How to join nearby bounding boxes in OpenCV Python

Here is a slightly different approach, using the OpenCV Wrapper library.

import cv2
import opencv_wrapper as cvw

image = cv2.imread("example.png")

gray = cvw.bgr2gray(image)
thresh = cvw.threshold_otsu(gray, inverse=True)

# dilation
img_dilation = cvw.dilate(thresh, 5)

# Find contours
contours = cvw.find_external_contours(img_dilation)
# Map contours to bounding rectangles, using bounding_rect property
rects = map(lambda c: c.bounding_rect, contours)
# Sort rects by top-left x (rect.x == rect.tl.x)
sorted_rects = sorted(rects, key=lambda r: r.x)

# Distance threshold
dt = 5

# List of final, joined rectangles
final_rects = [sorted_rects[0]]

for rect in sorted_rects[1:]:
    prev_rect = final_rects[-1]

    # Shift rectangle `dt` back, to find out if they overlap
    shifted_rect = cvw.Rect(rect.tl.x - dt, rect.tl.y, rect.width, rect.height)
    intersection = cvw.rect_intersection(prev_rect, shifted_rect)
    if intersection is not None:
        # Join the two rectangles
        min_y = min((prev_rect.tl.y, rect.tl.y))
        max_y = max((prev_rect.bl.y, rect.bl.y))
        max_x = max((prev_rect.br.x, rect.br.x))
        width = max_x - prev_rect.tl.x
        height = max_y - min_y
        new_rect = cvw.Rect(prev_rect.tl.x, min_y, width, height)
        # Add new rectangle to final list, making it the new prev_rect
        # in the next iteration
        final_rects[-1] = new_rect
    else:
        # If no intersection, add the box
        final_rects.append(rect)

for rect in sorted_rects:
    cvw.rectangle(image, rect, cvw.Color.MAGENTA, line_style=cvw.LineStyle.DASHED)

for rect in final_rects:
    cvw.rectangle(image, rect, cvw.Color.GREEN, thickness=2)

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

And the result

The green boxes are the final result, while the magenta boxes are the original ones.

I used the same threshold as @HansHirse.

The equals sign still needs some work. Either a higher dilation kernel size or use the same technique vertically.

Disclosure: I am the author of OpenCV Wrapper.

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!