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