GaussianHessianMatrix3d

Computes a pointwise Hessian matrix on a three-dimensional image.

Access to parameter description

This algorithm computes the local Hessian matrix

$\begin{pmatrix} I_{xx} & I_{xy}& I_{xz}\\ I_{xy} & I_{yy}& I_{yz}\\ I_{xz} & I_{yz}& I_{zz} \end{pmatrix}$ by convolving the input image with the second order derivatives of a Gaussian kernel.

Each element of the Hessian matrix represents a second order partial derivative.
For instance,

$I_{xx}=\frac{\partial^2 I}{\partial x^2}$ ,

$I_{xy}=\frac{\partial^2 I} {\partial x \partial y}$ .
The matrix elements are computed as explained in the GaussianDerivative3d documentation.

This filter provides a spectral image output where each channel represents a matrix element; for instance, a second order derivative set in the following order:

$I_{xx}$ ,

$I_{xy}$ ,

$I_{xz}$ ,

$I_{yy}$ ,

$I_{yz}$ ,

$I_{zz}$ .
To extract the eigenvalues or vectors of the Hessian image the EigenDecomposition2d can be applied on this output image.

See also

Function Syntax

This function returns outputTensorImage.

// Function prototype
std::shared_ptr< iolink::ImageView >
gaussianHessianMatrix3d( std::shared_ptr< iolink::ImageView > inputImage,
                         iolink::Vector3d standardDeviation,
                         std::shared_ptr< iolink::ImageView > outputTensorImage = NULL );

This function returns outputTensorImage.

// Function prototype.
gaussian_hessian_matrix_3d( input_image, standard_deviation = [1, 1, 1], output_tensor_image = None )

This function returns outputTensorImage.

// Function prototype.
public static IOLink.ImageView
GaussianHessianMatrix3d( IOLink.ImageView inputImage,
                         double[] standardDeviation = null,
                         IOLink.ImageView outputTensorImage = null );

Class Syntax

// Command constructor.
GaussianHessianMatrix3d();

/// Gets the inputImage parameter.
/// The input image.
std::shared_ptr< iolink::ImageView > inputImage() const;
/// Sets the inputImage parameter.
/// The input image.
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.
GaussianHessianMatrix3d.input_image
# Property of the standardDeviation parameter.
GaussianHessianMatrix3d.standard_deviation
# Property of the outputTensorImage parameter.
GaussianHessianMatrix3d.output_tensor_image

// Method to launch the command.
execute()

// Command constructor.
GaussianHessianMatrix3d()

// Property of the inputImage parameter.
GaussianHessianMatrix3d.inputImage
// Property of the standardDeviation parameter.
GaussianHessianMatrix3d.standardDeviation
// Property of the outputTensorImage parameter.
GaussianHessianMatrix3d.outputTensorImage

// Method to launch the command.
Execute()

Parameters

	Description	Type	Supported Values	Default Value
inputImage	The input image.	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.	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.	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" );

GaussianHessianMatrix3d gaussianHessianMatrix3dAlgo;
gaussianHessianMatrix3dAlgo.setInputImage( foam );
gaussianHessianMatrix3dAlgo.setStandardDeviation( {1.0, 1.0, 1.0} );
gaussianHessianMatrix3dAlgo.execute();

std::cout << "outputTensorImage:" << gaussianHessianMatrix3dAlgo.outputTensorImage()->toString();

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

gaussian_hessian_matrix_3d_algo = imagedev.GaussianHessianMatrix3d()
gaussian_hessian_matrix_3d_algo.input_image = foam
gaussian_hessian_matrix_3d_algo.standard_deviation = [1.0, 1.0, 1.0]
gaussian_hessian_matrix_3d_algo.execute()

print( "output_tensor_image:", str( gaussian_hessian_matrix_3d_algo.output_tensor_image ) )

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

GaussianHessianMatrix3d gaussianHessianMatrix3dAlgo = new GaussianHessianMatrix3d
{
    inputImage = foam,
    standardDeviation = new double[]{1.0, 1.0, 1.0}
};
gaussianHessianMatrix3dAlgo.Execute();

Console.WriteLine( "outputTensorImage:" + gaussianHessianMatrix3dAlgo.outputTensorImage.ToString() );

Function Examples

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

auto result = gaussianHessianMatrix3d( foam, {1.0, 1.0, 1.0} );

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

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

result = imagedev.gaussian_hessian_matrix_3d( foam, [1.0, 1.0, 1.0] )

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

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

IOLink.ImageView result = Processing.GaussianHessianMatrix3d( foam, new double[]{1.0, 1.0, 1.0} );

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

GaussianHessianMatrix3d

- Function Syntax

+ Class Syntax

Parameters

Object Examples

Function Examples

Function Syntax

Class Syntax