https://blog.csdn.net/Jacky_Ponder/article/details/70314919
1.1最小二乘擬合圓介紹與推導(dǎo)
最小二乘法(least squares analysis)是一種數(shù)學(xué)優(yōu)化技術(shù)，它通過最小化誤差的平方和找到一組數(shù)據(jù)的最佳函數(shù)匹配。最小二乘法是用最簡的方法求得一些絕對不可知的真值，而令誤差平方之和為最小來尋找一組數(shù)據(jù)的最佳匹配函數(shù)的計算方法，最小二乘法通常用于曲線擬合 (least squares fitting) 。最小二乘圓擬合方法是一種基于統(tǒng)計的檢測方法，即便是圖像中圓形目標(biāo)受光照強度不均等因素的影響而產(chǎn)生邊緣缺失，也不會影響圓心的定位和半徑的檢測，若邊緣定位精確輪廓清晰，最小二乘法可實現(xiàn)亞像素級別的精確擬合定位。
這里有擬合圓曲線的公式推導(dǎo)過程和vc實現(xiàn)。
1.2VC實現(xiàn)的代碼
[cpp] view plain copy
<code class="language-cpp">void CViewActionImageTool::LeastSquaresFitting()
{
if (m_nNum<3)
{
return;
}
int i=0;
double X1=0;
double Y1=0;
double X2=0;
double Y2=0;
double X3=0;
double Y3=0;
double X1Y1=0;
double X1Y2=0;
double X2Y1=0;
for (i=0;i<m_nNum;i++)
{
X1 = X1 + m_points[i].x;
Y1 = Y1 + m_points[i].y;
X2 = X2 + m_points[i].x*m_points[i].x;
Y2 = Y2 + m_points[i].y*m_points[i].y;
X3 = X3 + m_points[i].x*m_points[i].x*m_points[i].x;
Y3 = Y3 + m_points[i].y*m_points[i].y*m_points[i].y;
X1Y1 = X1Y1 + m_points[i].x*m_points[i].y;
X1Y2 = X1Y2 + m_points[i].x*m_points[i].y*m_points[i].y;
X2Y1 = X2Y1 + m_points[i].x*m_points[i].x*m_points[i].y;
}
double C,D,E,G,H,N;
double a,b,c;
N = m_nNum;
C = N*X2 - X1*X1;
D = N*X1Y1 - X1*Y1;
E = N*X3 + N*X1Y2 - (X2+Y2)*X1;
G = N*Y2 - Y1*Y1;
H = N*X2Y1 + N*Y3 - (X2+Y2)*Y1;
a = (H*D-E*G)/(C*G-D*D);
b = (H*C-E*D)/(D*D-G*C);
c = -(a*X1 + b*Y1 + X2 + Y2)/N;
double A,B,R;
A = a/(-2);
B = b/(-2);
R = sqrt(a*a+b*b-4*c)/2;
m_fCenterX = A;
m_fCenterY = B;
m_fRadius = R;
return;
}</code>
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作者：Jacky_Ponder
來源：CSDN
原文：https://blog.csdn.net/Jacky_Ponder/article/details/70314919
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