fitting a circle to a binary image

Question

I have been using skim age\'s thresholding algorithms to get some binary mask. For example, I obtain binary images like this:

Answer 1

Here is a solution that tries to make an optimal circle fit via minimization. It soon becomes apparent that the bubble isn't a circle :) Note the use of "regionprops" for easily determining area, centroid, etc. of regions.

from skimage import io, color, measure, draw, img_as_bool
import numpy as np
from scipy import optimize
import matplotlib.pyplot as plt


image = img_as_bool(color.rgb2gray(io.imread('bubble.jpg')))
regions = measure.regionprops(image)
bubble = regions[0]

y0, x0 = bubble.centroid
r = bubble.major_axis_length / 2.

def cost(params):
    x0, y0, r = params
    coords = draw.circle(y0, x0, r, shape=image.shape)
    template = np.zeros_like(image)
    template[coords] = 1
    return -np.sum(template == image)

x0, y0, r = optimize.fmin(cost, (x0, y0, r))

import matplotlib.pyplot as plt

f, ax = plt.subplots()
circle = plt.Circle((x0, y0), r)
ax.imshow(image, cmap='gray', interpolation='nearest')
ax.add_artist(circle)
plt.show()