Wilmar van Ommeren Wilmar van Ommeren - 6 months ago 32
Python Question

Applying a disc shaped mask to several locations in a NumPy array

I have a question which is similar to the one asked here: How to apply a disc shaped mask to a numpy array?. However, instead of masking a single circular sector, I would like to create a mask with multiple circular sectors (number is variable). These masks all have the same radius, but different centers. The coordinates of these centers are stored in a numpy 2d array. For example:

maskcenters = array([[1, 1],
[7, 2],
[2, 8]])


Now to create a round mask (radius 2) around a single center I could simply use the solution given by Bi Rico:

import numpy as np

a, b = maskcenters[0]
n = 10
r = 2

y,x = np.ogrid[-a:n-a, -b:n-b]
mask = x*x + y*y <= r*r


Where a and b represent the center of the mask; n the size of the array to mask; and r the radius.

This would result in a mask like:

#output
array([[ True, True, True, False, False, False, False, False, False],
[ True, True, True, True, False, False, False, False, False],
[ True, True, True, False, False, False, False, False, False],
[False, True, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False, False],
[False, False, False, False, False, False, False, False, False]], dtype=bool)


However, I have a variable number of centers around which I want to create masks. I know how to create multiple circular masks with a for loop, but this slows down the code. My optimal outcome, using the example mask centers in a 10x10 array, would be:

#output
array([[ True, True, True, False, False, False, False, False, True],
[ True, True, True, True, False, False, False, True, True],
[ True, True, True, False, False, False, True, True, True],
[False, True, False, False, False, False, False, True, True],
[False, False, False, False, False, False, False, False, True],
[False, False, True, False, False, False, False, False, False],
[False, True, True, True, False, False, False, False, False],
[ True, True, True, True, True, False, False, False, False],
[False, True, True, True, False, False, False, False, False]], dtype=bool)


Any idea how to create this mask without using loops?

Answer

You can use scipy's binary_dilation with a disk shaped kernel, like so -

# Define inputs
maskcenters = np.array([
   [1, 1],
   [7, 2],
   [2, 8]])

out_shp = (10,10) # Output array shape
r = 2 # Radius of circles

# Get a disk kernel
X,Y = [np.arange(-r,r+1)]*2
disk_mask = X[:,None]**2 + Y**2 <= r*r

# Initialize output array and set the maskcenters as 1s 
out = np.zeros(out_shp,dtype=bool)
out[maskcenters[:,0],maskcenters[:,1]] = 1

# Use binary dilation to get the desired output
out = binary_dilation(out,disk_mask)

Output -

In [64]: print out
[[ True  True  True False False False False False  True False]
 [ True  True  True  True False False False  True  True  True]
 [ True  True  True False False False  True  True  True  True]
 [False  True False False False False False  True  True  True]
 [False False False False False False False False  True False]
 [False False  True False False False False False False False]
 [False  True  True  True False False False False False False]
 [ True  True  True  True  True False False False False False]
 [False  True  True  True False False False False False False]
 [False False  True False False False False False False False]]

Here's another approach using simple indexing -

X,Y = [np.arange(-r,r+1)]*2
disk_mask = X[:,None]**2 + Y**2 <= r*r
Ridx,Cidx = np.where(disk_mask)

out = np.zeros(out_shp,dtype=bool)

absidxR = maskcenters[:,None,0] + Ridx-r
absidxC = maskcenters[:,None,1] + Cidx-r

valid_mask = (absidxR >=0) & (absidxR <out_shp[0]) & \
             (absidxC >=0) & (absidxC <out_shp[1])

out[absidxR[valid_mask],absidxC[valid_mask]] = 1
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