3D Ellipsoid measurements
This plugin will compute the different measurements based on the fitting of a 3D ellipsoid. The plugin will require one images as input, the will contain the objects to measure. The objects image can be a binary or labelled image, in case of a binary image, a labelling will be performed.
The ellipsoid axes and radii are computed using 3D moments :
- \( sxx = \sum{{(C_x-x)^2}\over{V_{obj}}} \)
- \( syy = \sum{{(C_y-y)^2}\over{V_{obj}}} \)
- \( szz = \sum{{(C_z-z)^2}\over{V_{obj}}} \)
- \( sxy = \sum{{(C_x-x).(C_y-y)}\over{V_{obj}}} \)
- \( sxz = \sum{{(C_x-x).(C_z-z)}\over{V_{obj}}} \)
- \( syz = \sum{{(C_y-y).(C_z-z)}\over{V_{obj}}} \)
The three eigen values and vectors are then computed from this matrix :
\( \begin{pmatrix} sxx & sxy & sxz \\ sxy & sy2 & syz \\ sxz & syz & szz \end{pmatrix} \)
The three radii are then : \(\sqrt{(5*value)}\). Review about 3D Moments computation is available here.
The different values in the results table are :
- Label: the name of the image
- Value: the pixel value of the object in the labelled image
- Channel: the channel number of the image
- Frame: the frame number of the image
Then the values based of the ellipsoid volume.
- VolEll(unit): the ellipsoid volume in calibrated unit
- Spareness: the ratio between the ellipsoid volume and the object volume
Then values based on the three radii.
- EllMajRad(unit): the length of the major radius of the ellipsoid in calibrated unit
- Elongation: the ratio between the length of the major radius to the length of the second radius
- Flatness: the ratio between the length of the second radius to the length of the third radius