参考:https://blog.csdn.net/liyuanbhu/article/details/50866802
描述:
- 最小二乘法直线拟合(不是常见的一元线性回归算法)
- 将离散点拟合为 a x + b y + c = 0 型直线
- 假设每个点的 X Y 坐标的误差都是符合 0 均值的正态分布的。
- 与一元线性回归算法的区别:一元线性回归算法假定 X 是无误差的,只有 Y 有误差。
注:points为存入多个点的容器,利用已知点,求出直线方程中的系数a,b,c,并在onpaint()函数中画出直线
double a, b, c; int size = points.size(); if(size < 2) { a = 0; b = 0; c = 0; } double x_mean = 0; double y_mean = 0; for(int i = 0; i < size; i++) { x_mean += points[i].x; y_mean += points[i].y; } x_mean /= size; y_mean /= size; //至此,计算出了 x y 的均值 double Dxx = 0, Dxy = 0, Dyy = 0; for(int i = 0; i < size; i++) { Dxx += (points[i].x - x_mean) * (points[i].x - x_mean); Dxy += (points[i].x - x_mean) * (points[i].y - y_mean); Dyy += (points[i].y - y_mean) * (points[i].y - y_mean); } double lambda = ( (Dxx + Dyy) - sqrt( (Dxx - Dyy) * (Dxx - Dyy) + 4 * Dxy * Dxy) ) / 2.0; double den = sqrt( Dxy * Dxy + (lambda - Dxx) * (lambda - Dxx) ); if(fabs(den) < 1e-5) { if( fabs(Dxx / Dyy - 1) < 1e-5) //这时没有一个特殊的直线方向,无法拟合 { } else { a = 1; b = 0; c = - x_mean; } } else { a = Dxy / den; b = (lambda - Dxx) / den; c = - a * x_mean - b * y_mean; } CDC *pDC1 = m_pic.GetWindowDC(); CPen pen1(PS_SOLID,1,RGB(0,0,255)); pDC1->SelectObject(&pen1); pDC1->MoveTo((points.at(0).x)/cx*width,-((a*points.at(0).x+c)/b)/cy*height); pDC1->LineTo((points.at(4).x)/cx*width,-((a*points.at(4).x+c)/b)/cy*height);
效果: