ImageDev

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 = nullptr );
This function returns outputTensorImage. 
// Function prototype.
gaussian_gradient_tensor_3d(input_image: idt.ImageType,
                            standard_deviation: Union[Iterable[int], Iterable[float]] = [1, 1, 1],
                            output_tensor_image: idt.ImageType = None) -> idt.ImageType
This function returns outputTensorImage. 
// Function prototype.
public static IOLink.ImageView
GaussianGradientTensor3d( IOLink.ImageView inputImage,
                          double[] standardDeviation = null,
                          IOLink.ImageView outputTensorImage = null );

Class Syntax

Parameters

Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. The image type can be integer or float. 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
Parameter Name Description Type Supported Values Default Value
input
input_image
The input image. The image type can be integer or float. image Binary, Label or Grayscale None
input
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
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
Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. The image type can be integer or float. Image Binary, Label or Grayscale null
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 {1f, 1f, 1f}
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 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() );