"""
Simple image blur by convolution with a Gaussian kernel
"""

import numpy as np
from scipy import fftpack
import matplotlib.pyplot as plt

# read image
img = plt.imread('../../data/elephant.png')

# prepare an 1-D Gaussian convolution kernel
t = np.linspace(-10, 10, 30)
bump = np.exp(-0.1*t**2)
bump /= np.trapz(bump) # normalize the integral to 1

# make a 2-D kernel out of it
kernel = bump[:, np.newaxis] * bump[np.newaxis, :]

# padded fourier transform, with the same shape as the image
kernel_ft = fftpack.fft2(kernel, shape=img.shape[:2], axes=(0, 1))

# convolve
img_ft = fftpack.fft2(img, axes=(0, 1))
img2_ft = kernel_ft[:, :, np.newaxis] * img_ft
img2 = fftpack.ifft2(img2_ft, axes=(0, 1)).real

# clip values to range
img2 = np.clip(img2, 0, 1)

# plot output
plt.imshow(img2)
plt.show()

# Further exercise (only if you are familiar with this stuff):
#
# A "wrapped border" appears in the upper left and top edges of the
# image. This is because the padding is not done correctly, and does
# not take the kernel size into account (so the convolution "flows out
# of bounds of the image").  Try to remove this artifact.