restore _inertia_eigvals_to_axes_lengths_3D for use in test case

python/cucim/src/cucim/skimage/measure/_regionprops.py

@@ -566,7 +566,6 @@ def axis_major_length(self):
             l1 = self.inertia_tensor_eigvals[0]
             return 4 * math.sqrt(l1)
         elif self._ndim == 3:
-            # equivalent to _inertia_eigvals_to_axes_lengths_3D(ev)[0]
             ev = self.inertia_tensor_eigvals
             return math.sqrt(10 * (ev[0] + ev[1] - ev[2]))
         else:
@@ -578,11 +577,10 @@ def axis_minor_length(self):
             l2 = self.inertia_tensor_eigvals[-1]
             return 4 * math.sqrt(l2)
         elif self._ndim == 3:
-            # equivalent to _inertia_eigvals_to_axes_lengths_3D(ev)[-1]
             ev = self.inertia_tensor_eigvals
             # use max to avoid possibly very small negative value due to
             # numeric error
-            return math.sqrt(max(10 * (-ev[0] + ev[1] + ev[2]), 0.0))
+            return math.sqrt(10 * max(-ev[0] + ev[1] + ev[2], 0.0))
         else:
             raise ValueError("axis_minor_length only available in 2D and 3D")
 

python/cucim/src/cucim/skimage/measure/tests/test_regionprops.py

@@ -24,7 +24,6 @@
     COL_DTYPES,
     OBJECT_COLUMNS,
     PROPS,
-    _inertia_eigvals_to_axes_lengths_3D,
     _parse_docs,
     _props_to_dict,
     _require_intensity_image,
@@ -1402,6 +1401,51 @@ def test_multichannel():
             assert_array_equal(p, p_multi[..., 1])
 
 
+def _inertia_eigvals_to_axes_lengths_3D(inertia_tensor_eigvals):
+    """Compute ellipsoid axis lengths from inertia tensor eigenvalues.
+
+    Parameters
+    ---------
+    inertia_tensor_eigvals : sequence of float
+        A sequence of 3 floating point eigenvalues, sorted in descending order.
+
+    Returns
+    -------
+    axis_lengths : list of float
+        The ellipsoid axis lengths sorted in descending order.
+
+    Notes
+    -----
+    Let a >= b >= c be the ellipsoid semi-axes and s1 >= s2 >= s3 be the
+    inertia tensor eigenvalues.
+
+    The inertia tensor eigenvalues are given for a solid ellipsoid in [1]_.
+    s1 = 1 / 5 * (a**2 + b**2)
+    s2 = 1 / 5 * (a**2 + c**2)
+    s3 = 1 / 5 * (b**2 + c**2)
+
+    Rearranging to solve for a, b, c in terms of s1, s2, s3 gives
+    a = math.sqrt(5 / 2 * ( s1 + s2 - s3))
+    b = math.sqrt(5 / 2 * ( s1 - s2 + s3))
+    c = math.sqrt(5 / 2 * (-s1 + s2 + s3))
+
+    We can then simply replace sqrt(5/2) by sqrt(10) to get the full axes
+    lengths rather than the semi-axes lengths.
+
+    References
+    ----------
+    ..[1] https://en.wikipedia.org/wiki/List_of_moments_of_inertia#List_of_3D_inertia_tensors
+    """  # noqa: E501
+    axis_lengths = []
+    for ax in range(2, -1, -1):
+        w = sum(
+            v * -1 if i == ax else v
+            for i, v in enumerate(inertia_tensor_eigvals)
+        )
+        axis_lengths.append(math.sqrt(10 * w))
+    return axis_lengths
+
+
 def test_3d_ellipsoid_axis_lengths():
     """Verify that estimated axis lengths are correct.