ImageDev

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

Parameters

Class Name GaussianHessianMatrix3d

Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. Image Binary, Label or Grayscale nullptr
input
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}
output
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

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() );