How to split book image into left and right parts in OpenCV?

I have a book image like this. I want to split the page into two parts from the middle line (just the left page and the right page).

my thought is to detect the middle line but it didn't work. I want to how to finish this work?

When I find white space it also has overlapping part.

this is the current version code I use

import cv2
import numpy as np
 

filef = 'image.jpg'
image = cv2.imread(filef)

# Convert image to grayscale
gray = cv2.cvtColor(image,cv2.COLOR_BGR2GRAY)
 
# Use canny edge detection
edges = cv2.Canny(gray,50,150,apertureSize=3)
 
# Apply HoughLinesP method to
# to directly obtain line end points
lines = cv2.HoughLinesP(
            edges, # Input edge image
            1, # Distance resolution in pixels
            np.pi/180, # Angle resolution in radians
            threshold=600, # Min number of votes for valid line
            minLineLength=600, # Min allowed length of line
            maxLineGap=30 # Max allowed gap between line for joining them
            )
 
lines_list = []
# Iterate over points
for points in lines:
      # Extracted points nested in the list
    x1,y1,x2,y2=points[0]
    # Draw the lines joing the points
    # On the original image
    cv2.line(image,(x1,y1),(x2,y2),(0,255,0),2)
    # Maintain a simples lookup list for points
    lines_list.append([(x1,y1),(x2,y2)])
     
# Save the result image
cv2.imwrite(filef[:-4]+'_line.jpg',image)