How to join nearby bounding boxes in OpenCV Python

Question

I am doing a college class project on image processing. This is my original image:

Answer 1

So, here comes my solution. I partially modified your (initial) code to my preferred naming, etc. Also, I commented all the stuff, I added.

import cv2
import numpy as np

image = cv2.imread('images/example.png')

gray = cv2.cvtColor(image, cv2.COLOR_BGR2GRAY)
_, thresh = cv2.threshold(gray, 127, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)

kernel = np.ones((5, 5), np.uint8)
img_dilated = cv2.dilate(thresh, kernel, iterations = 1)

cnts, _ = cv2.findContours(img_dilated.copy(), cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

# Array of initial bounding rects
rects = []

# Bool array indicating which initial bounding rect has
# already been used
rectsUsed = []

# Just initialize bounding rects and set all bools to false
for cnt in cnts:
    rects.append(cv2.boundingRect(cnt))
    rectsUsed.append(False)

# Sort bounding rects by x coordinate
def getXFromRect(item):
    return item[0]

rects.sort(key = getXFromRect)

# Array of accepted rects
acceptedRects = []

# Merge threshold for x coordinate distance
xThr = 5

# Iterate all initial bounding rects
for supIdx, supVal in enumerate(rects):
    if (rectsUsed[supIdx] == False):

        # Initialize current rect
        currxMin = supVal[0]
        currxMax = supVal[0] + supVal[2]
        curryMin = supVal[1]
        curryMax = supVal[1] + supVal[3]

        # This bounding rect is used
        rectsUsed[supIdx] = True

        # Iterate all initial bounding rects
        # starting from the next
        for subIdx, subVal in enumerate(rects[(supIdx+1):], start = (supIdx+1)):

            # Initialize merge candidate
            candxMin = subVal[0]
            candxMax = subVal[0] + subVal[2]
            candyMin = subVal[1]
            candyMax = subVal[1] + subVal[3]

            # Check if x distance between current rect
            # and merge candidate is small enough
            if (candxMin <= currxMax + xThr):

                # Reset coordinates of current rect
                currxMax = candxMax
                curryMin = min(curryMin, candyMin)
                curryMax = max(curryMax, candyMax)

                # Merge candidate (bounding rect) is used
                rectsUsed[subIdx] = True
            else:
                break

        # No more merge candidates possible, accept current rect
        acceptedRects.append([currxMin, curryMin, currxMax - currxMin, curryMax - curryMin])

for rect in acceptedRects:
    img = cv2.rectangle(image, (rect[0], rect[1]), (rect[0] + rect[2], rect[1] + rect[3]), (121, 11, 189), 2)

cv2.imwrite("images/result.png", image)

For your example

I get the following output

Now, you have to find a proper threshold to meet your expectations. Maybe, there is even some more work to do, especially to get the whole formula, since the distances don't vary that much.

Disclaimer: I'm new to Python in general, and specially to the Python API of OpenCV (C++ for the win). Comments, improvements, highlighting Python no-gos are highly welcome!