JPG学习笔记3（附完整代码）

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　　采样后，需要对8*8block进行DCT（离散余弦变换)。为什么要进行DCT？第一点是余弦变化后的图片能量主要集中在低频，我们只需要保存低频数据，默认高频0。第二点是，DCT后的图片很适合哈夫曼压缩，对于原图而言，区域相连的pixle数值差不多，哈夫曼压缩效果差。全部代码在 https://github.com/Cheemion/JPEG_COMPRESS。

function [ out ] = g( u,v )
p = zeros(8,8);
for i = 0:7
for j = 0:7
p(i + 1,j + 1) = cos((
56c
i + 0.5) * u * pi / 8) * cos((j + 0.5) * v * pi / 8);
end
end
out = p;
end

matlab画图代码

clc; clear; close all;
figure;
maximum = 0;
minimum = 100;
for u = 0:7
for v = 0:7
pp = g(u,v)
subplot(8, 8, u * 8 + v + 1);
imshow((pp + 1) ./ 2);
end
end

matlab画图代码主函数 乘以系数c(u)c(v)是使我们的G(i, j)变成单位向量。公式剩余部分就是点乘的过程。

 

 

 IDCT逆变换

3.代码

void DCT(Block& block) {
Bloc
ad8
k temp;
std::memcpy(&temp, &block, sizeof(Block)); //copy from original
//8 rows
//DCT行变化
for(uint i = 0; i < 8; i++) {
double* f = &temp[i * 8]; //one dimension Array , and will perform DCT on it
for(uint k = 0; k < 8; k++) {
double sum = 0.0;
for(uint n = 0; n < 8; n++){
sum = sum + f
 * std::cos(((n + 0.5) * M_PI * k / 8));
}
sum = (k == 0) ? (sum * std::sqrt(1.0 / 8)) : (sum * std::sqrt(2.0 / 8));
block[i * 8 + k] = sum;
}
}

std::memcpy(&temp, &block, sizeof(Block)); //copy from
//DCT列变化
for(uint i = 0; i < 8; i++) {
double* f = &temp[i]; //one dimension Array with 8 steps increment , and will perform DCT on it
for(uint k = 0; k < 8; k++) {
double sum = 0.0;
for(uint n = 0; n < 8; n++){
sum = sum + f[n * 8] * std::cos(((n + 0.5) * M_PI * k / 8));
}
sum = (k == 0) ? (sum * std::sqrt(1.0 / 8)) : (sum * std::sqrt(2.0 / 8));
block[i + k * 8] = sum;
}
}
}

 

 以上全部的代码在https://github.com/Cheemion/JPEG_COMPRESS/tree/main/Day3

 完结

  Thanks for reading.

   wish you have a good day.

                                                                                                                                                                                                                                                              >>>> JPG学习笔记4（附完整代码）

 

参考资料

[1]https://github.com/Cheemion/JPEG_COMPRESS/blob/main/resource/Compressed%20Image%20File%20Formats%20JPEG%2C%20PNG%2C%20GIF%2C%20XBM%2C%20BMP%20-%20John%20Miano.pdf