Boolean Masking¶
Boolean masking uses logical conditions to selectively operate on array subsets.
Filtering Basics¶
Boolean arrays select elements satisfying a condition.
1. 1D with List¶
import numpy as np
def main():
a = np.array([1, 2, 3])
b = [True, False, True]
c = a[b]
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
c = array([1, 3])
2. 1D with Array¶
import numpy as np
def main():
a = np.array([1, 2, 3])
b = np.array([True, False, True])
c = a[b]
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
c = array([1, 3])
3. Condition Filter¶
import numpy as np
def main():
a = np.array([1, 2, 3])
b = (a % 2 == 1)
print(f"{b = }")
print(f"{type(b) = }")
c = a[b]
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
b = array([ True, False, True])
type(b) = <class 'numpy.ndarray'>
c = array([1, 3])
2D Filtering¶
Multi-dimensional arrays require NumPy boolean arrays.
1. List Causes Error¶
import numpy as np
def main():
a = np.array([[1, 2, 3], [4, 5, 6]])
b = [[True, False, True], [False, True, False]]
try:
c = a[b]
print(f"{c = }")
except IndexError as e:
print(f"Error: {e}")
if __name__ == "__main__":
main()
2. Array Works¶
import numpy as np
def main():
a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([[True, False, True], [False, True, False]])
c = a[b]
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
c = array([1, 3, 5])
3. 2D Condition¶
import numpy as np
def main():
a = np.array([[1, 2, 3], [4, 5, 6]])
b = (a % 2 == 1)
print(f"{b = }")
c = a[b]
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
b = array([[ True, False, True],
[False, True, False]])
c = array([1, 3, 5])
Mask Assignment¶
Boolean masks can modify array elements in-place.
1. 1D Assignment¶
import numpy as np
def main():
a = np.array([1, 2, 3])
a[a % 2 == 1] = 0
print(a)
if __name__ == "__main__":
main()
Output:
[0 2 0]
2. 2D Assignment¶
import numpy as np
def main():
a = np.array([[1, 2, 3], [4, 5, 6]])
b = np.array([[True, False, True], [False, True, False]])
a[b] = 0
print(a)
if __name__ == "__main__":
main()
Output:
[[0 2 0]
[4 0 6]]
3. Condition Assignment¶
import numpy as np
def main():
a = np.array([[1, 2, 3], [4, 5, 6]])
a[a % 2 == 1] = 0
print(a)
if __name__ == "__main__":
main()
Output:
[[0 2 0]
[4 0 6]]
Image Masking¶
Apply masks to image regions.
1. Rectangle Mask¶
import numpy as np
import matplotlib.pyplot as plt
import PIL
import urllib
def main():
url = "https://upload.wikimedia.org/wikipedia/en/4/43/Pok%C3%A9mon_Mewtwo_art.png"
img = np.array(PIL.Image.open(urllib.request.urlopen(url)))
print(f"{img.shape = }")
print(f"{img.dtype = }")
mask = np.zeros(shape=img.shape[:2], dtype=bool)
mask[50:100, 50:100] = True
img_copy = img.copy()
img_copy[mask] = [255, 255, 255, 255]
fig, (ax0, ax1) = plt.subplots(1, 2, figsize=(6, 4))
ax0.set_title("Original", fontsize=15)
ax0.imshow(img)
ax1.set_title("Masked", fontsize=15)
ax1.imshow(img_copy)
for ax in (ax0, ax1):
ax.axis('off')
plt.tight_layout()
plt.show()
if __name__ == "__main__":
main()
2. Mask Shape¶
Create mask matching image height and width: img.shape[:2].
Combining Masks¶
Logical operators combine multiple conditions.
1. AND Operator¶
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
mask1 = arr > 2
mask2 = arr < 5
combined = mask1 & mask2
print(arr[combined]) # [3 4]
2. OR Operator¶
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
combined = (arr < 2) | (arr > 4)
print(arr[combined]) # [1 5]
3. NOT Operator¶
import numpy as np
arr = np.array([1, 2, 3, 4, 5])
mask = arr > 2
print(arr[~mask]) # [1 2]
Coin Flip Simulation¶
Boolean masking enables vectorized probability simulation.
1. Inverse Transform¶
import numpy as np
def main():
n = 10
p = 0.5
c = np.zeros(n)
u = np.random.rand(n)
c[u > 1 - p] = 1
for ui, ci in zip(u, c):
print(f"{ui = :.3f}, {ui > 1-p = }, {ci = }")
if __name__ == "__main__":
main()
2. Vectorized Flip¶
import numpy as np
def main():
n = 30
p = 0.5
uniform = np.random.uniform(size=(n,))
coin = np.zeros_like(uniform)
coin[uniform > 1 - p] = 1.
print(coin)
if __name__ == "__main__":
main()
3. Performance Benefit¶
Vectorized masking is faster than loop-based coin flips.
np.where Indices¶
np.where(condition) returns indices where condition is True.
1. 1D Indices¶
import numpy as np
def main():
a = np.array([1, 2, 2, 3, 2, 4, 4, 2])
b = np.where(a == 2)
print(f"{b = }")
if __name__ == "__main__":
main()
Output:
b = (array([1, 2, 4, 7]),)
2. 2D Indices¶
import numpy as np
def main():
a = np.array([[1, 2], [2, 3], [2, 4], [4, 2]])
b = np.where(a == 2)
print(f"{b = }")
if __name__ == "__main__":
main()
Output:
b = (array([0, 1, 2, 3]), array([1, 0, 0, 1]))
3. 3D Indices¶
import numpy as np
def main():
a = np.array([[1, 2], [2, 3], [2, 4], [4, 2]])
a = np.array([a, a])
b = np.where(a == 2)
print(f"{b = }")
if __name__ == "__main__":
main()
np.where Conditional¶
np.where(condition, x, y) selects from x or y based on condition.
1. Syntax Pattern¶
\[\begin{array}{ccccccc}
\text{c}&=&\text{np.where(}&\text{condition}&,&\text{if\_true}&,&\text{if\_false}&\text{)}
\end{array}\]
2. 1D Example¶
import numpy as np
def main():
a = np.array([1, 2, 2, 3, 2, 4, 4, 2])
b = a * 10
c = np.where(a == 2, a, b)
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
c = array([10, 2, 2, 30, 2, 40, 40, 2])
3. 2D Example¶
import numpy as np
def main():
a = np.array([[1, 2], [2, 3], [2, 4], [4, 2]])
b = a * 10
c = np.where(a == 2, a, b)
print(f"{c = }")
if __name__ == "__main__":
main()
Output:
c = array([[10, 2],
[ 2, 30],
[ 2, 40],
[40, 2]])
Image Clamping¶
Use np.where to clamp pixel values to valid range.
1. Noise and Clamp¶
import numpy as np
import matplotlib.pyplot as plt
import PIL
import urllib
def main():
url = "https://upload.wikimedia.org/wikipedia/en/4/43/Pok%C3%A9mon_Mewtwo_art.png"
img = np.array(PIL.Image.open(urllib.request.urlopen(url)))
img_noisy = img + np.random.randint(-100, 101, size=img.shape)
img_noisy = np.where(img_noisy >= 0, img_noisy, 0)
img_noisy = np.where(img_noisy <= 255, img_noisy, 255)
fig, ax = plt.subplots()
ax.imshow(img_noisy.astype(np.uint8))
ax.axis('off')
plt.show()
if __name__ == "__main__":
main()
2. Chained np.where¶
Apply multiple conditions sequentially to enforce bounds.