致謝
這學期有幸參加學習學校韓宇星教授的 數字圖像工程（全英） 課程，對機器視覺瞭解更進一步，對韓老師引用世事洞明皆學問，人情練達即文章那節課印象頗深。課程期間，通過網絡博客資料學習，收穫很多。爲表感謝，我記錄這篇學習筆記，希望爲全世界知識共享邁出一小步。
預備知識
- JPEG壓縮原理詳解：https://www.cnblogs.com/Arvin-JIN/p/9133745.html
- 二維離散餘弦變換2D-DCT實戰：https://blog.csdn.net/ahafg/article/details/48808443
- ZigZag變換加速，空間換時間做法：https://my.oschina.net/tigerBin/blog/1083549
- 使用Python如何將數據1比特1比特地寫進文件裏：https://blog.csdn.net/weixin_43690347/article/details/84146979
感謝這些博主樂於分享知識的無私精神。
Python代碼
接下來貼出本人的Python代碼，程序效果如下：
其中amilk.bmp是原圖，大小約2652KB；amilk.gpj是程序壓縮後存儲的文件，大小約380KB；resul.bmp是程序讀取amilk.gpj後恢復出來的BMP文件，大小約1990KB，文件大小變化是因爲JPEG是有損壓縮，這必然導致部分高頻信息丟失。
原圖效果：
根據amilk.gpj反壓縮得到的圖片效果：
實驗所用圖片來源：https://blog.csdn.net/c980129/article/details/88263654
python代碼如下：
import numpy as np
import os
from PIL import Image
class KJPEG:
def __init__(self):
# 初始化DCT變換的A矩陣，https://blog.csdn.net/ahafg/article/details/48808443
self.__dctA = np.zeros(shape=(8, 8))
for i in range(8):
c = 0
if i == 0:
c = np.sqrt(1 / 8)
else:
c = np.sqrt(2 / 8)
for j in range(8):
self.__dctA[i, j] = c * np.cos(np.pi * i * (2 * j + 1) / (2 * 8))
# 亮度量化矩陣
self.__lq = np.array([
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,
])
# 色度量化矩陣
self.__cq = np.array([
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,
])
# 標記矩陣類型，lt是亮度矩陣，ct是色度矩陣
self.__lt = 0
self.__ct = 1
# https://my.oschina.net/tigerBin/blog/1083549
# Zig編碼表
self.__zig = np.array([
0, 1, 8, 16, 9, 2, 3, 10,
17, 24, 32, 25, 18, 11, 4, 5,
12, 19, 26, 33, 40, 48, 41, 34,
27, 20, 13, 6, 7, 14, 21, 28,
35, 42, 49, 56, 57, 50, 43, 36,
29, 22, 15, 23, 30, 37, 44, 51,
58, 59, 52, 45, 38, 31, 39, 46,
53, 60, 61, 54, 47, 55, 62, 63
])
# Zag編碼表
self.__zag = np.array([
0, 1, 5, 6, 14, 15, 27, 28,
2, 4, 7, 13, 16, 26, 29, 42,
3, 8, 12, 17, 25, 30, 41, 43,
9, 11, 18, 24, 31, 40, 44, 53,
10, 19, 23, 32, 39, 45, 52, 54,
20, 22, 33, 38, 46, 41, 55, 60,
21, 34, 37, 47, 50, 56, 59, 61,
35, 36, 48, 49, 57, 58, 62, 63
])
def __Rgb2Yuv(self, r, g, b):
# 從圖像獲取YUV矩陣
y = 0.299 * r + 0.587 * g + 0.114 * b
u = -0.1687 * r - 0.3313 * g + 0.5 * b + 128
v = 0.5 * r - 0.419 * g - 0.081 * b + 128
return y, u, v
def __Fill(self, matrix):
# 圖片的長寬都需要滿足是16的倍數（採樣長寬會縮小1/2和取塊長寬會縮小1/8）
# 圖像壓縮三種取樣方式4:4:4、4:2:2、4:2:0
fh, fw = 0, 0
if self.height % 16 != 0:
fh = 16 - self.height % 16
if self.width % 16 != 0:
fw = 16 - self.width % 16
res = np.pad(matrix, ((0, fh), (0, fw)), 'constant',
constant_values=(0, 0))
return res
def __Encode(self, matrix, tag):
# 先對矩陣進行填充
matrix = self.__Fill(matrix)
# 將圖像矩陣切割成8*8小塊
height, width = matrix.shape
# 減少for循環語句，利用numpy的自帶函數來提升算法效率
# 參考吳恩達的公開課視頻，numpy的函數自帶並行處理，不用像for循環一樣串行處理
shape = (height // 8, width // 8, 8, 8)
strides = matrix.itemsize * np.array([width * 8, 8, width, 1])
blocks = np.lib.stride_tricks.as_strided(matrix, shape=shape, strides=strides)
res = []
for i in range(height // 8):
for j in range(width // 8):
res.append(self.__Quantize(self.__Dct(blocks[i, j]).reshape(64), tag))
return res
def __Dct(self, block):
# DCT變換
res = np.dot(self.__dctA, block)
res = np.dot(res, np.transpose(self.__dctA))
return res
def __Quantize(self, block, tag):
res = block
if tag == self.__lt:
res = np.round(res / self.__lq)
elif tag == self.__ct:
res = np.round(res / self.__cq)
return res
def __Zig(self, blocks):
ty = np.array(blocks)
tz = np.zeros(ty.shape)
for i in range(len(self.__zig)):
tz[:, i] = ty[:, self.__zig[i]]
tz = tz.reshape(tz.shape[0] * tz.shape[1])
return tz.tolist()
def __Rle(self, blist):
res = []
cnt = 0
for i in range(len(blist)):
if blist[i] != 0:
res.append(cnt)
res.append(int(blist[i]))
cnt = 0
elif cnt == 15:
res.append(cnt)
res.append(int(blist[i]))
cnt = 0
else:
cnt += 1
# 末尾全是0的情況
if cnt != 0:
res.append(cnt - 1)
res.append(0)
return res
def Compress(self, filename):
# 根據路徑image_path讀取圖片，並存儲爲RGB矩陣
image = Image.open(filename)
# 獲取圖片寬度width和高度height
self.width, self.height = image.size
image = image.convert('RGB')
image = np.asarray(image)
r = image[:, :, 0]
g = image[:, :, 1]
b = image[:, :, 2]
# 將圖像RGB轉YUV
y, u, v = self.__Rgb2Yuv(r, g, b)
# 對圖像矩陣進行編碼
y_blocks = self.__Encode(y, self.__lt)
u_blocks = self.__Encode(u, self.__ct)
v_blocks = self.__Encode(v, self.__ct)
# 對圖像小塊進行Zig編碼和RLE編碼
y_code = self.__Rle(self.__Zig(y_blocks))
u_code = self.__Rle(self.__Zig(u_blocks))
v_code = self.__Rle(self.__Zig(v_blocks))
# 計算VLI可變字長整數編碼並寫入文件，未實現Huffman部分
# 原理詳解：https://www.cnblogs.com/Arvin-JIN/p/9133745.html
buff = 0
tfile = os.path.splitext(filename)[0] + ".gpj"
if os.path.exists(tfile):
os.remove(tfile)
with open(tfile, 'wb') as o:
o.write(self.height.to_bytes(2, byteorder='big'))
o.flush()
o.write(self.width.to_bytes(2, byteorder='big'))
o.flush()
o.write((len(y_code)).to_bytes(4, byteorder='big'))
o.flush()
o.write((len(u_code)).to_bytes(4, byteorder='big'))
o.flush()
o.write((len(v_code)).to_bytes(4, byteorder='big'))
o.flush()
self.__Write2File(tfile, y_code, u_code, v_code)
# https://blog.csdn.net/weixin_43690347/article/details/84146979
def __Write2File(self, filename, y_code, u_code, v_code):
with open(filename, "ab+") as o:
buff = 0
bcnt = 0
data = y_code + u_code + v_code
for i in range(len(data)):
if i % 2 == 0:
td = data[i]
for ti in range(4):
buff = (buff << 1) | ((td & 0x08) >> 3)
td <<= 1
bcnt += 1
if bcnt == 8:
o.write(buff.to_bytes(1, byteorder='big'))
o.flush()
buff = 0
bcnt = 0
else:
td = data[i]
vtl, vts = self.__VLI(td)
for ti in range(4):
buff = (buff << 1) | ((vtl & 0x08) >> 3)
vtl <<= 1
bcnt += 1
if bcnt == 8:
o.write(buff.to_bytes(1, byteorder='big'))
o.flush()
buff = 0
bcnt = 0
for ts in vts:
buff <<= 1
if ts == '1':
buff |= 1
bcnt += 1
if bcnt == 8:
o.write(buff.to_bytes(1, byteorder='big'))
o.flush()
buff = 0
bcnt = 0
if bcnt != 0:
buff <<= (8 - bcnt)
o.write(buff.to_bytes(1, byteorder='big'))
o.flush()
buff = 0
bcnt = 0
def __IDct(self, block):
# IDCT變換
res = np.dot(np.transpose(self.__dctA), block)
res = np.dot(res, self.__dctA)
return res
def __IQuantize(self, block, tag):
res = block
if tag == self.__lt:
res *= self.__lq
elif tag == self.__ct:
res *= self.__cq
return res
def __IFill(self, matrix):
matrix = matrix[:self.height, :self.width]
return matrix
def __Decode(self, blocks, tag):
tlist = []
for b in blocks:
b = np.array(b)
tlist.append(self.__IDct(self.__IQuantize(b, tag).reshape(8 ,8)))
height_fill, width_fill = self.height, self.width
if height_fill % 16 != 0:
height_fill += 16 - height_fill % 16
if width_fill % 16 != 0:
width_fill += 16 - width_fill % 16
rlist = []
for hi in range(height_fill // 8):
start = hi * width_fill // 8
rlist.append(np.hstack(tuple(tlist[start: start + (width_fill // 8)])))
matrix = np.vstack(tuple(rlist))
res = self.__IFill(matrix)
return res
def __ReadFile(self, filename):
with open(filename, "rb") as o:
tb = o.read(2)
self.height = int.from_bytes(tb, byteorder='big')
tb = o.read(2)
self.width = int.from_bytes(tb, byteorder='big')
tb = o.read(4)
ylen = int.from_bytes(tb, byteorder='big')
tb = o.read(4)
ulen = int.from_bytes(tb, byteorder='big')
tb = o.read(4)
vlen = int.from_bytes(tb, byteorder='big')
buff = 0
bcnt = 0
rlist = []
itag = 0
icnt = 0
vtl, tb, tvtl = None, None, None
while len(rlist) < ylen + ulen + vlen:
if bcnt == 0:
tb = o.read(1)
if not tb:
break
tb = int.from_bytes(tb, byteorder='big')
bcnt = 8
if itag == 0:
buff = (buff << 1) | ((tb & 0x80) >> 7)
tb <<= 1
bcnt -= 1
icnt += 1
if icnt == 4:
rlist.append(buff & 0x0F)
elif icnt == 8:
vtl = buff & 0x0F
tvtl = vtl
itag = 1
buff = 0
else:
buff = (buff << 1) | ((tb & 0x80) >> 7)
tb <<= 1
bcnt -= 1
tvtl -= 1
if tvtl == 0 or tvtl == -1:
rlist.append(self.__IVLI(vtl, bin(buff)[2:].rjust(vtl, '0')))
itag = 0
icnt = 0
y_dcode = rlist[:ylen]
u_dcode = rlist[ylen:ylen+ulen]
v_dcode = rlist[ylen+ulen:ylen+ulen+vlen]
return y_dcode, u_dcode, v_dcode
pass
def __Zag(self, dcode):
dcode = np.array(dcode).reshape((len(dcode) // 64, 64))
tz = np.zeros(dcode.shape)
for i in range(len(self.__zag)):
tz[:, i] = dcode[:, self.__zag[i]]
rlist = tz.tolist()
return rlist
def __IRle(self, dcode):
rlist = []
for i in range(len(dcode)):
if i % 2 == 0:
rlist += [0] * dcode[i]
else:
rlist.append(dcode[i])
return rlist
def Decompress(self, filename):
y_dcode, u_dcode, v_dcode = self.__ReadFile(filename)
y_blocks = self.__Zag(self.__IRle(y_dcode))
u_blocks = self.__Zag(self.__IRle(u_dcode))
v_blocks = self.__Zag(self.__IRle(v_dcode))
y = self.__Decode(y_blocks, self.__lt)
u = self.__Decode(u_blocks, self.__ct)
v = self.__Decode(v_blocks, self.__ct)
r = (y + 1.402 * (v - 128))
g = (y - 0.34414 * (u - 128) - 0.71414 * (v - 128))
b = (y + 1.772 * (u - 128))
r = Image.fromarray(r).convert('L')
g = Image.fromarray(g).convert('L')
b = Image.fromarray(b).convert('L')
image = Image.merge("RGB", (r, g, b))
image.save("./result.bmp", "bmp")
image.show()
def __VLI(self, n):
# 獲取整數n的可變字長整數編碼
ts, tl = 0, 0
if n > 0:
ts = bin(n)[2:]
tl = len(ts)
elif n < 0:
tn = (-n) ^ 0xFFFF
tl = len(bin(-n)[2:])
ts = bin(tn)[-tl:]
else:
tl = 0
ts = '0'
return (tl, ts)
def __IVLI(self, tl, ts):
# 獲取可變字長整數編碼對應的整數n
if tl != 0:
n = int(ts, 2)
if ts[0] == '0':
n = n ^ 0xFFFF
n = int(bin(n)[-tl:], 2)
n = -n
else:
n = 0
return n
if __name__ == '__main__':
kjpeg = KJPEG()
kjpeg.Compress("./amilk.bmp")
kjpeg.Decompress("./amilk.gpj")