DCT实现的问题

Question

我必须在C++中实现一个离散余弦变换算法，下面是我现在的代码：

// 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算法进行了比较，结果如下：

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，所以我假设我的DCT算法是错误的，但我搜索了几个小时，仍然找不到我的错误，有人能告诉我我哪里做错了吗？

Answer 1

您的索引计算错误。在indexNumber = x * oBlock.rows + y;中，由于x计算的是行数，因此需要乘以列数：

indexNumber = x * oBlock.cols + y;

indexNumber = u * oBlock.rows + v;也是如此

indexNumber = u * oBlock.cols + v;