## Find Principal Axes Plugin

**Download this plugin** (installation instructions)

**Preprocessing:**

- Within Mango define ROIs of interest. Mango supports eight ROIs, each determined by a different color.
- From the Plugins menu select Find Principal Axes.

**Principal Axes Plugin Use:**

- Select ROI by color and press Analyze.
- Change to other ROIs if necessary and press Analyze.
- Results are printed one after the other to a scrolling window, and text can be copied for use elsewhere.

**Results:**

- The Principal Axes Plugin identifies each ROI by color name at the top of its results.
- General summary statistics follow including centroid, voxel volume, and volume in mm
^{3}. - Next is the raw covariance matrix.
- Next is the diagonalized covariance matrix with eigenvalues along its diagonal elements. These are arranged from smallest at upper left to largest at lower right.
- Last are the eigenvectors in column format. The x, y and z coordinates are from top to bottom row. The leftmost column eigenvector corresponds to the leftmost eigenvalue and so forth. Each eigenvector is unit length.

**Interpretation:**

- Each eigenvalue is the mean square distance from the centroid to voxels within the ROI in the direction of its corresponding eigenvector. To convert this value to a distance measure you MUST take the square root of the eigenvalue.
- The directed distances formed from the square root of the eigenvalues are along three principal axes with directions determined by the corresponding eigenvectors.
- The coordinate system used for centroid are x,y,z with x=0 at left, y=0 at anterior, and z=0 at superior ends of the image volume.
- The coordinate system used for covariance matrices and eigenvectors is referenced to the centroid with +x right, +y posterior, and +z inferior of the centroid. This is not a standard brain coordinate system, but was used to simplify processing.

**Version History**:

1.3 (06-05-2015) — Added script support.

1.2 (05-16-2014) — Changes to support plugin API updates.

1.1.3 (03-18-2014) — Minor change to support plugin API updates.

1.1.2 (01-24-2014) — Minor fix

1.1.1 — Can now resize window. Better support for multi-displays.

1.0.1 — Added support for new plugin format.