How can I use cv2.minAreaRect to obtain the largest contour, even if the image has broken regions?

This is the original image.

I want to use cv2.minAreaRect to obtain the maximum contour, as shown in the following image.

Attempt 1 - Fail

cnt, hierarchy  = cv2.findContours(im_bw, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
min_rect = cv2.minAreaRect(cnt[0])
box = np.int0(cv2.boxPoints(min_rect))
cv2.drawContours(temp_result, [box], 0, (255, 0, 0), 2)

Attempt 2 - Fail

I referred to this post to obtain the ordered coordinates for drawing. However, I obtained the following result, where the lines don't match and the four points cannot be used with cv2.minAreaRect.

def order_points(pts):
	# initialzie a list of coordinates that will be ordered
	# such that the first entry in the list is the top-left,
	# the second entry is the top-right, the third is the
	# bottom-right, and the fourth is the bottom-left
	rect = np.zeros((4, 2), dtype = "float32")

	# the top-left point will have the smallest sum, whereas
	# the bottom-right point will have the largest sum
	s = np.sum(pts, axis = 1)
	rect[0] = pts[np.argmin(s)] # top-left
	rect[2] = pts[np.argmax(s)] # bottom-right

	# now, compute the difference between the points, the
	# top-right point will have the smallest difference,
	# whereas the bottom-left will have the largest difference
	diff = np.diff(pts, axis = 1)
	rect[1] = pts[np.argmin(diff)] # top-right
	rect[3] = pts[np.argmax(diff)] # bottom-left

	# return the ordered coordinates
	return rect
#########################################################################
# pts = [(93, 50), (109, 82), (76, 47), (93, 77), (58, 38), (76, 72), (36, 32), (54, 67), (20, 27), (35, 62), (3, 22), (18, 56), (111, 54), (128, 87)]

t = order_points(pts)
cv2.line(temp_result, pt1=(int(t[0][0]), int(t[0][1])), pt2=(int(t[1][0]), int(t[1][1])), color=(0, 0, 255), thickness=2)
cv2.line(temp_result, pt1=(int(t[3][0]), int(t[3][1])), pt2=(int(t[2][0]), int(t[2][1])), color=(0, 0, 255), thickness=2)

Any help will be appreciated.

We may find the Convex hull of the merged contours:

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merged_cnt = cv2.convexHull(np.vstack(cnt))

Code sample:

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import cv2
import numpy as np

im_bw = cv2.imread('im_bw.png', cv2.IMREAD_GRAYSCALE)  # Read im_bw as grayscale

temp_result = cv2.cvtColor(im_bw, cv2.COLOR_GRAY2BGR)

cnt, hierarchy  = cv2.findContours(im_bw, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)

# Merge all the contours into one large contour - the result is the convex hull of all contour.
merged_cnt = cv2.convexHull(np.vstack(cnt))

cv2.drawContours(temp_result, [merged_cnt], 0, (255, 0, 0), 2)

# Show result for testing
cv2.imshow('temp_result', temp_result)
cv2.waitKey()
cv2.destroyAllWindows()

Result:

In case the objective is to approximate the contour to rectangular polygon, we may use simplify_contour method from the following answer

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approx = simplify_contour(merged_cnt)

cv2.drawContours(temp_result, [approx], 0, (0, 0, 255), 2)

Result:

In case the objective is to find minAreaRect as stated in the title:

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min_rect = cv2.minAreaRect(merged_cnt)  # Fine minAreaRect of the merged contours
box = np.int0(cv2.boxPoints(min_rect))

We are getting the following output: