Otsu’s Thresholding Method(大津法求阀值)
大津法由大津于1979年提出，对图像Image，记t为前景与背景的分割阈值，
前景点数占图像比例为 
，平均灰度为$$u_1(t)$$，方差为 $$D_1^2(t)$$；背景点数占图像 比例为$$q_2(t)$$，平均灰度为 $$u_2(t)$$，方差为 $$D_2^2(t)$$。图像的总平均灰度为：
$$u=q_1(t)*u_1(t) + q_2(t)*u_2(t)$$。
从最小灰度值到最大灰度值遍历t，当t使得值$$D_w^2=q_1(t)*D_1^2(t) + q_2(t)*D_2^2(t)$$
最小时 即为分割的最佳阈值 （ minimizes the weighte within class variance. ) 这个就意味着当取阀值为t时，前景和背景的方差加权和最小，即前景和背景每部分的像素都比较平稳。
$$q_1(t)=\sum_{i=0}^{t-1}P(i)$$ $$q_2(t)=\sum_{i=t}^{255}P(i)$$ ; $$u_1(t)=\sum_{i=0}^{t-1}\frac{i*P(i)}{q_1(t)}$$ $$u_2(t)=\sum_{i=t}^{255}\frac{i*P(i)}{q_2(t)}$$
$$D_1^2(t)=\sum_{i=0}^{t-1}[i-u_1(t)]^2\frac{P(i)}{q_1(t)}$$$$D_2^2(t)=\sum_{i=t}^{255}[i-u_2(t)]^2\frac{P(i)}{q_2(t)}$$;
$$D_1^2(t) q_1(t) = \sum_{i=1}^{t-1}[i-u_1(t)]^2P[i]=\sum_{i=0}^{t-1}i^2P[i]-2u_1(t)\sum_{i=0}^{t-1}i*P[i] + u_1^2(t)\sum_{i=0}^{k-1}P[i]$$
$$ = \sum_{i=0}^{t-1}i^2P[i]-q_1(t)u_1^2(t)
同理可得 $$D_2^2(t)q_2(t) = \sum_{i=t}^{255}i^2P[i]-q_2(t)u_2^2(t)
$$D_2=\sum_{i=0}^{255}i^2P[i] - u^2 = D_w^2 + q_1(t)u_1^2(t) + q_2(t)u_2^2(t) - (q_1(t)u_1(t) + q_2(t)u_2(t))^2
$$=D_w^2+q_1(t)(1-q_1(t))u_1^2(t) + q_2(t)(1-q_2(t))u_2^2(t) - 2q_1(t)q_2(t)u_1(t)u_2(t)
=D_w^2 + q_1(t)q_2(t)(u_1^2(t) + 2u_1(t)u_2(t) + u_2^2(t))
=D_w^2 + q_1(t)(1-q_1(t))(u_1(t)-u_2(t))^2
$$Min(D_w^2)=Max(q_1(t)(1-q_1(t))(u_1(t)-u_2(t))^2)
Program
q_1(t + 1) = q_1(t) + P[t + 1]
u_1(t+1) = \frac{u_1(t)q_1(t) + P[t+1](t+1)}{q_1(t+1)}
u_2(t+1) = \frac{u - u_1(t+1)q_1(t+1)}{1-q_1(t+1)}
<pre name = "code" class = "c++">
int MyImage::OtsuThreshMethod()
{
double s0, s1, u0, u1, u2, maxv = 0, totsum = 0;
int thr = 0, count = 0;
if(!Histogram)
GetHistogram();
for(int i = 0; i < 256; i ++)
{
totsum += i *Histogram[i];
count += Histogram[i];
}
s0 = 0; u0 = 0;
for(i = 1; i <= 256; i ++)
{
s1 = s0 + Histogram[i-1];
if(s1 == 0 )
u1 = 0;
else
u1= (u0 * s0 + Histogram[i-1] * (i - 1))/s1;
if(fabs(s1 - totsum) < 0.0001)
u2 = 0;
else
u2 = (totsum - s1 * u1)/ (count - s1);
if(s1 * (count - s1) * (u1 - u2) * (u1 - u2) > maxv)
{
maxv = s1 * (count - s1) * (u1 - u2) * (u1 - u2);
thr = i;
}
s0 = s1;
u0 = u1;
}
return thr;
}
</pre>
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온라인 카지노 커뮤니티 온카허브 입니다. 온카허브는 카지노 먹튀 사이트들과 안전한 카지노 사이트 정보를 공유하고 있습니다. 카지노 먹튀검증 전문팀을 자체적으로 운영함으로써 철저한 검증을 진행하고 있습니다
2024年4月06日 16:35
A few things i have seen in terms of laptop or computer memory is that often there are features such as SDRAM, DDR etc, that must fit in with the specs of the mother board. If the personal computer’s motherboard is reasonably current while there are no operating-system issues, improving the memory literally will take under a couple of hours. It’s one of the easiest computer upgrade types of procedures one can envision. Thanks for sharing your ideas. Carpal Tunnel Surgery St. Louis
2024年4月08日 10:38
온라인 카지노 커뮤니티 온카허브 입니다. 온카허브는 카지노 먹튀 사이트들과 안전한 카지노 사이트 정보를 공유하고 있습니다. 카지노 먹튀검증 전문팀을 자체적으로 운영함으로써 철저한 검증을 진행하고 있습니다.