#filters

import math

import numpy

import scipy.fftpack as fftim

from PIL import Image

a = Image.open('/home/koju/Desktop/Image_processing/images.png').convert('L')

b = numpy.asarray(a)

c = fftim.fft2(b)

d = fftim.fftshift(c)

# initializing variables

M = d.shape[0]

N = d.shape[1]

H = numpy.ones((M, N))

center1 = M / 2

center2 = N / 2

d_0 = 30.0 # cut_off radius

# order of BLPF

# t1 = 1

# t2 = 2 * t1

# for gaussian

t1 = 2 * d_0

for i in range(1, M):

for j in range(1, N):

r1 = (i - center1) * 2 + (j - center2) * 2

# euclidean distancefrom origin

r = math.sqrt(r1)

# using cut_off radius to eliminate high freq

# if r > d_0:

# for ideal low pass

# H[i, j] = 0.0

# for butterworth low pass

# H[i, j] = 1 / (1 + (r / d_0) ** t1)

# for Gaussian low pass

# H[i, j] = math.exp(-r * 2 / t1 * 2)

if 0 < r < d_0:

# for ideal high pass

# H[i, j] = 1.0

# for butterworth high pass filter

H[i, j] = 1 / (1 + (d_0 / r) ** t1)

# for gaussian high pass

# H[i, j] = 1 - math.exp(-r * 2 / t1 * 2)

# # converting H to image

H = Image.fromarray(H)

# performing convolution

con = d * H

# computing mag of inverse FFT

e = abs(fftim.ifft2(con))

# from array to image

f = Image.fromarray(e)

Image._showxv(f, " lowpass filter")