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i have the following 2D numpy array M
M = np.array([[1,1,1,0,0,0,0,0,0,0,0],
[1,1,1,0,0,0,0,0,0,1,1],
[1,1,1,0,0,0,0,0,0,1,1],
[0,0,0,0,0,1,1,1,0,0,0],
[0,0,0,0,0,1,1,1,0,0,0],
[1,1,1,0,1,1,1,1,0,0,0],
[1,1,1,0,0,1,1,1,0,0,0],
[1,1,1,0,0,1,1,1,0,0,0]])
which I want to identify its spots (Pixels with value==1 and connected to each other).
Thanks to the function 'label' from scipy, I can identify all of my spots in the matrix. The output should seem like this:
Output, Nbr= label(M)
#Output= array([[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2],
# [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0],
# [0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0],
# [4, 4, 4, 0, 3, 3, 3, 3, 0, 0, 0],
# [4, 4, 4, 0, 0, 3, 3, 3, 0, 0, 0],
# [4, 4, 4, 0, 0, 3, 3, 3, 0, 0, 0]])
I want only to have spots with 9 elements, that means the first and fourth spot.
using a for loop like this works fine:
for i in range(Nbr+1):
Spot= np.argwhere(components[:,:]== i)
if len(Spot)!=9:
M[Spot[:, 0], Spot[:, 1]]=0
#M= array([[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
# [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0],
# [1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0]])
The porblem is when my Spots are more than 4, my code is slower.
Is there any faster alternative that can do the job of the for loop?
Thanks.
I'm currently working on something were I need to find groups of values in a 2d list that are surrounded by another value and then change the values of the surrounded elements. Start/end of a sub-list counts as surrounded.
For exemple if I have this list :
[[1, 2, 1, 1, 1, 0, 0, 0, 0],
[2, 2, 2, 2, 2, 1, 0, 0, 0],
[1, 2, 2, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 2, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]]
I want the function to change it to this:
[[1, 3, 1, 1, 1, 0, 0, 0, 0],
[3, 3, 3, 3, 3, 1, 0, 0, 0],
[1, 3, 3, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 3, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]]
I have no idea how to do it. Can anyone please help me ?
lst = [
[1, 2, 1, 1, 1, 0, 0, 0, 0],
[2, 2, 2, 2, 2, 1, 0, 0, 0],
[1, 2, 2, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 2, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
]
for row in range(len(lst)):
for col in range(len(lst[row])):
if lst[row][col] == 1:
continue
v1 = lst[row][col - 1] >= 1 if col - 1 >= 0 else 1
v2 = lst[row - 1][col] >= 1 if row - 1 >= 0 else 1
v3 = lst[row][col + 1] >= 1 if col + 1 < len(lst[row]) else 1
v4 = lst[row + 1][col] >= 1 if row + 1 < len(lst) else 1
if v1 + v2 + v3 + v4 == 4:
lst[row][col] += 1
from pprint import pprint
pprint(lst)
Prints:
[[1, 3, 1, 1, 1, 0, 0, 0, 0],
[3, 3, 3, 3, 3, 1, 0, 0, 0],
[1, 3, 3, 1, 1, 0, 0, 0, 0],
[0, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 1, 3, 1, 0, 0, 1, 1, 0],
[0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0]]
I have two lists:
import random
board = [
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0],
]
boxes = [random.sample(range(1, 10), 9), random.sample(range(1, 10), 9), random.sample(range(1, 10), 9)]
The first one is a sudoku board and the second one is three lists of 9 random non-repeating numbers.
And I want to insert the random numbers into the sudoku board so the result board looks something like this:
[5, 4, 3, 0, 0, 0, 0, 0, 0],
[2, 9, 1, 0, 0, 0, 0, 0, 0],
[6, 7, 8, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 6, 3, 0, 0, 0],
[0, 0, 0, 4, 5, 8, 0, 0, 0],
[0, 0, 0, 9, 2, 7, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 3, 8, 2],
[0, 0, 0, 0, 0, 0, 5, 9, 6],
[0, 0, 0, 0, 0, 0, 7, 1, 4]
I can achieve what I want with this code:
# BOX 1
board[0][0] = boxes[0][0]
board[0][1] = boxes[0][1]
board[0][2] = boxes[0][2]
board[1][0] = boxes[0][3]
board[1][1] = boxes[0][4]
board[1][2] = boxes[0][5]
board[2][0] = boxes[0][6]
board[2][1] = boxes[0][7]
board[2][2] = boxes[0][8]
# BOX 2
board[3][3] = boxes[1][0]
board[3][4] = boxes[1][1]
board[3][5] = boxes[1][2]
board[4][3] = boxes[1][3]
board[4][4] = boxes[1][4]
board[4][5] = boxes[1][5]
board[5][3] = boxes[1][6]
board[5][4] = boxes[1][7]
board[5][5] = boxes[1][8]
# BOX 3
board[6][6] = boxes[2][0]
board[6][7] = boxes[2][1]
board[6][8] = boxes[2][2]
board[7][6] = boxes[2][3]
board[7][7] = boxes[2][4]
board[7][8] = boxes[2][5]
board[8][6] = boxes[2][6]
board[8][7] = boxes[2][7]
board[8][8] = boxes[2][8]
But obviously that is a super long and dumb way to do this but for the love of god I cannot figure out how to do this using a nested for loop, but it seems like it should be possible?
I thought I could atleast fill the first box with this code:
for x in range(9):
for y in range(3):
board[y][x] = boxes[0][x]
But even that does not work as intended...please help...
This will do it. There are better ways if you are willing to use numpy.
for box in range(3):
# Get starting location in board.
dx = box*3
for k in range(9):
x = k % 3
y = k // 3
board[dx+y][dx+x] = boxes[box][k]
Alternatively:
for box in range(3):
# Get starting location in board.
dx = box*3
for y in range(3):
for k in range(3):
board[dx+y][dx+x] = boxes[box][y*3+x]
You can directly generate board like this:
import random
board = [random.sample(range(1, 10), 3)+[0]*6, random.sample(range(1, 10), 3)+[0]*6, random.sample(range(1, 10), 3)+[0]*6,
[0]*3+random.sample(range(1, 10), 3)+[0]*3, [0]*3+random.sample(range(1, 10), 3)+[0]*3, [0]*3+random.sample(range(1, 10), 3)+[0]*3, [0]*6+random.sample(range(1, 10), 3), [0]*6+random.sample(range(1, 10), 3), [0]*6+random.sample(range(1, 10), 3)]
print(board)
Output
[
[9, 6, 7, 0, 0, 0, 0, 0, 0],
[2, 6, 3, 0, 0, 0, 0, 0, 0],
[8, 7, 4, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 7, 3, 8, 0, 0, 0],
[0, 0, 0, 5, 1, 6, 0, 0, 0],
[0, 0, 0, 6, 8, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 2, 9, 7],
[0, 0, 0, 0, 0, 0, 3, 4, 8],
[0, 0, 0, 0, 0, 0, 9, 5, 6]
]
A more neater version using functions:
import random
def f1():
return random.sample(range(1, 10), 3)+[0]*6
def f2():
return [0]*3+random.sample(range(1, 10), 3)+[0]*3
def f3():
return [0]*6+random.sample(range(1, 10), 3)
board = [f1(),f1(),f1(),f2(),f2(),f2(),f3(),f3(),f3()]
print(board)
import numpy as np
def rand3x3():
return np.random.randint(1,9,(3,3))
board = np.zeros((9,9), dtype=int)
for square3x3 in [[0,3],[3,6],[6,9]]:
start = square3x3[0]
end = square3x3[1]
board[start:end, start:end] += rand3x3()
board.tolist()
Output
[[2, 6, 4, 0, 0, 0, 0, 0, 0],
[4, 3, 3, 0, 0, 0, 0, 0, 0],
[8, 4, 6, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 4, 6, 1, 0, 0, 0],
[0, 0, 0, 6, 7, 3, 0, 0, 0],
[0, 0, 0, 7, 2, 6, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 8, 2],
[0, 0, 0, 0, 0, 0, 3, 2, 6],
[0, 0, 0, 0, 0, 0, 7, 4, 1]]
I have two labelled 2D numpy arrays a and b with identical shapes. I would like to re-label the array b by something similar to a GIS geometric union of the two arrays, such that cells with unique combination of values in array a and b are assigned new unique IDs:
I'm not concerned with the specific numbering of the regions in the output, so long as the values are all unique. I have attached sample arrays and desired outputs below: my real datasets are much larger, with both arrays having integer labels which range from "1" to "200000". So far I've experimented with concatenating the array IDs to form unique combinations of values, but ideally I would like to output a simple set of new IDs in the form of 1, 2, 3..., etc.
import numpy as np
import matplotlib.pyplot as plt
# Example labelled arrays a and b
input_a = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 0],
[0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 0, 0],
[0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
input_b = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 3, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 3, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
# Plot inputs
plt.imshow(input_a, cmap="spectral", interpolation='nearest')
plt.imshow(input_b, cmap="spectral", interpolation='nearest')
# Desired output, union of a and b
output = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 2, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 4, 7, 7, 7, 7, 0, 0],
[0, 0, 5, 5, 5, 6, 7, 7, 7, 7, 0, 0],
[0, 0, 5, 5, 5, 6, 7, 7, 7, 7, 0, 0],
[0, 0, 5, 5, 5, 6, 7, 7, 7, 7, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
# Plot desired output
plt.imshow(output, cmap="spectral", interpolation='nearest')
If I understood the circumstances correctly, you are looking to have unique pairings from a and b. So, 1 from a and 1 from b would have one unique tag in the output; 1 from a and 3 from b would have another unique tag in the output. Also looking at the desired output in the question, it seems that there is an additional conditional situation here that if b is zero, the output is to be zero as well irrespective of the unique pairings.
The following implementation tries to solve all of that -
c = a*(b.max()+1) + b
c[b==0] = 0
_,idx = np.unique(c,return_inverse= True)
out = idx.reshape(b.shape)
Sample run -
In [21]: a
Out[21]:
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0],
[0, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 0],
[0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 0, 0],
[0, 0, 3, 3, 3, 3, 2, 2, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
In [22]: b
Out[22]:
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 3, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 3, 3, 3, 3, 3, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
In [23]: out
Out[23]:
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 1, 1, 3, 5, 5, 5, 5, 0, 0],
[0, 0, 1, 1, 1, 3, 5, 5, 5, 5, 0, 0],
[0, 0, 1, 1, 1, 2, 4, 4, 4, 4, 0, 0],
[0, 0, 6, 6, 6, 7, 4, 4, 4, 4, 0, 0],
[0, 0, 6, 6, 6, 7, 4, 4, 4, 4, 0, 0],
[0, 0, 6, 6, 6, 7, 4, 4, 4, 4, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
Sample plot -
# Plot inputs
plt.figure()
plt.imshow(a, cmap="spectral", interpolation='nearest')
plt.figure()
plt.imshow(b, cmap="spectral", interpolation='nearest')
# Plot output
plt.figure()
plt.imshow(out, cmap="spectral", interpolation='nearest')
Here is a way to do it conceptually in terms of set union, but not to GIS geometric union, since that was mentioned after I answered.
Make a list of all possible unique 2-tuples of values with one from a and the other from b in that order. Map each tuple in that list to its index in it. Create the union array using that map.
For example say a and b are arrays each containing values in range(4) and assume for simplicity they have the same shape. Then:
v = range(4)
from itertools import permutations
p = list(permutations(v,2))
m = {}
for i,x in enumerate(p):
m[x] = i
union = np.empty_like(a)
for i,x in np.ndenumerate(a):
union[i] = m[(x,b[i])]
For demonstration, generating a and b with
np.random.randint(4, size=(3, 3))
produced:
a = array([[3, 0, 3],
[1, 3, 2],
[0, 0, 3]])
b = array([[1, 3, 1],
[0, 0, 1],
[2, 3, 0]])
m = {(0, 1): 0,
(0, 2): 1,
(0, 3): 2,
(1, 0): 3,
(1, 2): 4,
(1, 3): 5,
(2, 0): 6,
(2, 1): 7,
(2, 3): 8,
(3, 0): 9,
(3, 1): 10,
(3, 2): 11}
union = array([[10, 2, 10],
[ 3, 9, 7],
[ 1, 2, 9]])
In this case the property that a union should be bigger or equal to its composits is reflected in increased numerical values rather than increase in number of elements.
An issue with using itertools permutations is that the number of permutations could be much larger than needed. It would be much larger if the number of overlaps per area is much smaller than the number of areas.
The question uses Union but the picture shows an Intersection. Divakar's answer replicates the pictured Intersection, and is more elegant than my solution below, which produces the Union.
One could make a dictionary of only the actual overlaps, and then work from that. Flattening the input arrays first makes this easier for me to see, I'm not sure if that is feasible for you:
shp = numpy.shape(input_a)
a = input_a.flatten()
b = input_b.flatten()
s = set(((i,j) for i,j in zip(a,b))) # unique pairings
d = {p:i for i,p in enumerate(sorted(list(s))} # dict{pair:index}
output_c = numpy.array([d[i,j] for i,j in zip(a,b)]).reshape(shp)
array([[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 0],
[ 0, 1, 1, 1, 1, 1, 5, 5, 5, 5, 5, 0],
[ 0, 1, 2, 2, 2, 4, 7, 7, 7, 7, 5, 0],
[ 0, 1, 2, 2, 2, 4, 7, 7, 7, 7, 5, 0],
[ 0, 1, 2, 2, 2, 3, 6, 6, 6, 6, 5, 0],
[ 0, 8, 9, 9, 9, 10, 6, 6, 6, 6, 5, 0],
[ 0, 0, 9, 9, 9, 10, 6, 6, 6, 6, 0, 0],
[ 0, 0, 9, 9, 9, 10, 6, 6, 6, 6, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
How can I keep a ring of pixels around labeled regions in a numpy array?
In a simple case, I'd subtract the erosion. That approach doesn't work when the labels touch. How can I get get B from A?
A = array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
B = array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
I'm working with large arrays with many labels, so separate erosions on each label isn't an option.
New Answer
Actually, I just thought of a better way:
B = A * (np.abs(scipy.ndimage.laplace(A)) > 0)
As a full example:
import numpy as np
import scipy.ndimage
A = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
B = A * (np.abs(scipy.ndimage.laplace(A)) > 0)
I think this should work in all cases (of "labeled" arrays like A, at any rate...).
If you're worried about performance, you can split this into a few pieces to reduce memory overhead:
B = scipy.ndimage.laplace(A)
B = np.abs(B, B) # Preform abs in-place
B /= B # This will produce a divide by zero warning that you can safely ignore
B *= A
This version is a lot more verbose, but should use much less memory.
Old Answer
I can't think of a good way to do it in one step with the usual scipy.ndimage functions. (I feel like a tophat filter should do what you want, but I can't quite figure it out.)
However, doing several separate erosions is an option, as you mentioned.
You should get reasonable performance even on very large arrays if you use find_objects to extract the subregion of each label, and then just do the erosion on the subregion.
For example:
import numpy as np
import scipy.ndimage
A = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
regions = scipy.ndimage.find_objects(A)
mask = np.zeros_like(A).astype(np.bool)
for val, region in enumerate(regions, start=1):
if region is not None:
subregion = A[region]
mask[region] = scipy.ndimage.binary_erosion(subregion == val)
B = A.copy()
B[mask] = 0
This yields:
array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0],
[0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0],
[0, 0, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
The performance should be reasonable for large arrays, but it's going to depend strongly on how large of an area the different labeled objects span and the number of labeled objects that you have....