Perhaps this will give you some idea about morphology in Python/OpenCV. First I use a square "open" kernel about the size of the small white spots to remove them. Then I use a horizontal rectangle "close" kernel about the size of the black gap to fill it. "Open" removes white regions (or fills black gaps) and close removes black regions (or fills white gaps)

Input:

import cv2
import numpy as np

# read image as grayscale
img = cv2.imread('blob3.png', cv2.IMREAD_GRAYSCALE)

# threshold to binary
thresh = cv2.threshold(img, 0, 255, cv2.THRESH_BINARY)[1]

# apply morphology open with square kernel to remove small white spots
kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (19,19))
morph1 = cv2.morphologyEx(thresh, cv2.MORPH_OPEN, kernel)

# apply morphology close with horizontal rectangle kernel to fill horizontal gap
kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (101,1))
morph2 = cv2.morphologyEx(morph1, cv2.MORPH_CLOSE, kernel)

# write results
cv2.imwrite("blob3_morph1.png", morph1)
cv2.imwrite("blob3_morph2.png", morph2)

# show results
cv2.imshow("thresh", thresh)
cv2.imshow("morph1", morph1)
cv2.imshow("morph2", morph2)
cv2.waitKey(0)

Morphology Square Open:

Morphology Rectangle Close:

Alternate Morphology Square Close:

This answer explains how to use MORPH_CLOSE around the edge of an image by adding a buffer to the image.

You can add a buffer by creating an image of zeros using numpy:

# Import packages
import cv2
import numpy as np
import matplotlib.pyplot as plt
# Read in the image
img = cv2.imread('/home/stephen/Desktop/OKoUh.png', 0)
# Create a black bufffer around the image
h,w = img.shape
buffer = max(h,w)
bg = np.zeros((h+buffer*2, w+buffer*2), np.uint8)
bg[buffer:buffer+h, buffer:buffer+w] = img

Then you can iterate and check how it looks at different kernel sizes:

for close_size in range(1,11):
    temp  = bg.copy()
    kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (close_size, close_size))
    result = cv2.morphologyEx(temp, cv2.MORPH_CLOSE, kernel)
    results = result[buffer:buffer+h, buffer:buffer+w]
    cv2.imshow('img', result)
    cv2.waitKey()

My results: