Otsu算法_otsu算法步骤

Otsu算法步骤如下：
设图象包含L个灰度级(0,1…,L-1)，灰度值为i的的象素点数为Ni ，图象总的象素点数为N=N0+N1+...+N(L-1)。灰度值为i的点的概率为：
P(i) = N(i)/N.
门限t将整幅图象分为暗区c1和亮区c2两类，则类间方差σ是t的函数：
σ=a1*a2(u1-u2)^2 (2)
式中，aj 为类cj的面积与图象总面积之比，a1 = sum(P(i)) i->t, a2 = 1-a1; uj为类cj的均值，u1 = sum(i*P(i))/a1 0->t,
u2 = sum(i*P(i))/a2, t+1->L-1
该法选择最佳门限t^ 使类间方差最大，即：
令Δu=u1-u2，σb = max{a1(t)*a2(t)Δu^2}

代码实现：
int otsu (IplImage *image, int rows, int cols, int x0, int y0, int dx, int dy, int vvv)
{

unsigned char *np; // 图像指针
int thresholdValue=1; // 阈值
int ihist[256]; // 图像直方图，256个点

int i, j, k; // various counters
int n, n1, n2, gmin, gmax;
double m1, m2, sum, csum, fmax, sb;

// 对直方图置零
memset(ihist, 0, sizeof(ihist));

gmin=255; gmax=0;
// 生成直方图
/**//*for (i = y0 + 1; i < y0 + dy - 1; i++) {
np = &image[i*cols+x0+1];
for (j = x0 + 1; j < x0 + dx - 1; j++) {
ihist[*np]++;
if(*np > gmax) gmax=*np;
if(*np < gmin) gmin=*np;
np++; /* next pixel
}
}*/
for(j=y0;j<dy;j++)
{
    for(i=0;i<dx;i++)
    {
         unsigned char temp=CV_IMAGE_ELEM(image,uchar,j,i);
         ihist[temp]++;
     }
}

// set up everything
sum = csum = 0.0;
n = 0;

for (k = 0; k <= 255; k++) {
sum += (double) k * (double) ihist[k]; /**//* x*f(x) 质量矩*/
n += ihist[k]; /**//* f(x) 质量 */
}

if (!n) {
// if n has no value, there is problems
fprintf (stderr, "NOT NORMAL thresholdValue = 160/n");
return (160);
}

// do the otsu global thresholding method
fmax = -1.0;
n1 = 0;
for (k = 0; k < 255; k++) {
n1 += ihist[k];
if (!n1) { continue; }
n2 = n - n1;
if (n2 == 0) { break; }
csum += (double) k *ihist[k];
m1 = csum / n1;
m2 = (sum - csum) / n2;
sb = (double) n1 *(double) n2 *(m1 - m2) * (m1 - m2);
/**//* bbg: note: can be optimized. */
if (sb > fmax) {
fmax = sb;
thresholdValue = k;
}
}

// at this point we have our thresholding value

// debug code to display thresholding values
if ( vvv & 1 )
fprintf(stderr,"# OTSU: thresholdValue = %d gmin=%d gmax=%d/n",thresholdValue, gmin, gmax);

return(thresholdValue);
}