ImageDev

Shearing3d

Applies a three-dimensional shear transformation along a user-defined direction.

Access to parameter description

This algorithm applies a shear transformation which can be seen as the translation of axis-aligned slices along a user-defined direction. It shears the input volume using 2 axes. The first axis (slice axis) is the axis of influence; it, together with the shear angle, determines the shift value. The second axis (shift axis) defines the direction along which the slices are translated.

For instance, if the shift axis is z and the slice axis is y, then the transformation only affects the z-coordinate of an input point, resulting in the newly transformed coordinate z'. $$ z' = z + \tan(\alpha) y $$ Using the matrix notation, the transformation $T(X)$ of a point $X \in R^3$ is given by: $$ T(X) = SX $$ $S$ is a $3 \times 3$ matrix where all diagonal elements are equal to 1, and all non-diagonal elements are equal to 0 except the one at position $(i, j)$, which takes the value $\tan(\alpha)$. Here, $i$ represents the index of the shift axis, $j$ represents the index of the slice axis (0 for x, 1 for y, 2 for z), and $\alpha$ represents the shearing angle.

If the slice axis is y (i=1), and the shift axis z (j=2), then $$ S = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & \tan(\alpha) & 1 \\ \end{bmatrix} $$



Figure 1. : (left) the original image; (right) shearing with y as the shift axis, z as the slice axis (xy slices are shifted), angle is 38°

See also

Function Syntax

This function returns outputImage. 
// Function prototype
std::shared_ptr< iolink::ImageView >
shearing3d( std::shared_ptr< iolink::ImageView > inputImage,
            Shearing3d::Axis sliceAxis,
            Shearing3d::Axis shiftAxis,
            double angle,
            double sliceAxisOrigin,
            Shearing3d::OutputSpacingMode outputSpacingMode,
            const iolink::Vector3d& outputSpacing,
            double paddingValue,
            std::shared_ptr< iolink::ImageView > outputImage = nullptr );
This function returns outputImage. 
// Function prototype.
shearing_3d(input_image: idt.ImageType,
            slice_axis: Shearing3d.Axis = Shearing3d.Axis.Y_AXIS,
            shift_axis: Shearing3d.Axis = Shearing3d.Axis.Z_AXIS,
            angle: float = 38,
            slice_axis_origin: float = 0,
            output_spacing_mode: Shearing3d.OutputSpacingMode = Shearing3d.OutputSpacingMode.SAME_AS_INPUT,
            output_spacing: Union[Iterable[int], Iterable[float]] = [1, 1, 1],
            padding_value: float = 0,
            output_image: idt.ImageType = None) -> idt.ImageType
This function returns outputImage. 
// Function prototype.
public static IOLink.ImageView
Shearing3d( IOLink.ImageView inputImage,
            Shearing3d.Axis sliceAxis = ImageDev.Shearing3d.Axis.Y_AXIS,
            Shearing3d.Axis shiftAxis = ImageDev.Shearing3d.Axis.Z_AXIS,
            double angle = 38,
            double sliceAxisOrigin = 0,
            Shearing3d.OutputSpacingMode outputSpacingMode = ImageDev.Shearing3d.OutputSpacingMode.SAME_AS_INPUT,
            double[] outputSpacing = null,
            double paddingValue = 0,
            IOLink.ImageView outputImage = null );

Class Syntax

Parameters

Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. Image Binary, Label, Grayscale or Multispectral nullptr
input
sliceAxis
The axis orthogonal to the slices that are shifted. If the z-axis is selected as the slice axis, the xy slices are shifted along the x or y direction.
X_AXIS The slice axis is the x-axis, the yz slices are shifted.
Y_AXIS The slice axis is the y-axis, the xz slices are shifted.
Z_AXIS The slice axis is the z-axis, the xy slices are shifted.
Enumeration Y_AXIS
input
shiftAxis
The direction toward which the slices are shifted. If the z-axis is selected as the slice axis and the y-axis as the shift axis, the xy-slices are shifted along the y direction.
X_AXIS The slices are shifted along the x-axis.
Y_AXIS The slices are shifted along the y-axis.
Z_AXIS The slices are shifted along the z-axis.
Enumeration Z_AXIS
input
sliceAxisOrigin
The slice index along the slice axis which defines the origin of the transformation, that is the plane that is not shifted by the shearing transform. Float64 Any value 0
input
angle
The shear angle. It represents the angle in degrees between the initial slice axis and the shifted axis. Float64 [-90, 90] 38
input
outputSpacingMode
This parameter defines how to calculate the voxel size of the output volume.
SAME_AS_INPUT Set the output spacing to the same values as the inputvoxel size. However, the output may differ slightly due to numerical sampling and rounding.
OTHER Use the outputSpacing parameter to set the output voxel size. It may be useful to change it when the input has an anisotropic voxel size, for instance when the z-axis has a greater spacing than x and y. The output voxel size uses the same unit as the input image.
Enumeration SAME_AS_INPUT
input
outputSpacing
The voxel size of the output volume along the x, y, and z axes, expressed in the same unit as the input image. It is used only when the outputSpacingMode parameter is set to OTHER. In this case, these values must be chosen carefully, ensuring consistency with those of the input volume and the unit used. A value that is too large may generate an output volume that is empty or consists of few voxels, while a value that is too small may lead to memory overflow. This parameter is not used when the spacing mode is set to SAME_AS_INPUT Vector3d >0 {1.f, 1.f, 1.f}
input
paddingValue
The background value for output voxels which are outside the input image domain. Float64 Any value 0
output
outputImage
The output image. Its type is forced to the same values as the input. The slice and shift axes have dimensions greater than the input image and the third axes has identical dimensions. Image nullptr
Parameter Name Description Type Supported Values Default Value
input
input_image
The input image. image Binary, Label, Grayscale or Multispectral None
input
slice_axis
The axis orthogonal to the slices that are shifted. If the z-axis is selected as the slice axis, the xy slices are shifted along the x or y direction.
X_AXIS The slice axis is the x-axis, the yz slices are shifted.
Y_AXIS The slice axis is the y-axis, the xz slices are shifted.
Z_AXIS The slice axis is the z-axis, the xy slices are shifted.
enumeration Y_AXIS
input
shift_axis
The direction toward which the slices are shifted. If the z-axis is selected as the slice axis and the y-axis as the shift axis, the xy-slices are shifted along the y direction.
X_AXIS The slices are shifted along the x-axis.
Y_AXIS The slices are shifted along the y-axis.
Z_AXIS The slices are shifted along the z-axis.
enumeration Z_AXIS
input
slice_axis_origin
The slice index along the slice axis which defines the origin of the transformation, that is the plane that is not shifted by the shearing transform. float64 Any value 0
input
angle
The shear angle. It represents the angle in degrees between the initial slice axis and the shifted axis. float64 [-90, 90] 38
input
output_spacing_mode
This parameter defines how to calculate the voxel size of the output volume.
SAME_AS_INPUT Set the output spacing to the same values as the inputvoxel size. However, the output may differ slightly due to numerical sampling and rounding.
OTHER Use the outputSpacing parameter to set the output voxel size. It may be useful to change it when the input has an anisotropic voxel size, for instance when the z-axis has a greater spacing than x and y. The output voxel size uses the same unit as the input image.
enumeration SAME_AS_INPUT
input
output_spacing
The voxel size of the output volume along the x, y, and z axes, expressed in the same unit as the input image. It is used only when the outputSpacingMode parameter is set to OTHER. In this case, these values must be chosen carefully, ensuring consistency with those of the input volume and the unit used. A value that is too large may generate an output volume that is empty or consists of few voxels, while a value that is too small may lead to memory overflow. This parameter is not used when the spacing mode is set to SAME_AS_INPUT vector3d >0 [1, 1, 1]
input
padding_value
The background value for output voxels which are outside the input image domain. float64 Any value 0
output
output_image
The output image. Its type is forced to the same values as the input. The slice and shift axes have dimensions greater than the input image and the third axes has identical dimensions. image None
Parameter Name Description Type Supported Values Default Value
input
inputImage
The input image. Image Binary, Label, Grayscale or Multispectral null
input
sliceAxis
The axis orthogonal to the slices that are shifted. If the z-axis is selected as the slice axis, the xy slices are shifted along the x or y direction.
X_AXIS The slice axis is the x-axis, the yz slices are shifted.
Y_AXIS The slice axis is the y-axis, the xz slices are shifted.
Z_AXIS The slice axis is the z-axis, the xy slices are shifted.
Enumeration Y_AXIS
input
shiftAxis
The direction toward which the slices are shifted. If the z-axis is selected as the slice axis and the y-axis as the shift axis, the xy-slices are shifted along the y direction.
X_AXIS The slices are shifted along the x-axis.
Y_AXIS The slices are shifted along the y-axis.
Z_AXIS The slices are shifted along the z-axis.
Enumeration Z_AXIS
input
sliceAxisOrigin
The slice index along the slice axis which defines the origin of the transformation, that is the plane that is not shifted by the shearing transform. Float64 Any value 0
input
angle
The shear angle. It represents the angle in degrees between the initial slice axis and the shifted axis. Float64 [-90, 90] 38
input
outputSpacingMode
This parameter defines how to calculate the voxel size of the output volume.
SAME_AS_INPUT Set the output spacing to the same values as the inputvoxel size. However, the output may differ slightly due to numerical sampling and rounding.
OTHER Use the outputSpacing parameter to set the output voxel size. It may be useful to change it when the input has an anisotropic voxel size, for instance when the z-axis has a greater spacing than x and y. The output voxel size uses the same unit as the input image.
Enumeration SAME_AS_INPUT
input
outputSpacing
The voxel size of the output volume along the x, y, and z axes, expressed in the same unit as the input image. It is used only when the outputSpacingMode parameter is set to OTHER. In this case, these values must be chosen carefully, ensuring consistency with those of the input volume and the unit used. A value that is too large may generate an output volume that is empty or consists of few voxels, while a value that is too small may lead to memory overflow. This parameter is not used when the spacing mode is set to SAME_AS_INPUT Vector3d >0 {1f, 1f, 1f}
input
paddingValue
The background value for output voxels which are outside the input image domain. Float64 Any value 0
output
outputImage
The output image. Its type is forced to the same values as the input. The slice and shift axes have dimensions greater than the input image and the third axes has identical dimensions. Image null

Object Examples

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

Shearing3d shearing3dAlgo;
shearing3dAlgo.setInputImage( polystyrene );
shearing3dAlgo.setSliceAxis( Shearing3d::Axis::Y_AXIS );
shearing3dAlgo.setShiftAxis( Shearing3d::Axis::Z_AXIS );
shearing3dAlgo.setAngle( 38.0 );
shearing3dAlgo.setSliceAxisOrigin( 0.0 );
shearing3dAlgo.setOutputSpacingMode( Shearing3d::OutputSpacingMode::SAME_AS_INPUT );
shearing3dAlgo.setOutputSpacing( {1.0, 1.0, 1.0} );
shearing3dAlgo.setPaddingValue( 0.0 );
shearing3dAlgo.execute();

std::cout << "outputImage:" << shearing3dAlgo.outputImage()->toString();

polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))

shearing_3d_algo = imagedev.Shearing3d()
shearing_3d_algo.input_image = polystyrene
shearing_3d_algo.slice_axis = imagedev.Shearing3d.Y_AXIS
shearing_3d_algo.shift_axis = imagedev.Shearing3d.Z_AXIS
shearing_3d_algo.angle = 38.0
shearing_3d_algo.slice_axis_origin = 0.0
shearing_3d_algo.output_spacing_mode = imagedev.Shearing3d.SAME_AS_INPUT
shearing_3d_algo.output_spacing = [1.0, 1.0, 1.0]
shearing_3d_algo.padding_value = 0.0
shearing_3d_algo.execute()

print("output_image:", str(shearing_3d_algo.output_image))

ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" );

Shearing3d shearing3dAlgo = new Shearing3d
{
    inputImage = polystyrene,
    sliceAxis = Shearing3d.Axis.Y_AXIS,
    shiftAxis = Shearing3d.Axis.Z_AXIS,
    angle = 38.0,
    sliceAxisOrigin = 0.0,
    outputSpacingMode = Shearing3d.OutputSpacingMode.SAME_AS_INPUT,
    outputSpacing = new double[]{1.0, 1.0, 1.0},
    paddingValue = 0.0
};
shearing3dAlgo.Execute();

Console.WriteLine( "outputImage:" + shearing3dAlgo.outputImage.ToString() );

Function Examples

auto polystyrene = ioformat::readImage( std::string( IMAGEDEVDATA_IMAGES_FOLDER ) + "polystyrene.tif" );

auto result = shearing3d( polystyrene, Shearing3d::Axis::Y_AXIS, Shearing3d::Axis::Z_AXIS, 38.0, 0.0, Shearing3d::OutputSpacingMode::SAME_AS_INPUT, {1.0, 1.0, 1.0}, 0.0 );

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

polystyrene = ioformat.read_image(imagedev_data.get_image_path("polystyrene.tif"))

result = imagedev.shearing_3d(polystyrene, imagedev.Shearing3d.Y_AXIS, imagedev.Shearing3d.Z_AXIS, 38.0, 0.0, imagedev.Shearing3d.SAME_AS_INPUT, [1.0, 1.0, 1.0], 0.0)

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

ImageView polystyrene = ViewIO.ReadImage( @"Data/images/polystyrene.tif" );

IOLink.ImageView result = Processing.Shearing3d( polystyrene, Shearing3d.Axis.Y_AXIS, Shearing3d.Axis.Z_AXIS, 38.0, 0.0, Shearing3d.OutputSpacingMode.SAME_AS_INPUT, new double[]{1.0, 1.0, 1.0}, 0.0 );

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





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