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Continue path of vertical lines

I need to segment touching characters from an image

image description

I used skeletonization to get the outline of the image

image description

Now I want to connect the vertical lines and in order to identify separating lines for characters

image description

I tried using morphological operations but it is difficult to identify a kernel that works with different images. Can anyone suggest a better method to connect the marked lines and get the required region?

Here's my code

  import cv2
  import numpy as np
  import matplotlib.pyplot as plt

 from skimage.morphology import skeletonize
 from skimage.util import invert
 from skimage.measure import label

 org = cv2.imread('crop.png')
 image = cv2.copyMakeBorder(org, top=3, bottom=3, left=3, right=3,
                               borderType=cv2.BORDER_CONSTANT,
                               value=[0, 0, 0])
 img = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
 img = invert(img)

 skele = skeletonize(img//255)
 skele = (skele * 255).astype(np.uint8)

 labels = label(skele)
 assert(labels.max() != 0 )
 largestCC = labels == np.argmax(np.bincount(labels.flat)[1:])+1
 largestCC = (largestCC * 255).astype(np.uint8)

 kernel = cv2.getStructuringElement(cv2.MORPH_RECT,(1,8))
 d_im = cv2.dilate(largestCC, kernel, iterations=1)
 e_im = cv2.erode(d_im, kernel, iterations=1)
 plt.imshow(largestCC)
 plt.show()
 plt.imshow(e_im)
 plt.show()