Computes the two dimensional discrete cosine transform of an image with a single non-zero point

dct2d.py

"""
Computes the two dimensional discrete cosine transform, first over rows, than over columns
"""

import numpy as np
import matplotlib.pyplot as plt

# create input image
N1, N2 = 100, 100
x = np.zeros((N1, N2))
x[N1 // 2, N2 // 2] = 1


# define one dimensional dct function
def dct1d(x):
    N = len(x)
    X = np.zeros(N)
    n = np.arange(N)
    for k in range(N):
        X[k] = np.dot(x, np.cos(np.pi * k * (2 * n + 1) / (2 * N)))
    return X

# create output
Xr, X = np.zeros((2, N1, N2))

# transform rows
for i in range(N1):
    Xr[i] = dct1d(x[i])
# transform columns
for j in range(N2):
    X[:, j] = dct1d(Xr[:, j])

# plot the data
fig, ax = plt.subplots(1, 2)
ax[0].imshow(x, interpolation='nearest')
ax[0].set_title("Input Image")
ax[1].imshow(X, interpolation='nearest')
ax[1].set_title("Discrete Cosine Transform")
plt.show()

Generates the following image ...