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.

ellipsoid

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