How to find the diameter of objects using image processing in Python?

Question

Given an image with some irregular objects in it, I want to find their individual diameter.

Thanks to this answer, I know how to identify the objects. However, is it possible to measure the maximum diameter of the objects shown in the image?

I have looked into the scipy-ndimage documentation and haven't found a dedicated function.

Code for object identification:

import numpy as np
from scipy import ndimage
from matplotlib import pyplot as plt

# generate some lowpass-filtered noise as a test image
gen = np.random.RandomState(0)
img = gen.poisson(2, size=(512, 512))
img = ndimage.gaussian_filter(img.astype(np.double), (30, 30))
img -= img.min()
img /= img.max()

# use a boolean condition to find where pixel values are > 0.75
blobs = img > 0.75

# label connected regions that satisfy this condition
labels, nlabels = ndimage.label(blobs)

# find their centres of mass. in this case I'm weighting by the pixel values in
# `img`, but you could also pass the boolean values in `blobs` to compute the
# unweighted centroids.
r, c = np.vstack(ndimage.center_of_mass(img, labels, np.arange(nlabels) + 1)).T

# find their distances from the top-left corner
d = np.sqrt(r*r + c*c)

# plot
fig, ax = plt.subplots(1, 2, sharex=True, sharey=True, figsize=(10, 5))
ax[0].imshow(img)
ax[1].hold(True)
ax[1].imshow(np.ma.masked_array(labels, ~blobs), cmap=plt.cm.rainbow)
for ri, ci, di in zip(r, c, d):
    ax[1].annotate('', xy=(0, 0), xytext=(ci, ri),
                   arrowprops={'arrowstyle':'<-', 'shrinkA':0})
    ax[1].annotate('d=%.1f' % di, xy=(ci, ri),  xytext=(0, -5),
                   textcoords='offset points', ha='center', va='top',
                   fontsize='x-large')
for aa in ax.flat:
    aa.set_axis_off()
fig.tight_layout()
plt.show()

Image:

Answer 1

You could use skimage.measure.regionprops to determine the bounding box of all the regions in your image. For roughly circular blobs the diameter of the minimum enclosing circle can be approximated by the largest side of the bounding box. To do so you just need to add the following snippet at the end of your script:

from skimage.measure import regionprops

properties = regionprops(labels)
print 'Label \tLargest side'
for p in properties:
    min_row, min_col, max_row, max_col = p.bbox
    print '%5d %14.3f' % (p.label, max(max_row - min_row, max_col - min_col))

fig = plt.figure()
ax = fig.add_subplot(111)    
ax.imshow(np.ma.masked_array(labels, ~blobs), cmap=plt.cm.gist_rainbow) 
ax.set_title('Labeled objects')
plt.xticks([])
plt.yticks([])
for ri, ci, li in zip(r, c, range(1, nlabels+1)):
    ax.annotate(li, xy=(ci, ri), fontsize=24)
plt.show()

And this is the output you get:

Label   Largest side
    1        106.000
    2         75.000
    3         79.000
    4         56.000
    5        161.000
    6         35.000
    7         47.000