https://blog.csdn.net/Jacky_Ponder/article/details/70314919
1.1最小二乘擬合圓介紹與推導
最小二乘法(least squares analysis)是一種數學優化技術，它通過最小化誤差的平方和找到一組數據的最佳函數匹配。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據的最佳匹配函數的計算方法，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計的檢測方法，即便是圖像中圓形目標受光照強度不均等因素的影響而產生邊緣缺失，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過程和vc實現。
1.2VC實現的代碼
[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>
---------------------
作者：Jacky_Ponder
來源：CSDN
原文：https://blog.csdn.net/Jacky_Ponder/article/details/70314919
版權聲明：本文為博主原創文章，轉載請附上博文鏈接！