DCT变换及量化的c++实现（基于opencv矩阵运算）
由于DCT的数学原理不好描述，直接放代码了：
#include
#include
#include
#include
using namespace std;
using namespace cv;
const double pi = 3.141592;
void initDctMat(Mat &A) //计算8x8块的离散余弦变换系数
{
for (int i = 0; i < 8; ++i)
for (int j = 0; j < 8; ++j)
{
float a;
if (i == 0)
a = sqrt(1.0 / 8.0);
else
a = sqrt(2.0 / 8.0);
A.ptr(i)[j] = a*cos((j + 0.5)*pi*i / 8);
}
}
//dct变换
void myDct(Mat &image, const Mat &A, const Mat &mask)
{
//分块 8x8
for(int i = 0; i < 256; i+=8)
for (int j = 0; j < 256; j += 8)
{
//X = AXAT
image(Range(i, i + 8), Range(j, j + 8)) = A * image(Range(i, i + 8), Range(j, j + 8)) *A.t();
//用mask量化
image(Range(i, i + 8), Range(j, j + 8)) /= mask;
}
}
//dct反变换
void myiDct(Mat &image, const Mat &A, const Mat &mask)
{
//分块8x8
for (int i = 0; i < 256; i += 8)
for (int j = 0; j < 256; j += 8)
{
//还原量化
image(Range(i, i + 8), Range(j, j + 8)) = image(Range(i, i + 8), Range(j, j + 8)).mul(mask);
//X = ATXA
image(Range(i, i + 8), Range(j, j + 8)) = A.t() * image(Range(i, i + 8), Range(j, j + 8)) * A;
}
}
int main()
{
//读取图像，图像为灰度图，单通道
Mat image = imread("lena.bmp",CV_LOAD_IMAGE_GRAYSCALE);
Mat fimage;
Mat A(Size(8, 8), CV_32FC1);// 离散余弦系数矩阵
//初始化mask量化矩阵
float msk[8][8] = { {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}};
Mat mask(8, 8, CV_32FC1, msk);
//显示原图
if (!image.empty())
imshow("image", image);
//计算A系数
initDctMat(A);
//转换成浮点数矩阵，进行dct变换
image.convertTo(fimage, CV_32FC1);
myDct(fimage, A, mask);
//计算压缩率， 用非零矩阵点数量比总数量、
fimage.convertTo(image, CV_8UC1);
double dctRate = countNonZero(image) / (256.0 * 256.0);
cout << "the size becomes " << dctRate * 100 << "% of the original." << endl;
imshow("压缩图", fimage);
//dct反变换
myiDct(fimage, A, mask);
//显示还原的图像
fimage.convertTo(image, CV_8UC1);
imshow("还原图", image);
waitKey(0);
return 0;
}
