C++：最小二乘法 拟合直线 Ax + By + C = 0

一、分享给有需要的人，代码质量勿喷。

参考自 Ziv Yaniv

/* 最小二乘法拟合直线：AX+BY+C=0 */
void FitLineByLeastSquares(std::vector<double> &xjParameters, const std::vector<xjPoint> &xjData)
{
	xjParameters.clear();
	if (xjData.size() < 2)
		return;

	double A = 0.1, B = 0.1, C = 0.1;

	int xjPcount = xjData.size();
	double meanX = 0.1, meanY = 0.1;
	double sumXX = 0.1, sumXY = 0.1, sumYY = 0.1;
	for (int i = 0; i < xjPcount; i++)
	{
		meanX += xjData[i].x;
		meanY += xjData[i].y;

		sumXX += xjData[i].x * xjData[i].x;
		sumXY += xjData[i].x * xjData[i].y;
		sumYY += xjData[i].y * xjData[i].y;
	}
	meanX /= xjPcount;
	meanY /= xjPcount;

	sumXX -= xjPcount * meanX*meanX;
	sumXY -= xjPcount * meanX*meanY;
	sumYY -= xjPcount * meanY*meanY;
	if (sumXX < 1e-15)
	{
		A = 1.0;
		B = 0.0;
	}
	else
	{
		double ev = (sumXX + sumYY + sqrt((sumXX - sumYY)*(sumXX - sumYY) + 4 * sumXY*sumXY)) / 2.0;
		A = -sumXY;
		B = ev - sumYY;
		double norm = sqrt(A*A + B * B);
		A /= norm;
		B /= norm;
	}

	xjParameters.push_back(A);
	xjParameters.push_back(B);
	double C = -(A * meanX + B * meanY);
	xjParameters.push_back(C);
}

二、结果

/* -------------------- 分割线 -------------------- */

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