I'm trying to find the two end points of a hand drawn line I have written this snippet which finds the contours, but the end points is not correct:

img = cv2.imread("my_img.jpeg")

img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

# Binary Threshold:
_, thr_img = cv2.threshold(img_gray, 0, 255, cv2.THRESH_BINARY_INV + cv2.THRESH_OTSU)

cv2.imshow(winname="after threshold", mat=thr_img)
cv2.waitKey(0)

contours, _ = cv2.findContours(image=thr_img, mode=cv2.RETR_TREE, method=cv2.CHAIN_APPROX_SIMPLE)

for idx, cnt in enumerate(contours):
    print("Contour #", idx)
    cv2.drawContours(image=img, contours=[cnt], contourIdx=0, color=(255, 0, 0), thickness=3)
    cv2.circle(img, tuple(cnt[0][0]), 5, (255, 255, 0), 5) # Result in wrong result
    cv2.circle(img, tuple(cnt[-1][0]), 5, (0, 0, 255), 5)  # Result in wrong result
    cv2.imshow(winname="contour" + str(idx), mat=img)
    cv2.waitKey(0)

Original image:

I have also tried cornerHarris but it gave me some extra points,

Can someone please suggest an accurate and better approach?