DCT

刘旭 — Tue, 30 Oct 2007 15:55:00 GMT

DCT是仅次与K-L变换的信息集中能力优秀的算法，K-L算法需要对每个子图象求变换矩阵,所以DCT是替代它的实用算法。

1. 8*8 2D DCT 直接变换

   for (u = 0; u < 8; u++)
   for (v = 0; v < 8; v++)
for (x = 0; x < 8; x++)
   for (y = 0; y < 8; y++)
   MAT(F,u,v)) += MAT(f,x,y)*c*cos((2*x+1)*u*pi/(2*nrow))*cos((2*y+1)*v*pi/(2*ncol));

x,y是像素坐标， x,y = 0,1,2,...,7;
u,v是像素坐标对应的DCT坐标;

MAT(m,i,j)表示8*8点矩阵m中第i行第j列的元素,一维算法计算量大,不实用,算法忽略。
C(0) = 1/sqrt(2), C(i) = 1     i = 1,2,...,7。
c = 1/4*C(u)*C(v)

2. 8*8 2D DCT 分解为一维形式

  for (v = 0; v < 8; v++)
for (u = 0; u < 8; u++)
for (x = 0; x < 8; x++)
MAT(tmpF,u,v) += MAT(f,x,v)*coff*cos((2*x+1)*pi*u/(2*nrow)):

for (u = 0; u < 8; u++)
for (v = 0; v < 8; v++)
for (y = 0; y < 8; y++)
MAT(F,u,v) += coff*MAT(tmpF,u,y)*cos((2*y+1)*pi*v/(2*ncol)):

coff[0] = 1/sqrt(8);
coff[i] = sqrt(2)/sqrt(8); i = 1,2,...,7;
算法实现:
#define PI 3.14159265358979323846
void DCT(double *f, double *F, int r)
{
    // 离散余弦变换点数
    int count;
    count = 1<    // 循环变量
    int  m,n,x;
    // 中间变量
    double *dTemp = new double[count*count];
    double *coff = new double[count];

    // 设定系数coff
    coff[0]=1/sqrt(count);
    for (m = 1;m < count;m++)
    {
        coff[m]=sqrt(2)/sqrt(count);
    }
   //dTemp赋初值
    memset(dTemp, 0, sizeof(double) * count * count);
    memset(F, 0, sizeof(double) * count * count);
    // 求F[m,n]
    for (n = 0; n < count; n++)
   {
        for (m = 0; m < count; m++)
       {
           for (x = 0; x < count; x++)
          {
               dTemp[m*count+n] += f[x*count+n]*coff[m]*cos((2*x+1)*PI*m/(2*count));
           }
       }
   }

   for (m=0; m< count; m++)
{
    for (n = 0; n < count; n++)
     {
         for (x = 0; x < count; x++)
        {
              F[m*count+n] += dTemp[m*count+x]*coff[n]*cos((2*x+1)*PI*n/(2*count));
         }
     }
}

   // 释放内存
   delete dTemp;
   delete coff;
}

刘旭 2007-10-30 23:55 发表评论

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DCT