#### Dilation Operation

I
```from pathlib import Path

import numpy as np
from PIL import Image

def rgb_to_gray(rgb: np.ndarray) -> np.ndarray:
"""
Return gray image from rgb image
>>> rgb_to_gray(np.array([[[127, 255, 0]]]))
array([[187.6453]])
>>> rgb_to_gray(np.array([[[0, 0, 0]]]))
array([[0.]])
>>> rgb_to_gray(np.array([[[2, 4, 1]]]))
array([[3.0598]])
>>> rgb_to_gray(np.array([[[26, 255, 14], [5, 147, 20], [1, 200, 0]]]))
array([[159.0524,  90.0635, 117.6989]])
"""
r, g, b = rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
return 0.2989 * r + 0.5870 * g + 0.1140 * b

def gray_to_binary(gray: np.ndarray) -> np.ndarray:
"""
Return binary image from gray image
>>> gray_to_binary(np.array([[127, 255, 0]]))
array([[False,  True, False]])
>>> gray_to_binary(np.array([[0]]))
array([[False]])
>>> gray_to_binary(np.array([[26.2409, 4.9315, 1.4729]]))
array([[False, False, False]])
>>> gray_to_binary(np.array([[26, 255, 14], [5, 147, 20], [1, 200, 0]]))
array([[False,  True, False],
[False,  True, False],
[False,  True, False]])
"""
return (gray > 127) & (gray <= 255)

def dilation(image: np.ndarray, kernel: np.ndarray) -> np.ndarray:
"""
Return dilated image
>>> dilation(np.array([[True, False, True]]), np.array([[0, 1, 0]]))
array([[False, False, False]])
>>> dilation(np.array([[False, False, True]]), np.array([[1, 0, 1]]))
array([[False, False, False]])
"""
output = np.zeros_like(image)
image_padded = np.zeros(
(image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)
)

# Copy image to padded image
image_padded[kernel.shape[0] - 2 : -1 :, kernel.shape[1] - 2 : -1 :] = image

# Iterate over image & apply kernel
for x in range(image.shape[1]):
for y in range(image.shape[0]):
summation = (
kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
).sum()
output[y, x] = int(summation > 0)
return output

if __name__ == "__main__":
# read original image
lena_path = Path(__file__).resolve().parent / "image_data" / "lena.jpg"
lena = np.array(Image.open(lena_path))
# kernel to be applied
structuring_element = np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
output = dilation(gray_to_binary(rgb_to_gray(lena)), structuring_element)
# Save the output image
pil_img = Image.fromarray(output).convert("RGB")
pil_img.save("result_dilation.png")
```