python - How to locate a particular "region" of values in a 2D numpy array?

Question

I am working with a 2D numpy array made of 101x101=10201 values. Such values are of float type and range from 0.0 to 1.0. The array has an X,Y coordinate system which originates in the top left corner: thus, position (0,0) is in the top left corner, while position (101,101) is in the bottom right corner.

This is how the 2D array looks like (just an excerpt):

X,Y,Value
0,0,0.482
0,1,0.49
0,2,0.496
0,3,0.495
0,4,0.49
0,5,0.489
0,6,0.5
0,7,0.504
0,8,0.494
0,9,0.485

I would like to be able to:

1) Count the number of regions of cells (see image below) which value exceeds a given threshold, say 0.3;

2) Determine the distance between the visual centers of such regions and the top left corner, which has coordinates (0,0).

How could this be done in Python 2.7?

This is a visual representation of a 2D array with 2 regions highlighted (the darker the color, the higher the value):

Answer 1

You can find which pixels satisfy your cut-off using a simple boolean condition, then use scipy.ndimage.label and scipy.ndimage.center_of_mass to find the connected regions and compute their centers of mass:

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()