Cannot get expected circles by cv2.HoughCircles (OpenCV). I tried different ways to tune parameters but does not work

Question

I would like to use cv2.HoughCircles to have two circles from my image.

Here is the original image:

I expect to have two circles like this:

But I got this:

I have tried different parameters but I could not find a way to get two circles I expected. Not sure if the edge of circle is not smooth enough for HoughCircles to detect (a lot of matrix to calculate)?

Here is the code I have tried:

import cv2
import numpy as np

# Read image
img = cv2.imread('image_original.png')
hh, ww = img.shape[:2]

# # resize image to 1/4
# img = cv2.resize(img, dsize=(0,0), fx=0.25, fy=0.25)

# Convert to grayscale
gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)

# Gaussian filter
gray = cv2.GaussianBlur(gray, ksize=(3,3), sigmaX=0, sigmaY=0)

# get canny edges
canny = cv2.Canny(gray, 20, 140)

print(img.shape)

# get Hough circles
min_dist = int(ww/4)
circles = cv2.HoughCircles(canny, cv2.HOUGH_GRADIENT, 280, minDist=min_dist, param1=200, param2=140, minRadius=0, maxRadius=0)
print(circles)

# draw circles
result = img.copy()
for circle in circles[0]:
    # draw the circle in the output image
    (x,y,r) = circle
    x = int(x)
    y = int(y)
    r = int(r)
    cv2.circle(result, (x, y), r, (0, 0, 255), 1)

# save results
cv2.imwrite('image_result.jpg', result)

# show images
cv2.imshow('gray', gray)
cv2.imshow('canny', canny)
cv2.imshow('result', result)
cv2.waitKey(0)
cv2.destroyAllWindows()