用Python写一个程序,对一个灰度图像进行图像分割8X8,并将各像素值减去128,进行D CT正向变换,再通过量化,最后进行Z字形重排序的编码过程,然后再进行解码
时间: 2023-03-29 08:02:24 浏览: 85
您好,这是一个关于图像处理的问题。我可以回答这个问题。以下是Python代码实现:
```python
import numpy as np
from scipy.fftpack import dct
# 读取灰度图像
img = cv2.imread('image.jpg', cv2.IMREAD_GRAYSCALE)
# 图像分割8X8
blocks = [img[i:i+8, j:j+8] for i in range(, img.shape[], 8) for j in range(, img.shape[1], 8)]
# 将各像素值减去128
blocks = [block - 128 for block in blocks]
# DCT正向变换
dct_blocks = [dct(block.astype(float), norm='ortho') for block in blocks]
# 量化
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]])
quantized_blocks = [np.round(dct_block / quantization_matrix) for dct_block in dct_blocks]
# Z字形重排序的编码过程
zigzag_order = np.array([[, 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, 51, 55, 60],
[21, 34, 37, 47, 50, 56, 59, 61],
[35, 36, 48, 49, 57, 58, 62, 63]])
encoded_blocks = [quantized_block[zigzag_order].flatten() for quantized_block in quantized_blocks]
# 解码
decoded_blocks = [np.zeros((8, 8)) for _ in range(len(encoded_blocks))]
for i, encoded_block in enumerate(encoded_blocks):
decoded_block = np.zeros((8, 8))
decoded_block[zigzag_order.flatten()] = encoded_block
decoded_block = decoded_block.reshape((8, 8))
decoded_block = decoded_block * quantization_matrix
decoded_block = dct(decoded_block, norm='ortho')
decoded_block = decoded_block + 128
decoded_blocks[i] = decoded_block
# 合并图像块
decoded_img = np.zeros_like(img)
for i in range(, decoded_img.shape[], 8):
for j in range(, decoded_img.shape[1], 8):
decoded_img[i:i+8, j:j+8] = decoded_blocks.pop()
# 显示解码后的图像
cv2.imshow('decoded image', decoded_img)
cv2.waitKey()
cv2.destroyAllWindows()
```
希望能对您有所帮助。