Compressão de Imagens via DCT

In [2]:

    

%matplotlib inline
import io
import os
from PIL import Image
import numpy as np
import matplotlib.pyplot as plt
from scipy import fftpack
import urllib2
import IPython


    

In [73]:

    

def mydct(img):
    dct = fftpack.dct(fftpack.dct(img.T, norm='ortho').T, norm='ortho')
    return dct

def myidct(coef):
    idct = fftpack.idct(fftpack.idct(coef.T, norm='ortho').T, norm='ortho')
    return idct

def myimagem_reconstruida(g):
    img = g.clip(0, 255)
    img = img.astype('uint8')
    img = Image.fromarray(img)
    return img

def histogram(f):

    return np.bincount(f.ravel())


    

In [77]:

    

#Teste com imagem sintética
#imagem =np.zeros((8, 8))
#imagem[2:4, 2:6]=255
#imagem[2:6, 4:6]=255
#plt.imshow(imagem)
#plt.show()

imagem = Image.open('../data/cameraman.tif')
img = np.array(imagem, dtype=np.float)
dct_size = img.shape[0]
#dct_size = 10
dct = mydct(img)
#img_reconstruida = myimagem_reconstruida(dct)


    

In [78]:

    

img_reconstruidas = []
for ii in range(dct_size):
    dct_copy = dct.copy()
    dct_copy[ii:,:] = 0
    dct_copy[:,ii:] = 0
    
    #Reconstrução da imagem
    img_r = myidct(dct_copy)
    img_reconstruida = myimagem_reconstruida(img_r)
    
    #Lista de imagens
    img_reconstruidas.append(img_reconstruida)


    

In [80]:

    

# Histograma em escala logarítmica
#plt.hist(np.log10(np.abs(dct.ravel())), bins=100, color='#348ABD', alpha=.3, histtype='stepfilled');
#plt.show()


    

In [86]:

    

# Coeficientes
plt.matshow(np.abs(dct[:50, :50]))
plt.title('Primeiros 2500 coefficientes em Grid')
plt.axis('off')
plt.show()


    

In [89]:

    

fig = plt.figure(figsize=(16, 16))
for ii in range(64):
    plt.subplot(8, 8, ii + 1)
    plt.imshow(img_reconstruidas[ii], cmap=plt.cm.gray)
    plt.grid(False)
    plt.xticks([])
    plt.yticks([])


    

In [90]:

    

fig = plt.figure(figsize=(16, 16))
for ii in range(64, 128):
    plt.subplot(8, 8, ii - 63)
    plt.imshow(img_reconstruidas[ii], cmap=plt.cm.gray)
    plt.grid(False)
    plt.xticks([])
    plt.yticks([])


    

In [91]:

    

fig = plt.figure(figsize=(16, 16))
for ii in range(128, 192):
    plt.subplot(8, 8, ii - 127)
    plt.imshow(img_reconstruidas[ii], cmap=plt.cm.gray)
    plt.grid(False)
    plt.xticks([])
    plt.yticks([])


    

In [92]:

    

fig = plt.figure(figsize=(16, 16))
for ii in range(64):
    plt.subplot(8, 8, ii + 1)
    plt.imshow(img_reconstruidas[-ii-1], cmap=plt.cm.gray)
    plt.grid(False)
    plt.xticks([])
    plt.yticks([])


    

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