You can perform a three-dimensional rotation of the image using the Rotation tool. Enter values for the Phi, Theta, and Psi Euler rotation angles, or enter a single angle to rotate about one axis. This feature is useful when images are not aligned with the structure's inherent axis and empty space is found around them.

For the Rotation Mode select either Euler Angles or Rotate around X, Y, or Z Axis.

The Euler rotation angles are applied following the order Phi → Theta → Psi.

For Rotate around X, Y, or Z Axis enter the angle for the rotation about X, Y, or Z.

Check the Enlarge Image Automatically box to avoid cropping after rotation.

When you check Automatic Rotation, the entered parameters for the rotation angles are ignored and become inactive. Instead, the Euler rotation angles are calculated automatically based on principal component analysis for the imported gray value image. From the pull-down menu for Automation Mode select Volume or Plane. For Volume the algorithm tries to align the structure to all three coordinate axes. For Plane only two major axes are aligned. Aligning only to two major axes can minimize unwanted rotations inside a planar structure.

Checking Automatic Rotation causes the entered parameters for the rotation angles to become inactive and ignored. Instead, the Euler rotation angles are automatically calculated based on principal component analysis of the imported gray value image. From the Automation Mode pull-down menu, select Volume or Plane. For Volume, the algorithm tries to align the structure to all three coordinate axes. For Plane, only two major axes are aligned. Aligning to only two major axes can minimize unwanted rotations inside a planar structure.

Alternatively, you can use the Suggest buttons to suggest values for rotation first. This functionality uses the same calculation as Automatic Rotation, and the two modes, Volume and Plane, are also available. Click one of these options to obtain suggested values for Phi, Theta, and Psi.

A structure is required to compute the alignment to either two or all three major axes for the suggestion or automatic rotation. Global Thresholding is used to obtain such a structure. If the Automatic Threshold is enabled, the Otsu method is used to threshold the image. Otherwise, enter a Manual Threshold.

Click Apply to rotate the structure with the current settings.

Example

First, a structure model is obtained without rotation. o obtain a structure that has been rotated 90° or 180° about the Y-axis, the following Euler angles are used:

• 90° around Z-axis (fixed) + 180° around new X-axis (fixed) + -90° around new Z-axis (fixed)
• 90° around Z-axis (fixed) + 90° around new X-axis (fixed) + -90° around new Z-axis (fixed)

Of course, these two rotations can be obtained more easily by selecting Rotate around Y-Axis for Rotation Mode, but the example helps to understand the Euler angles. Since they can rotate the 3D image in any direction, they are more powerful when the image needs to be rotated about more than one axis.

Selecting Rotate as the Overlay visualizes the resulting rotation in the 2D Slice Visualization area. Diagonal red, green, and blue lines show the resulting new center lines. In the following example, the image is rotated about the X-axis. Therefore, in the YZ plane, blue and green diagonals can be seen. These are the new center lines after rotating.