ITK—空間點的直線擬合

基於最小二乘的直線擬合。

一、二維座標點

typedef  itk::Image<short, 3>      ITKImageType;
typedef ITKImageType::PointType PointType;

void FittingLine(vector<PointType> phy_point)
{
	int number = phy_point.size();
	double x_sum = 0;
	double y_sum = 0;
	double xy_sum = 0;
	double x2_sum = 0;
	for (int i = 0; i < phy_point.size(); i++)
	{
		x_sum = x_sum + phy_point[i][0];
		y_sum = y_sum + phy_point[i][1];
		xy_sum = xy_sum + phy_point[i][0] * phy_point[i][1];
		x2_sum = x2_sum + phy_point[i][0] * phy_point[i][0];
	}
	double temp = number*x2_sum - x_sum*x_sum;
	//y =ax+b
	double a = 0;
	double b = 0;
	if (temp != 0)// 判斷分母不爲0
	{
		a = (number*xy_sum - x_sum*y_sum) / temp;
		b = (x2_sum*y_sum - x_sum*xy_sum) / temp;
	}
	else
	{
		a = 1;
		b = 0;
	}

}

二、三維座標點

typedef  itk::Image<short, 3>      ITKImageType;
typedef ITKImageType::PointType PointType;

void FittingLine(vector<PointType> phy_point)
{
	cout << "開始擬合軸線:" << endl;
	double x_sum = 0;
	double y_sum = 0;
	double z_sum = 0;
	double xz_sum = 0;
	double yz_sum = 0;
	double z2_sum = 0;

	for (int i = 0; i < phy_point.size(); i++)
	{
		x_sum = x_sum + phy_point[i][0];
		y_sum = y_sum + phy_point[i][1];
		z_sum = z_sum + phy_point[i][2];
		xz_sum = xz_sum + phy_point[i][0] * phy_point[i][2];
		yz_sum = yz_sum + phy_point[i][1] * phy_point[i][2];
		z2_sum = z2_sum + phy_point[i][2] * phy_point[i][2];
	}
	//cout << x_sum <<" " << y_sum<<" "<< z_sum<<" "<< xz_sum<<" "<< yz_sum<<" "<< z2_sum<<endl;

	typedef itk::Matrix <double, 2, 2> MatrixType;
	MatrixType A;
	MatrixType B;
	A(0, 0) = xz_sum;
	A(0, 1) = x_sum;
	A(1, 0) = yz_sum;
	A(1, 1) = y_sum;

	B(0, 0) = z2_sum;
	B(0, 1) = z_sum;
	B(1, 0) = z_sum;
	B(1, 1) = phy_point.size();

	MatrixType P;
	P = A*B.GetInverse();
	//cout << P<< endl;
	vector<double> line;
	line.push_back(P(0, 0));
	line.push_back(P(0, 1));
	line.push_back(P(1, 0));
	line.push_back(P(1, 1));
	return line;

}