c++ - DCT 实现的问题

Question

我必须在 C++ 中实现 DCT 算法，这是我目前的代码:

// dct: computes the discrete cosinus tranform of a 8x8 block
template<typename Tin=uchar,typename Tout=float>
inline cv::Mat_<Tout> dct(const cv::Mat_<Tin>& oBlock) {

int indexNumber;
float pi = 3.14159265359;
float fcoscos, fxy, cos1, cos2, forCos1, forCos2;

cv::Mat_<Tout> resultBloc(8, 8);

for (int u = 0; u < oBlock.rows; u++){
    for (int v = 0; v < oBlock.cols; v++){

        float cu=0, cv=0, Result=0;

        // calcul c(u)
        if (u == 0){
            cu = (float)sqrt((float)1 / (float)oBlock.rows);
        }
        else {
            cu = (float)sqrt((float)2 / (float)oBlock.rows);
        }

        // calcul c(v)
        if (v == 0){
            cv = (float)sqrt((float)1 / (float)oBlock.cols);
        }
        else {
            cv = (float)sqrt((float)2 / (float)oBlock.cols);
        }

        float sums = 0;

        for (int x = 0; x < oBlock.rows; x++){
            for (int y = 0; y < oBlock.cols; y++){

                indexNumber = x * oBlock.rows + y;
                fxy = (int)oBlock.data[indexNumber];

                forCos1 = (pi*((2 * x) + 1)*u) / (2 * oBlock.rows);
                forCos2 = (pi*((2 * y) + 1)*v) / (2 * oBlock.cols);

                cos1 = cos(forCos1);
                cos2 = cos(forCos2);

                fcoscos = fxy * cos1 * cos2; 

                sums += fcoscos;

            }
        }

        // calcul total
        Result = sums*cu*cv;

        indexNumber = u * oBlock.rows + v;
        resultBloc.data[indexNumber] = Result;

    }
}

return resultBloc;

}

我将结果与 cv DCT 算法进行了如下比较:

cv::Mat_<float> tempImage(8,8);

for (int i = 0; i < vecImageCut[0].cols*vecImageCut[0].rows; i++){
    tempImage.data[i] = (int)vecImageCut[0].data[i];
}
cv::Mat_<float> dctCV;
cv::dct(tempImage, dctCV);
for (int i = 0; i < blocksAfterDCT[0].cols*blocksAfterDCT[0].rows; i++){
    std::cerr << "Difference DCT for pixel " << i << " : " << dctCV.data[i] - blocksAfterDCT[0].data[i] << std::endl;
}

我的 DCT 和 cv DCT 之间的结果非常不同，所以我认为我的 DCT 算法是错误的，但我搜索了几个小时也找不到我的错误，谁能告诉我我哪里做错了什么？

Answer 1

您的指数计算有误。在 indexNumber = x * oBlock.rows + y; 中，由于 x 正在计算行数，因此需要将其乘以列数:

indexNumber = x * oBlock.cols + y;

同样适用于 indexNumber = u * oBlock.rows + v;

indexNumber = u * oBlock.cols + v;