Break the curve wherever there is a significant change in the curve

Wherever there's a significant change in the curve, I need to break the curve with a break thickness of just 1 pixel (I just want to break the curves into multiple parts). I have attached an image for reference. So after i read the image, i am thinning the curve and wherever there are red dots, i need to split it around that area.

The first image is the input image and red dots indicate where I want the cut (the image will not actually have the red dot)/ The second image is the current output that I am getting. The third image is the unaltered image for reference.

I have tried implementing the following codes:

import cv2
import numpy as np
from matplotlib import pyplot as plt

image_path = rf'C:\Users\User\Desktop\output.png'
img = cv2.imread(image_path, 0)

ret, binary = cv2.threshold(img, 128, 255, cv2.THRESH_BINARY)


binary = cv2.ximgproc.thinning(binary, thinningType=cv2.ximgproc.THINNING_GUOHALL)

coords = np.column_stack(np.where(binary > 0))
def calculateAngle(p1, p2, p3):
    v1 = np.array(p2) - np.array(p1)
    v2 = np.array(p3) - np.array(p2)
    angle = np.arctan2(v2[1], v2[0]) - np.arctan2(v1[1], v1[0])
    angle = np.degrees(angle)
    if angle < 0:
        angle += 360
    return angle

startBlackImg = np.zeros((binary.shape[0], binary.shape[1], 1), np.uint8)
i = 1
while i < (len(coords) - 1):
    p1 = coords[i - 1]
    p2 = coords[i]
    p3 = coords[i + 1]
    i += 1
    angle = calculateAngle(p1, p2, p3)
    
    if angle < 45 or angle > 315:
        startBlackImg[p2[0], p2[1]] = 255
    else:
        startBlackImg[p2[0], p2[1]] = 0

cv2.namedWindow('Check', 0)
cv2.imshow('Check', startBlackImg)
cv2.waitKey(0)
cv2.destroyAllWindows()

and the other logic is

while kk < len(cutContour) - 10:
            xCdte = cutContour[kk][0][0]
            yCdte = cutContour[kk][0][1]
            xNextCdte = cutContour[kk + 10][0][0]
            yNextCdte = cutContour[kk + 10][0][1]
            kk += 1
            if totalDistance <= 0.3048:
                startBlackImg[yCdte, xCdte] = np.array([255, 255, 255])
                startBlackImg[yNextCdte, xNextCdte] = np.array([255, 255, 255])
            else:
                if (abs(xCdte - xNextCdte) < 10 and abs(yCdte - yNextCdte) >= 10) or (abs(xCdte - xNextCdte) >= 10 and abs(yCdte - yNextCdte) < 10):
                    startBlackImg[yCdte, xCdte] = np.array([255, 255, 255])
                    startBlackImg[yNextCdte, xNextCdte] = np.array([255, 255, 255])
                else:
                    startBlackImg[yCdte, xCdte] = np.array([0, 0, 0])
                    kk += 10

So far I am not getting what I want. Its breaking at multiple points and not just where I intend it to. Is there any library or and code to do this?

1. Hough Transform https://en.wikipedia.org/wiki/Hough_transform

2. K-means iterations with different K's - find how many line groups

3. K-means again with the right K

4. Pixel clustering by min distance to lines

import math

import cv2 as cv
import numpy as np

import matplotlib.pyplot as plt

orig_im = cv.imread("/home/ophir/temp/stackoverflow2.png",cv.IMREAD_GRAYSCALE)

# use Hough Transform to get lots of straight lines
lines = cv.HoughLines(orig_im, 1, np.pi/180, 30);

im = cv.cvtColor(orig_im, cv.COLOR_GRAY2BGR)

im2 = im.copy()
im3 = im.copy()

plt.figure()
plt.imshow(im)

# draw all straight lines on image
rho_vals = []
theta_vals = []
for line in lines:
    for rho,theta in line:
        rho_vals.append(rho)
        theta_vals.append(theta)
        a = np.cos(theta)
        b = np.sin(theta)
        x0 = a*rho
        y0 = b*rho
        x1 = int(x0 + 1000*(-b))
        y1 = int(y0 + 1000*(a))
        x2 = int(x0 - 1000*(-b))
        y2 = int(y0 - 1000*(a))

        cv.line(im2,(x1,y1),(x2,y2),(0,0,255),2)

rho_vals = np.array(rho_vals)
rho_vals = np.expand_dims(rho_vals, axis=0)

theta_vals = np.array(theta_vals)
theta_vals = np.expand_dims(theta_vals, axis=0)

Z = np.vstack((rho_vals,theta_vals)).T

Z = np.float32(Z)

# use K-means to cluster all straight lines to groups
# I don't know how many groups, so I check several K's
criteria = (cv.TERM_CRITERIA_EPS + cv.TERM_CRITERIA_MAX_ITER, 10, 1.0)
compactness = []
for i in range(2, 9):
    ret,label,center=cv.kmeans(Z,i + 1,None,criteria,10,cv.KMEANS_RANDOM_CENTERS)
    compactness.append(ret)

compactness = np.array(compactness)

# choose the right k, where the compactness isn't getting any better
derivative = compactness[1:] - compactness[:-1]
amax = np.argmax(derivative > -800) + 2

# do K-means again, this time with the right K
ret,label,center=cv.kmeans(Z, amax,None,criteria,10,cv.KMEANS_RANDOM_CENTERS)

# draw the centers of thr clusters on the lines parameters graph
lines = []
for rho, theta in center:
    a = np.cos(theta)
    b = np.sin(theta)
    x0 = a*rho
    y0 = b*rho
    x1 = int(x0 + 1000*(-b))
    y1 = int(y0 + 1000*(a))
    x2 = int(x0 - 1000*(-b))
    y2 = int(y0 - 1000*(a))

    lines.append((x1,y1,x2,y2))
    cv.line(im3,(x1,y1),(x2,y2),(0,0,255),2)

# cluster the pixels in the original image by the minimum distance to a line
pixels = cv.findNonZero(orig_im)
labels = []
for pixel in pixels:
    x0, y0 = pixel[0]
    distances = []
    for line in lines:
        x1, y1, x2, y2 = line
        # https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
        dist = abs((y2 - y1) * x0 - (x2 - x1) * y0 + x2 * y1 - y2 * x1) / math.sqrt((y2 - y1)**2 + (x2 - x1)**2)
        distances.append(dist)
    labels.append(np.argmin(np.array(distances)))

im4 = np.zeros(im2.shape)

colors = [[0, 0, 255], [0, 255, 0], [255, 0, 0], [255, 255, 0], [255, 0, 255], [0, 255, 255]]

# assign different color to each pixel by the label of the clustering
for pixel, label in zip(pixels, labels):
    x, y = pixel[0]
    color = colors[label]
    im4[y,x, 0] = color[0]
    im4[y,x, 1] = color[1]
    im4[y,x, 2] = color[2]

plt.figure()
plt.plot(list(range(2,9)), compactness)
plt.scatter(amax, compactness[amax - 2], c = 'r')
plt.ylabel("compactness")
plt.xlabel("K")
plt.title("K-means compactness")

plt.figure()
plt.imshow(im2)

plt.figure()
plt.imshow(im3)

plt.figure()
plt.imshow(im4)

plt.figure()
plt.scatter(rho_vals, theta_vals)
plt.scatter(center[:,0],center[:,1],s = 80,c = 'y', marker = 's')
plt.xlabel("rho")
plt.ylabel("theta")
plt.title("lines parameters")
plt.show()

It's not perfect, there are still some issues, but you get the idea.