How to deduce automatically if the processed image needs morphological post-processing or not?

• I have done segmentation using Deep-Learning, after that, I have noticed that sometimes the segmented shapes seems to be good, and sometimes, it needs more post-processing with morphological operations.
• The segmented shape is a ring, and in rare cases is filled circle, as you can see in the attached images.
• When this ring segmentation is closed shape, there are no issues, but when the ring is open there is a problem, because I can't measure the internal area (inside the ring) correctly and the area calculation is the objective of the whole project.
• So how can I detect automatically if my segmented image needs post-processing (using morphological operations) and what kind of morphology is preferred in this case? so I can calculate the area as mentioned here.

Thanks in Advance

import numpy as np
import matplotlib.pyplot as plt
from skimage.io import imread, imsave
# import scipy.ndimage as ndi 
from skimage import morphology, filters, feature

seg = imread('prediction.png')
# meijering alpha=None,
# rem2 = morphology.remove_small_objects(seg, 4)
resf = filters.meijering(seg, sigmas=range(1, 3, 1),  black_ridges=False)

sobel = filters.sobel(resf)
# diam = morphology.diameter_closing(sobel, 64, connectivity=2)
gaussian = filters.gaussian(sobel, sigma= 1)
val = filters.threshold_otsu(gaussian)
resth = gaussian < val 

# Morphology
SE = morphology.diamond(2)
# SE = np.ones((3,3))
# SE = morphology.disk(2)
# SE = square(7)
# SE = rectangle(3,3)
# SE = octagon(3, 3)

erosion  = morphology.binary_erosion( resth, SE).astype(np.uint8)
dilation = morphology.binary_dilation(resth, SE).astype(np.uint8)
opening  = morphology.binary_opening( resth, SE).astype(np.uint8)
closing  = morphology.binary_closing( resth, SE).astype(np.uint8)
#thinner = morphology.thin(erosion, max_iter=4)

rem  = morphology.remove_small_holes(resth, 2)

# entropy  = filters.rank.entropy(resth, SE) 
# print(seg.shape)

plt.figure(num='PProc')
# 1
plt.subplot('335')
plt.imshow(rem,cmap='gray')
plt.title('rem')
plt.axis('off')
# 2
plt.subplot('336')
plt.imshow(dilation,cmap='gray')
plt.title('dilation')
plt.axis('off')
# 3
plt.subplot('337')
plt.imshow(opening,cmap='gray')
plt.title('opening')
plt.axis('off')
# 4
plt.subplot('338')
plt.imshow(closing,cmap='gray')
plt.title('closing')
plt.axis('off')
# 5
plt.subplot('332')
plt.imshow(seg,cmap='gray')
plt.title('segmented')
plt.axis('off')
# 6
plt.subplot('333')
plt.imshow(resf,cmap='gray')
plt.title('meijering')
plt.axis('off')
# 7
# 8
plt.subplot('334')
plt.imshow(resth,cmap='gray')
plt.title('threshold_otsu')
plt.axis('off')
# 9
plt.subplot('339')
plt.imshow(erosion,cmap='gray')
plt.title('erosion')
plt.axis('off')
#
plt.show()

By reproducing the answer on this post, and tweaking it a little bit, the answered is: by checking the number of labelled areas, so if there is less than 3 areas, mostly a morphological operation is needed, otherwise I have a closed ring, then there is 3 labelled areas.

from skimage.io import imread
import numpy as np
from skimage.measure import label, regionprops
from skimage.color import label2rgb

img = imread(os.path.join(path,im_name))
labeled = label(img, background=2)
overlay = label2rgb(labeled)

LV = overlay[...,0] + overlay[...,1]
LV = LV > 1

if (np.sum(LV)):
    print('This image doesnt need Morphological processing')
else:
    print('This image needs Morphological processing')