零均值单位方差

这几天在看文章的时候，看到这么一段话：

“First, we normalize the grayscale intensity in the eye region for each of the aligned facial images to zero mean and unit variance.”

意思就是第一步对眼睛的区域进行零均值单位方差。第一次知道还有这玩意。。

经过查阅matlab prestd函数就代表了这个意思：

试验一下：

>> a=[1 2 3 4]

a =

     1     2     3     4

>> [pn m std]=prestd(a)
Warning: PRESTD is an obsolete function.
> In obs_fcn at 18
  In prestd at 10
          Use MAPSTD instead.

pn =

   -1.1619   -0.3873    0.3873    1.1619

m =

    2.5000

std =

    1.2910

>>

其中pn代表已经零均值单位方差的矩阵，m代表a的均值  std代表a的方差

转成C++代码就应该是这样：

    int a = 2;
    int b = 2;
    double  gray[2 * 2] = { 1,2,3,4 };
    double total = 0.0;
    for (int i = 0; i < b; i++)
    {
        for (int j = 0; j < a; j++)
        {
            total += (double)gray[i*a + j];
        }
    }
    double meanvalue = total / (a*b);
    //零均值单位方差
    double stdp = 0.0;
    for (int i = 0; i < b; i++)
    {
        for (int j = 0; j < a; j++)
        {
            double temp = gray[i*a + j];
            stdp += ((temp - meanvalue)*(temp - meanvalue));
        }
    }

    stdp = sqrt(stdp / (a*b));

    qDebug() << meanvalue << " " << stdp;

    for (int i = 0; i < b; i++)
    {
        for (int j = 0; j < a; j++)
        {
            double temp = gray[i*a + j];
            qDebug()<<i<<" "<<j<<" "<<(temp - meanvalue) / stdp;
        }
    }

咱们看一下结果输出：

发现在方差的值就不一样了。为什么呢，

原来方差还存在偏差的概念；

 double meanvalue = total / (a*b);//有偏差为n

 double meanvalue = total / (a*b-1);//无偏差的方差n-1而matlab默认是无偏差的方差，所以我们只要用无偏差替换到有偏差就和metlab相对应了。