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将拟合类函数独立成一个模块

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jerryzeng 2026-02-08 22:47:35 +08:00
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#include "SG_baseDataType.h"
#include "SG_baseAlgo_Export.h"
#include <vector>
#ifdef __WIN32
#include <corecrt_math_defines.h>
#endif // __WIN32
#include <cmath>
#include <unordered_map>
#include <Eigen/dense>
void lineFitting(std::vector< SVzNL3DPoint>& inliers, double* _k, double* _b)
{
//最小二乘拟合直线参数
double xx_sum = 0;
double x_sum = 0;
double y_sum = 0;
double xy_sum = 0;
int num = 0;
for (int i = 0; i < inliers.size(); i++)
{
x_sum += inliers[i].x; //x的累加和
y_sum += inliers[i].y; //y的累加和
xx_sum += inliers[i].x * inliers[i].x; //x的平方累加和
xy_sum += inliers[i].x * inliers[i].y; //x，y的累加和
num++;
}
*_k = (num * xy_sum - x_sum * y_sum) / (num * xx_sum - x_sum * x_sum); //根据公式求解k
*_b = (-x_sum * xy_sum + xx_sum * y_sum) / (num * xx_sum - x_sum * x_sum);//根据公式求解b
}
//拟合成通用直线方程ax+by+c=0，包括垂直
void lineFitting_abc(std::vector< SVzNL3DPoint>& inliers, double* _a, double* _b, double* _c)
{
//判断是否为垂直
int dataSize = (int)inliers.size();
if (dataSize < 2)
return;
double deltaX = abs(inliers[0].x - inliers[dataSize - 1].x);
double deltaY = abs(inliers[0].y - inliers[dataSize - 1].y);
std::vector< SVzNL3DPoint> fittingData;
if (deltaX < deltaY)
{
//x=ky+b 拟合
for (int i = 0; i < dataSize; i++)
{
SVzNL3DPoint a_fitPt;
a_fitPt.x = inliers[i].y;
a_fitPt.y = inliers[i].x;
a_fitPt.z = inliers[i].z;
fittingData.push_back(a_fitPt);
}
double k = 0, b = 0;
lineFitting(fittingData, &k, &b);
//ax+by+c
*_a = 1.0;
*_b = -k;
*_c = -b;
}
else
{
//y = kx+b拟合
double k = 0, b = 0;
lineFitting(inliers, &k, &b);
//ax+by+c
*_a = k;
*_b = -1;
*_c = b;
}
return;
}
//圆最小二乘拟合
double fitCircleByLeastSquare(
const std::vector<SVzNL3DPoint>& pointArray,
SVzNL3DPoint& center,
double& radius)
{
int N = pointArray.size();
if (N < 3) {
return std::numeric_limits<double>::max();
}
double sumX = 0.0;
double sumY = 0.0;
double sumX2 = 0.0;
double sumY2 = 0.0;
double sumX3 = 0.0;
double sumY3 = 0.0;
double sumXY = 0.0;
double sumXY2 = 0.0;
double sumX2Y = 0.0;
for (int pId = 0; pId < N; ++pId) {
sumX += pointArray[pId].x;
sumY += pointArray[pId].y;
double x2 = pointArray[pId].x * pointArray[pId].x;
double y2 = pointArray[pId].y * pointArray[pId].y;
sumX2 += x2;
sumY2 += y2;
sumX3 += x2 * pointArray[pId].x;
sumY3 += y2 * pointArray[pId].y;
sumXY += pointArray[pId].x * pointArray[pId].y;
sumXY2 += pointArray[pId].x * y2;
sumX2Y += x2 * pointArray[pId].y;
}
double C, D, E, G, H;
double a, b, c;
C = N * sumX2 - sumX * sumX;
D = N * sumXY - sumX * sumY;
E = N * sumX3 + N * sumXY2 - (sumX2 + sumY2) * sumX;
G = N * sumY2 - sumY * sumY;
H = N * sumX2Y + N * sumY3 - (sumX2 + sumY2) * sumY;
a = (H * D - E * G) / (C * G - D * D);
b = (H * C - E * D) / (D * D - G * C);
c = -(a * sumX + b * sumY + sumX2 + sumY2) / N;
center.x = -a / 2.0;
center.y = -b / 2.0;
radius = sqrt(a * a + b * b - 4 * c) / 2.0;
double err = 0.0;
double e;
double r2 = radius * radius;
for (int pId = 0; pId < N; ++pId) {
e = pow(pointArray[pId].x - center.x, 2) + pow(pointArray[pId].y - center.y, 2) - r2;
if (e > err) {
err = e;
}
}
return err;
}
#if 0
bool leastSquareParabolaFit(const std::vector<cv::Point2d>& points,
double& a, double& b, double& c,
double& mse, double& max_err)
{
// 校验点集数量（至少3个点才能拟合抛物线）
int n = points.size();
if (n < 3) {
return false;
}
// 初始化各项求和参数
double sum_x = 0.0, sum_x2 = 0.0, sum_x3 = 0.0, sum_x4 = 0.0;
double sum_y = 0.0, sum_xy = 0.0, sum_x2y = 0.0;
// 计算各项求和
for (const auto& p : points) {
double x = p.x;
double y = p.y;
double x2 = x * x;
double x3 = x2 * x;
double x4 = x3 * x;
sum_x += x;
sum_x2 += x2;
sum_x3 += x3;
sum_x4 += x4;
sum_y += y;
sum_xy += x * y;
sum_x2y += x2 * y;
}
// 构建线性方程组 M * [a,b,c]^T = N
// M矩阵：3x3
double M[3][3] = {
{sum_x4, sum_x3, sum_x2},
{sum_x3, sum_x2, sum_x},
{sum_x2, sum_x, (double)n}
};
// N向量：3x1
double N[3] = { sum_x2y, sum_xy, sum_y };
// 高斯消元法求解线性方程组（3元一次方程组）
// 步骤1：将M转化为上三角矩阵
for (int i = 0; i < 3; i++) {
// 选主元（避免除数为0）
int pivot = i;
for (int j = i; j < 3; j++) {
if (fabs(M[j][i]) > fabs(M[pivot][i])) {
pivot = j;
}
}
// 交换行
std::swap(M[i], M[pivot]);
std::swap(N[i], N[pivot]);
// 归一化主元行
double div = M[i][i];
if (fabs(div) < 1e-10) {
return false;
}
for (int j = i; j < 3; j++) {
M[i][j] /= div;
}
N[i] /= div;
// 消去下方行
for (int j = i + 1; j < 3; j++) {
double factor = M[j][i];
for (int k = i; k < 3; k++) {
M[j][k] -= factor * M[i][k];
}
N[j] -= factor * N[i];
}
}
// 步骤2：回代求解
c = N[2];
b = N[1] - M[1][2] * c;
a = N[0] - M[0][1] * b - M[0][2] * c;
// 计算拟合误差
mse = 0.0;
max_err = 0.0;
for (const auto& p : points) {
double y_fit = a * p.x * p.x + b * p.x + c;
double err = y_fit - p.y;
double err_abs = fabs(err);
mse += err * err;
if (err_abs > max_err) {
max_err = err_abs;
}
}
mse /= n; // 均方误差
return true;
}
#endif
//抛物线最小二乘拟合 y=ax^2 + bx + c
bool leastSquareParabolaFitEigen(
const std::vector<cv::Point2d>& points,
double& a, double& b, double& c,
double& mse, double& max_err)
{
int n = points.size();
if (n < 3) {
return false;
}
// 构建系数矩阵A和目标向量B
Eigen::MatrixXd A(n, 3);
Eigen::VectorXd B(n);
for (int i = 0; i < n; i++) {
double x = points[i].x;
A(i, 0) = x * x;
A(i, 1) = x;
A(i, 2) = 1.0;
B(i) = points[i].y;
}
// 最小二乘求解：Ax = B，直接调用Eigen的求解器
Eigen::Vector3d coeffs = A.bdcSvd(Eigen::ComputeThinU | Eigen::ComputeThinV).solve(B);
a = coeffs(0);
b = coeffs(1);
c = coeffs(2);
// 计算误差
mse = 0.0;
max_err = 0.0;
for (const auto& p : points) {
double y_fit = a * p.x * p.x + b * p.x + c;
double err = y_fit - p.y;
double err_abs = fabs(err);
mse += err * err;
if (err_abs > max_err) {
max_err = err_abs;
}
}
mse /= n;
return true;
}
//计算面参数: z = Ax + By + C
//res: [0]=A, [1]= B, [2]=-1.0, [3]=C,
void vzCaculateLaserPlane(std::vector<cv::Point3f> Points3ds, std::vector<double>& res)
{
//最小二乘法拟合平面
//获取cv::Mat的坐标系以纵向为x轴，横向为y轴，而cvPoint等则相反
//系数矩阵
cv::Mat A = cv::Mat::zeros(3, 3, CV_64FC1);
//
cv::Mat B = cv::Mat::zeros(3, 1, CV_64FC1);
//结果矩阵
cv::Mat X = cv::Mat::zeros(3, 1, CV_64FC1);
double x2 = 0, xiyi = 0, xi = 0, yi = 0, zixi = 0, ziyi = 0, zi = 0, y2 = 0;
for (int i = 0; i < Points3ds.size(); i++)
{
x2 += (double)Points3ds[i].x * (double)Points3ds[i].x;
y2 += (double)Points3ds[i].y * (double)Points3ds[i].y;
xiyi += (double)Points3ds[i].x * (double)Points3ds[i].y;
xi += (double)Points3ds[i].x;
yi += (double)Points3ds[i].y;
zixi += (double)Points3ds[i].z * (double)Points3ds[i].x;
ziyi += (double)Points3ds[i].z * (double)Points3ds[i].y;
zi += (double)Points3ds[i].z;
}
A.at<double>(0, 0) = x2;
A.at<double>(1, 0) = xiyi;
A.at<double>(2, 0) = xi;
A.at<double>(0, 1) = xiyi;
A.at<double>(1, 1) = y2;
A.at<double>(2, 1) = yi;
A.at<double>(0, 2) = xi;
A.at<double>(1, 2) = yi;
A.at<double>(2, 2) = (double)((int)Points3ds.size());
B.at<double>(0, 0) = zixi;
B.at<double>(1, 0) = ziyi;
B.at<double>(2, 0) = zi;
//计算平面系数
X = A.inv() * B;
//A
res.push_back(X.at<double>(0, 0));
//B
res.push_back(X.at<double>(1, 0));
//Z的系数为-1
res.push_back(-1.0);
//C
res.push_back(X.at<double>(2, 0));
return;
}
/**
* @brief 空间直线最小二乘拟合
* @param points 输入的三维点集（至少2个点，否则无意义）
* @param center 输出：拟合直线的质心（基准点P0）
* @param direction 输出：拟合直线的方向向量v（单位化）
* @return 拟合是否成功（点集有效返回true）
*/
bool fitLine3DLeastSquares(const std::vector<SVzNL3DPoint>& points, SVzNL3DPoint& center, SVzNL3DPoint& direction)
{
// 检查点集有效性
if (points.size() < 2) {
std::cerr << "Error: 点集数量必须大于等于2！" << std::endl;
return false;
}
int n = points.size();
Eigen::MatrixXd A(n, 3); // 点集矩阵：每行一个点的(x,y,z)
// 1. 计算质心（center）
double cx = 0.0, cy = 0.0, cz = 0.0;
for (const auto& p : points) {
cx += p.x;
cy += p.y;
cz += p.z;
A.row(points.size() - n) << p.x, p.y, p.z; // 填充点集矩阵
n--;
}
cx /= points.size();
cy /= points.size();
cz /= points.size();
center = { cx, cy, cz };
// 2. 构造去中心化的协方差矩阵（3x3）
// 关键修复：使用RowVector3d（行向量）做rowwise减法，匹配维度
Eigen::RowVector3d centroid_row(cx, cy, cz);
Eigen::MatrixXd centered = A.rowwise() - centroid_row; // 维度匹配，无报错
// 协方差矩阵计算（n-1为无偏估计，工程中也可直接用n）
Eigen::Matrix3d cov = centered.transpose() * centered; // / (points.size() - 1);
// 3. 特征值分解：求协方差矩阵的特征值和特征向量
Eigen::SelfAdjointEigenSolver<Eigen::Matrix3d> eigensolver(cov);
if (eigensolver.info() != Eigen::Success) {
std::cerr << "Error: 特征值分解失败！" << std::endl;
return false;
}
// 最大特征值对应的特征向量即为方向向量（Eigen默认按特征值升序排列，取最后一个）
Eigen::Vector3d dir = eigensolver.eigenvectors().col(2);
// 单位化方向向量（可选，但工程中通常标准化）
dir.normalize();
direction = { dir(0), dir(1), dir(2) };
return true;
}