AffineTransformation3D¶

MLModule¶

genre	`SpatialTransformation`
author	`MeVis Medical Solutions AG`
package	`MeVisLab/Standard`
dll	`MLTransformation`
definition	MLTransformation.def
keywords	`rotate`, `translate`, `shear`, `scale`, `image`

Purpose¶

The module AffineTransformation3D warps an input volume according to a three-dimensional affine coordinate transformation, using trilinear interpolation.

Usage¶

Translation, rotation, shearing, and scaling can be entered and reset. The field for the transformation matrix is read-only.

Limitations:

the field Matrix is not updated when no output image is demanded.
works efficiently only with data types of < uint16

Details¶

The module uses the well-known backward mapping technique (see, e.g., the excellent monograph by George Wolberg: Digital image warping).

From the given parameters, the module constructs a transformation matrix for the backward mapping. This transformation matrix B maps a point y in the output volume onto the corresponding point x in the input volume:

The idea of backward mapping graphically:

To achieve subvoxel resolution, trilinear interpolation is applied in the input volume. The origin of the coordinate system is in the center of the output volume.

The order for constructing the matrix is shearing, rotation, scaling, translation (the translation is applied after the other transformations).

Windows¶

Default Panel¶

Images/Screenshots/AffineTransformation3D._default.png

Input Fields¶

input0¶

name: input0, type: Image¶: The input volume.

Output Fields¶

output0¶

name: output0, type: Image¶: The output volume is the warped input volume.

Parameter Fields¶

Field Index¶

`Is World Transformation`: `Bool`	`Scaling Y`: `Double`	`Translation Z`: `Double`
`Matrix`: `Matrix`	`Scaling Z`: `Double`	`World Voxel Transformation`: `Matrix`
`Opt Parameters`: `String`	`Shearing X`: `Double`
`Reset`: `Trigger`	`Shearing Y`: `Double`
`Rotation X`: `Double`	`Shearing Z`: `Double`
`Rotation Y`: `Double`	`Transformation Mode`: `Enum`
`Rotation Z`: `Double`	`Translation X`: `Double`
`Scaling X`: `Double`	`Translation Y`: `Double`

Visible Fields¶

Reset¶

name: reset, type: Trigger¶: When pressed, all transformation parameters are set back to their default value.

Opt Parameters¶

name: optParameters, type: String, default: 0 0 0 0 0 0 1 1 1 0 0 0¶

Sets optionally all values in one string.

The order is: translations, rotations, shearings and scalings. This is used, e.g., for coupling to an Optimizer module.

Translation X¶

name: translationX, type: Double, default: 0¶: Sets the translation in the x direction.

Note

This is a relative value; the actual displacement in voxels is calculated according to the formula displayed in field Matrix.

Translation Y¶

name: translationY, type: Double, default: 0¶: Equivalent to Translation X.

Translation Z¶

name: translationZ, type: Double, default: 0¶: Equivalent to Translation X.

Rotation X¶

name: rotationX, type: Double, default: 0¶: Sets the rotation around the x-axis in radians. The origin is the center of the volume.

Note

Forward interpretation is clockwise, backward interpretation is counterclockwise, which is against mathematical convention. See Matrix for the explicit rotation matrix.

Rotation Y¶

name: rotationY, type: Double, default: 0¶: Equivalent to Rotation X.

Rotation Z¶

name: rotationZ, type: Double, default: 0¶: Equivalent to Rotation X.

Shearing X¶

name: shearingX, type: Double, default: 0¶: Sets the shearing in the x direction.

Shearing Y¶

name: shearingY, type: Double, default: 0¶: Sets the shearing in the y direction.

Shearing Z¶

name: shearingZ, type: Double, default: 0¶: Sets the shearing in the z direction.

Scaling X¶

name: scalingX, type: Double, default: 1¶

Sets the scaling in the x direction.

Scaling behaves reciprocally to the value (e.g., 0.5 zooms in the image by 2).

Scaling Y¶

name: scalingY, type: Double, default: 1¶: Equivalent to Scaling X.

Scaling Z¶

name: scalingZ, type: Double, default: 1¶: Equivalent to Scaling X.

Matrix¶

name: matrix, type: Matrix, persistent: no¶

Sets the backward mapping matrix B as a 4x4 matrix.

Note

The matrix is according to ML convention, not Open Inventor convention. One may use the “DecomposeMatrix” macro to format this field in a 4x4 matrix.

The matrix B is constructed by the module from the parameters according to the following formula:

with

Translation:

Scaling:

Shearing:

Rotation in X:

and Rotation in Z and Y accordingly. The entries for the displacement vector in B are in voxels.

Transformation Mode¶

name: transformationMode, type: Enum, default: Affine¶: Defines the transformation mode.

Values:

Title	Name
Translation	Translation
Rigid	Rigid
Similarity	Similarity
Rigid + Scale	Rigid + Scale
Affine	Affine

Is World Transformation¶

name: isWorldTransformation, type: Bool, default: FALSE¶: If checked, the transformation is performed in world space.

World Voxel Transformation¶

name: worldVoxelTransformation, type: Matrix, persistent: no¶: Shows the world-to-voxel matrix.