Here, I'm using OpenCV (Python) to simulate DCT + quantization + IDCT, without Huffman coding.
jpeg.org
wikipedia/jpeg
opencv
Ref:
"Image and Video Compression for Multimedia Engineering", Yun Q.Shi, Huifang Sun, CRC Press, 2000.
"Digital Image Processing", Third Ed., Rafael C. Gonzalez, Richard E. Woods, Pearson Prentice Hall, 2008.
Basically in this simulation, an image (grayscale and indexed-color) is compressed (transformed by DCT, then quantized), then decompressed (inverse DCT). We can see that original and the result is almost the same.
By adding Huffman coding, it is the standard JPEG compression/decompression.
Image is divided into 8x8 blocks before being processed.
According to JPEG standard, it is recommended that any incomplete (not 8x8) MCUs be completed by replication of the right-most column and the bottom row of each component.
This is simulation code for grayscale image,
"""
Simulation of basic JPEG compression,
only DCT + quantization IDCT,
not including entropy-encoding/Huffman-coding
"""
# jpeggraysim.py
import cv2
import numpy as np
std_luminance_quant_tbl = [
[16, 11, 10, 16, 24, 40, 51, 61],
[12, 12, 14, 19, 26, 58, 60, 55],
[14, 13, 16, 24, 40, 57, 69, 56],
[14, 17, 22, 29, 51, 87, 80, 62],
[18, 22, 37, 56, 68, 109, 103, 77],
[24, 35, 55, 64, 81, 104, 113, 92],
[49, 64, 78, 87, 103, 121, 120, 101],
[72, 92, 95, 98, 112, 100, 103, 99]
]
def JPEG_DCT(imgfile):
# 1 channel x 8 bits, grayscale
img = cv2.imread(imgfile, cv2.CV_LOAD_IMAGE_GRAYSCALE)
wndName = "original grayscale"
cv2.namedWindow(wndName, cv2.WINDOW_AUTOSIZE)
cv2.imshow(wndName, img)
iHeight, iWidth = img.shape[:2]
print "size:", iWidth, "x", iHeight
# set size to multiply of 8
if (iWidth % 8) != 0:
filler = img[:,iWidth-1:]
#print "width filler size", filler.shape
for i in range(8 - (iWidth % 8)):
img = np.append(img, filler, 1)
if (iHeight % 8) != 0:
filler = img[iHeight-1:,:]
#print "height filler size", filler.shape
for i in range(8 - (iHeight % 8)):
img = np.append(img, filler, 0)
iHeight, iWidth = img.shape[:2]
print "new size:", iWidth, "x", iHeight
# array as storage for DCT + quant.result
img2 = np.empty(shape=(iHeight, iWidth))
# FORWARD ----------------
# do calc. for each 8x8 non-overlapping blocks
for startY in range(0, iHeight, 8):
for startX in range(0, iWidth, 8):
block = img[startY:startY+8, startX:startX+8]
# apply DCT for a block
blockf = np.float32(block) # float conversion
dst = cv2.dct(blockf) # dct
# quantization of the DCT coefficients
blockq = np.around(np.divide(dst, std_luminance_quant_tbl))
blockq = np.multiply(blockq, std_luminance_quant_tbl)
# store the result
for y in range(8):
for x in range(8):
img2[startY+y, startX+x] = blockq[y, x]
# INVERSE ----------------
for startY in range(0, iHeight, 8):
for startX in range(0, iWidth, 8):
block = img2[startY:startY+8, startX:startX+8]
blockf = np.float32(block) # float conversion
dst = cv2.idct(blockf) # inverse dct
np.place(dst, dst>255.0, 255.0) # saturation
np.place(dst, dst<0.0, 0.0) # grounding
block = np.uint8(np.around(dst))
# store the results
for y in range(8):
for x in range(8):
img[startY+y, startX+x] = block[y, x]
wndName1 = "DCT + quantization + inverseDCT"
cv2.namedWindow(wndName1, cv2.WINDOW_AUTOSIZE)
cv2.imshow(wndName1, img)
cv2.waitKey(0)
cv2.destroyWindow(wndName1)
cv2.destroyWindow(wndName)
if __name__ == "__main__":
JPEG_DCT("cat01.jpg")
This is simulation code for indexed-color image,
"""
@Soesilo Wijono
Simulation of basic JPEG compression,
only DCT + quantization + IDCT,
not including entropy-encoding/Huffman-coding
"""
# jpegcolorsim.py
#import sys
#import time
import cv2
import numpy as np
# table of [luminance, chrominance, chrominance]
std_quant_tbl = [
[
[16, 11, 10, 16, 24, 40, 51, 61],
[12, 12, 14, 19, 26, 58, 60, 55],
[14, 13, 16, 24, 40, 57, 69, 56],
[14, 17, 22, 29, 51, 87, 80, 62],
[18, 22, 37, 56, 68, 109, 103, 77],
[24, 35, 55, 64, 81, 104, 113, 92],
[49, 64, 78, 87, 103, 121, 120, 101],
[72, 92, 95, 98, 112, 100, 103, 99]
],
[
[17, 18, 24, 47, 99, 99, 99, 99],
[18, 21, 26, 66, 99, 99, 99, 99],
[24, 26, 56, 99, 99, 99, 99, 99],
[47, 66, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99]
],
[
[17, 18, 24, 47, 99, 99, 99, 99],
[18, 21, 26, 66, 99, 99, 99, 99],
[24, 26, 56, 99, 99, 99, 99, 99],
[47, 66, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99],
[99, 99, 99, 99, 99, 99, 99, 99]
]
]
def JPEG_DCT(imgfile):
# 3 channels x 8 bits, indexed-colors
img = cv2.imread(imgfile, cv2.CV_LOAD_IMAGE_COLOR)
wndName = "original indexed-color"
cv2.namedWindow(wndName, cv2.WINDOW_AUTOSIZE)
cv2.imshow(wndName, img)
iHeight, iWidth = img.shape[:2]
print "size:", iWidth, "x", iHeight
# set size to multiply of 8
if (iWidth % 8) != 0:
filler = img[:,iWidth-1:,:]
#print "width filler size", filler.shape
for i in range(8 - (iWidth % 8)):
img = np.append(img, filler, 1)
if (iHeight % 8) != 0:
filler = img[iHeight-1:,:,:]
#print "height filler size", filler.shape
for i in range(8 - (iHeight % 8)):
img = np.append(img, filler, 0)
iHeight, iWidth = img.shape[:2]
print "new size:", iWidth, "x", iHeight
# convert to YCrCb, Y=luminance, Cr/Cb=red/blue-difference chrominance
img = cv2.cvtColor(img, cv2.COLOR_BGR2YCR_CB)
# array as storage for DCT + quant.result
img2 = np.empty(shape=(iHeight, iWidth, 3))
# FORWARD ----------------
# do calc. for each 8x8 non-overlapping blocks
for startY in range(0, iHeight, 8):
for startX in range(0, iWidth, 8):
for c in range(0, 3):
block = img[startY:startY+8, startX:startX+8, c:c+1].reshape(8,8)
# apply DCT for a block
blockf = np.float32(block) # float conversion
dst = cv2.dct(blockf) # dct
# quantization of the DCT coefficients
blockq = np.around(np.divide(dst, std_quant_tbl[c]))
blockq = np.multiply(blockq, std_quant_tbl[c])
# store the result
for y in range(8):
for x in range(8):
img2[startY+y, startX+x, c] = blockq[y, x]
# INVERSE ----------------
for startY in range(0, iHeight, 8):
for startX in range(0, iWidth, 8):
for c in range(0, 3):
block = img2[startY:startY+8, startX:startX+8, c:c+1].reshape(8,8)
blockf = np.float32(block) # float conversion
dst = cv2.idct(blockf) # inverse dct
np.place(dst, dst>255.0, 255.0) # saturation
np.place(dst, dst<0.0, 0.0) # grounding
block = np.uint8(np.around(dst))
# store the results
for y in range(8):
for x in range(8):
img[startY+y, startX+x, c] = block[y, x]
# convert to BGR
img = cv2.cvtColor(img, cv2.COLOR_YCR_CB2BGR)
wndName1 = "DCT + quantization + inverseDCT"
cv2.namedWindow(wndName1, cv2.WINDOW_AUTOSIZE)
cv2.imshow(wndName1, img)
cv2.waitKey(0)
cv2.destroyWindow(wndName1)
cv2.destroyWindow(wndName)
if __name__ == "__main__":
JPEG_DCT("cat02.png")
Source Image:
After processing, DCT + quantization + IDCT:
