The 3D ellipsoid fitting plugin will fit a 3D ellipsoid to objects in a labelled image.

The ellipsoid axes and radii are computed using 3D moments :

• sx² = ∑(x-Cx)²/Vobj
• sy² = ∑(y-Cy)²/Vobj
• sz² = ∑(z-Cz)²/Vobj
• sxy = ∑(x-Cx)(y-Cy)/Vobj
• sxz = ∑(x-Cx)(z-Cz)/Vobj
• syz= ∑(y-Cy)(z-Cz)/Vobj

The three eigen values and vectors are then computed from this matrix :

The three radii are then : √(5*eigen value)

The different results are :

• Cx,Cy,Cz : centre of the object (in pixel coordinate)
• Vx, Vy, Vz : coordinate of the main elongation axis
• R1, R2, R3 : the tree radii of the fitted ellipsoid
• XY, XZ, YZ : angle between the main axis of the ellipsoid and the 3 planes
• Vobj : volume of the object
• Vell : volume of the fitted ellipsoid
• Vbb : volume of the bounding box around the object
• Vbbo (experimental) : volume of the bounding box oriented in the direction of the main axis
• The two poles of the object as the two voxels used to compute Feret diameter, and the two poles of the fitting ellipsoid.

Object and fitted ellipsoid with main elongation axis

Bounding box and oriented bounding box