This plugin calculates the three orthogonal principal axes and moments of inertia around those axes. It includes pixels with values between upper and lower limits, which can be defined in terms of unitless grey values or Hounsfield units (HU). It optionally creates a new stack with the image centred and rotated so that the principal axes are parallel to the image stack's x, y and z axes. Calculations are limited to a rectangular ROI if one is drawn. The plugin will guess whether the image is HU calibrated, and if so, apply HU limits of bone (0-4000 HU), otherwise it will calculate auto-thresholds based on the stack's histogram. If a calibration curve is known, the coefficients can be added to get weighted calculations. Aligning a bone with Moments of Inertia may be a useful step prior to Slice Geometry if bones are not aligned with the image z axis.

- Input
- Binary, 8-bit or 16-bit image stack

- Options
- Start slice: First slice to include in calculations
- End slice: Last slice to include in calculations
- HU Calibrated: Plugin will guess whether the image is HU calibrated. If image is HU calibrated, make sure the box is checked and enter HU calibrated numeric values in the following fields
- Bone Min: Lower threshold, in either uncalibrated greys or HU
- Bone Max: Upper threshold, in either uncalibrated greys or HU
- Slope: m where physical density = m × pixel value + c
- Y Intercept: c where physical density = m × pixel value + c
- Align result: Draw a new stack with the principal axes parallel to the image axes
- Show axes (2D): Draw the axes in white on the aligned image
- Show axes (3D): Display the stack and its principal axes in a 3D Viewer window

- Output
- Image: Image file name
- Xc: Centroid x-coordinate (mass-weighted by calibrated density)
- Yc: Centroid y-coordinate
- Zc: Centroid z-coordinate
- Vol: Total volume of thresholded voxels
- Mass: Mass of bone, from pixel values and density calibration coefficients
- Icxx: Moment around x axis passing through centroid
- Icyy: Moment around y axis passing through centroid
- Iczz: Moment around z axis passing through centroid
- Icxy: Off-axis term for constructing inertia tensor
- Icxz: Off-axis term for constructing inertia tensor
- Icyz: Off-axis term for constructing inertia tensor
- I1: Moment around the shortest principal axis
- I2: Moment around the middle principal axis
- I3: Moment around the longest principal axis
- Verbose output in Log window:
- Eigenvalues: Result of of eigenvalue decomposition. Moments of inertia
- Eigenvectors of principal axes: orientation of input image
- Inverse eigenvector matrix: used to map voxel positions in the aligned image back to voxel positions in the original image

- Optional 3D display of principal axes

This file last modified 1345hrs 29 May 2020 © Michael Doube 2004-2020 :: Designed to be interoperable and standards-compliant.