# Matrices for image blurring¶

In [7]:
import numpy as np
import matplotlib.pyplot as plt
In [8]:
from PIL import Image

with Image.open("cat.jpeg").resize((500,500)) as img:
img = np.array(img).sum(axis=-1)

h, w = img.shape
In [17]:
plt.figure(figsize=(8,8))
plt.imshow(img, cmap="gray")
Out[17]:
<matplotlib.image.AxesImage at 0xb08cf0ec>

Now make a Gaussian with as many pixels as the image is wide.

In [10]:
x = np.linspace(-1, 1, w)
gaussian = np.exp(-500*x**2)
gaussian = np.roll(gaussian, -w//2)
plt.plot(x, gaussian)
Out[10]:
[<matplotlib.lines.Line2D at 0xb0ba3c2c>]

Now, fill a $w\times w$ matrix with shifted versions of this:

In [11]:
A = np.zeros((w,w))
for i in range(w):
A[:, i] = np.roll(gaussian, i)

Here's a plot to show what just happened:

In [14]:
plt.imshow(A)
Out[14]:
<matplotlib.image.AxesImage at 0xb09728ec>

Multiply the cat by this.

In [15]:
blurrycat = A.dot(img)
In [16]:
plt.figure(figsize=(8,8))
plt.imshow(blurrycat, cmap="gray")
Out[16]:
<matplotlib.image.AxesImage at 0xb091e5cc>
In [ ]: