#### Gaussian Filter

p
```"""
Implementation of gaussian filter algorithm
"""

from itertools import product

from cv2 import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uint8, zeros

def gen_gaussian_kernel(k_size, sigma):
center = k_size // 2
x, y = mgrid[0 - center : k_size - center, 0 - center : k_size - center]
g = 1 / (2 * pi * sigma) * exp(-(square(x) + square(y)) / (2 * square(sigma)))
return g

def gaussian_filter(image, k_size, sigma):
height, width = image.shape[0], image.shape[1]
# dst image height and width
dst_height = height - k_size + 1
dst_width = width - k_size + 1

# im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
image_array = zeros((dst_height * dst_width, k_size * k_size))
for row, (i, j) in enumerate(product(range(dst_height), range(dst_width))):
window = ravel(image[i : i + k_size, j : j + k_size])
image_array[row, :] = window

#  turn the kernel into shape(k*k, 1)
gaussian_kernel = gen_gaussian_kernel(k_size, sigma)
filter_array = ravel(gaussian_kernel)

# reshape and get the dst image
dst = dot(image_array, filter_array).reshape(dst_height, dst_width).astype(uint8)

return dst

if __name__ == "__main__":
# read original image
img = imread(r"../image_data/lena.jpg")
# turn image in gray scale value
gray = cvtColor(img, COLOR_BGR2GRAY)

# get values with two different mask size
gaussian3x3 = gaussian_filter(gray, 3, sigma=1)
gaussian5x5 = gaussian_filter(gray, 5, sigma=0.8)

# show result images
imshow("gaussian filter with 3x3 mask", gaussian3x3)
imshow("gaussian filter with 5x5 mask", gaussian5x5)
waitKey()
```