam, [1, 1, 1] )

print( "output_tensor_image:", str( result ) )

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

IOLink.ImageView result = Processing.GaussianGradientTensor3d( foam, new double[]{1, 1, 1} );

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

GaussianGradientTensor3d

- Function Syntax

+ Class Syntax

Parameters

Object Examples

Function Examples

Function Syntax

Class Syntax