请对一个RBG图像手动实现JPEG压缩,复杂的过程可以使用库函数,Python实现,并请详细注释代码意思
时间: 2024-02-19 18:01:37 浏览: 34
首先,我们需要导入必要的库和读入一张RGB图像。这里使用Python的Pillow库来读入图像。
```python
from PIL import Image
import numpy as np
# 读入RGB图像
img = Image.open('test.jpg').convert('RGB')
```
接下来,我们需要将RGB图像进行分块并对每个分块进行离散余弦变换(Discrete Cosine Transform, DCT)。这里我们使用Scipy库中的DCT函数来实现。具体过程是将RGB图像拆分成8x8的小块,对每个小块进行DCT变换,并将结果存储在8x8的矩阵中。
```python
from scipy.fftpack import dct
# 拆分成8x8小块
blocks = []
for i in range(0, img.height-7, 8):
for j in range(0, img.width-7, 8):
blocks.append(np.asarray(img.crop((j, i, j+8, i+8))))
# 对每个小块进行DCT变换
dct_blocks = []
for block in blocks:
dct_block = np.zeros((8, 8, 3))
for i in range(3):
dct_block[:, :, i] = dct(dct(block[:, :, i], axis=0, norm='ortho'), axis=1, norm='ortho')
dct_blocks.append(dct_block)
```
接下来,我们需要对每个小块进行量化(Quantization)。这里我们使用一个8x8的量化矩阵,该矩阵中的每个元素代表对应位置的系数在量化后的值。量化的过程就是将DCT变换后得到的矩阵与量化矩阵相乘得到量化后的矩阵。
```python
# 量化矩阵
quantization_matrix = 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]])
# 对每个小块进行量化
quantized_blocks = []
for block in dct_blocks:
quantized_block = np.zeros((8, 8, 3))
for i in range(3):
quantized_block[:, :, i] = np.round(block[:, :, i] / quantization_matrix)
quantized_blocks.append(quantized_block)
```
接下来,我们需要对量化后的小块进行编码。这里我们采用霍夫曼编码(Huffman Encoding)的方法。具体过程是将每个小块的系数按照霍夫曼编码表进行编码,并将编码结果存储到二进制文件中。
```python
from collections import Counter
# 构建霍夫曼编码表
def build_huffman_table(freq_dict):
nodes = []
for symbol, freq in freq_dict.items():
nodes.append((freq, symbol, ''))
while len(nodes) > 1:
nodes = sorted(nodes, key=lambda x: x[0])
left = nodes[0]
right = nodes[1]
for node in left[1:]:
node[2] = '0' + node[2]
for node in right[1:]:
node[2] = '1' + node[2]
nodes = [(left[0] + right[0], left, right)] + nodes[2:]
huffman_table = {}
for node in nodes[0][1:]:
huffman_table[node[1]] = node[2]
return huffman_table
# 编码并保存到二进制文件
encoded_blocks = []
with open('output.bin', 'wb') as f:
for block in quantized_blocks:
# 将矩阵展开成一维数组
flattened = block.flatten().tolist()
# 统计每个系数出现次数
freq_dict = Counter(flattened)
# 构建霍夫曼编码表
huffman_table = build_huffman_table(freq_dict)
# 将每个系数按照编码表进行编码
encoded = ''
for symbol in flattened:
encoded += huffman_table[symbol]
# 将编码结果转换为二进制并写入文件
while len(encoded) % 8 != 0:
encoded += '0'
encoded_bytes = bytes([int(encoded[i:i+8], 2) for i in range(0, len(encoded), 8)])
f.write(encoded_bytes)
```
最后,我们需要将编码后的二进制文件进行解码,并还原成RGB图像。解码的过程就是将二进制文件读入并按照霍夫曼编码表进行解码,将解码后的系数乘以量化矩阵得到DCT系数,然后将DCT系数进行逆DCT变换得到原始的RGB图像。
```python
from bitarray import bitarray
# 从二进制文件中读取编码结果
encoded_blocks = []
with open('output.bin', 'rb') as f:
encoded_bytes = f.read()
encoded_bits = bitarray()
encoded_bits.frombytes(encoded_bytes)
encoded = encoded_bits.to01()
# 解码
decoded_blocks = []
for i in range(len(quantized_blocks)):
block = np.zeros((8, 8, 3))
# 将编码结果按照霍夫曼编码表进行解码
current_code = ''
for j in range(8*8*3):
current_code += encoded[j]
if current_code in huffman_table:
block.flat[j] = int(huffman_table[current_code])
current_code = ''
# 将解码后的系数乘以量化矩阵得到DCT系数
dct_block = np.zeros((8, 8, 3))
for k in range(3):
dct_block[:, :, k] = block[:, :, k] * quantization_matrix
# 将DCT系数进行逆DCT变换得到原始的RGB图像
decoded_block = np.zeros((8, 8, 3))
for l in range(3):
decoded_block[:, :, l] = dct(dct_block[:, :, l], axis=0, norm='ortho')
decoded_block[:, :, l] = dct(decoded_block[:, :, l], axis=1, norm='ortho')
decoded_blocks.append(decoded_block)
# 还原RGB图像
decoded_img = Image.new('RGB', (img.width, img.height))
index = 0
for i in range(0, img.height-7, 8):
for j in range(0, img.width-7, 8):
decoded_img.paste(Image.fromarray(np.uint8(decoded_blocks[index])), (j, i))
index += 1
# 保存还原后的RGB图像
decoded_img.save('decoded.jpg')
```
完整代码如下:
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