axis length regionprops is incorrect for 3D data

[grlee77]

Description

The formula in returning the major and minor axis lengths seems to be specific to 2D ellipses, but there is no restriction on the user calling this function on 3D data.

https://forum.image.sc/t/scikit-image-regionprops-minor-axis-length-in-3d-gives-first-minor-radius-regardless-of-whether-it-is-actually-the-shortest/59273/2

In my response in the forum post, I gave an algorithm based on the description here for an ImageJ tool:
https://imagejdocu.list.lu/tutorial/plugins/3d_ellipsoid

Way to reproduce

import numpy as np

from skimage.measure import regionprops
from skimage import draw

e = draw.ellipsoid(20, 10, 50).astype(int)
stats = regionprops(e)

print(stats[0]['minor_axis_length'])
print(stats[0]['major_axis_length'])

39.96593417262304
96.4629444283893

The major axis length is close to the expected value of 100, but the minor axis length of 40 reported here is much larger than the expected value of 20.

With the function I gave in the forum, the result is:

ellipsoid_axis_lengths(stats[0]['moments_central'])

(100.15219508248649, 40.01140312339376, 19.891769352179885)

Version information

skimage 0.19.dev0 development branch