Question about Detecting Circles centers in an image?

I have this image with this kind of shapes:

myplot

and what I do is to detect circle shapes with a certain radius range, using the Hough Transform through the scikit-image library:

# Load picture and detect edges
sf_img = np.load('/..../sf_images.npy') # (num_img x 256 x 256)
image = img_as_ubyte(sf_img[0,:,:])
edges = canny(image, sigma=3, low_threshold=10, high_threshold=50)


# Detect two radii
hough_radii = np.arange(235, 236, 2)
hough_res = hough_circle(edges, hough_radii)

# Select the most prominent 40 circles
accums, cx, cy, radii = hough_circle_peaks(hough_res, hough_radii,
                                       total_num_peaks=40)

# Draw them
fig, ax = plt.subplots(ncols=1, nrows=1, figsize=(10, 4))
image = color.gray2rgb(image)
for center_y, center_x, radius in zip(cy, cx, radii):
   circy, circx = circle_perimeter(center_y, center_x, radius,
                                shape=image.shape)
   image[circy, circx] = (220, 20, 20)

ax.imshow(image, cmap=plt.cm.gray)
ax.scatter(cx[0],cy[0], marker= 'o')
plt.show()

and running this script I obtain this image:

which is quite good because I obtain also an array with the centers of the circles and I can select also the center of the circular shape that got the most on the accumulator. In this case che coordinate of the center is [204,4].

FOR THE CURIOUS I’m trying to use the information of this soundfield image to detect the coordinate of a source which is emitting it, on the x-axis

Now, what I want to achieve is to have the same result but in a different unit scale for the axis:

myplotdddaaa

that is, the new scale is [-2,2] (meters) for the x-axis and [2,4] (meters) for the y-axis.

I could of course modify the extent parameter of the image from the script like this:

ax.imshow(image, cmap=plt.cm.gray, extent= [-2,2,2,4])

but when I add the scatter function to show the center I got this:

and this is happening because the center coordinate keep the old corrdinates in the range 0,256 and not the new one, soo I was wandering if there was a way to change the center values in order for them to be coherent with the new scale of the image.