386 lines
9.1 KiB
C++
386 lines
9.1 KiB
C++
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#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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//<2F><>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֱ<EFBFBD>߲<EFBFBD><DFB2><EFBFBD>
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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<><78><EFBFBD>ۼӺ<DBBC>
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y_sum += inliers[i].y; //y<><79><EFBFBD>ۼӺ<DBBC>
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xx_sum += inliers[i].x * inliers[i].x; //x<><78>ƽ<EFBFBD><C6BD><EFBFBD>ۼӺ<DBBC>
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xy_sum += inliers[i].x * inliers[i].y; //x<><78>y<EFBFBD><79><EFBFBD>ۼӺ<DBBC>
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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); //<2F><><EFBFBD>ݹ<EFBFBD>ʽ<EFBFBD><CABD><EFBFBD><EFBFBD>k
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*_b = (-x_sum * xy_sum + xx_sum * y_sum) / (num * xx_sum - x_sum * x_sum);//<2F><><EFBFBD>ݹ<EFBFBD>ʽ<EFBFBD><CABD><EFBFBD><EFBFBD>b
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}
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//<2F><><EFBFBD>ϳ<EFBFBD>ͨ<EFBFBD><CDA8>ֱ<EFBFBD>߷<EFBFBD><DFB7><EFBFBD>ax+by+c=0<><30><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֱ
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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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//<2F>ж<EFBFBD><D0B6>Ƿ<EFBFBD>Ϊ<EFBFBD><CEAA>ֱ
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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 <20><><EFBFBD><EFBFBD>
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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<><62><EFBFBD><EFBFBD>
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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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//Բ<><D4B2>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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// У<><D0A3><EFBFBD>㼯<EFBFBD><E3BCAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>3<EFBFBD><33><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ߣ<EFBFBD>
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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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// <20><>ʼ<EFBFBD><CABC><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ͳ<EFBFBD><CDB2><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Է<EFBFBD><D4B7><EFBFBD><EFBFBD><EFBFBD> M * [a,b,c]^T = N
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// M<><4D><EFBFBD><EFBFBD><EFBFBD><EFBFBD>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<><4E><EFBFBD><EFBFBD><EFBFBD><EFBFBD>3x1
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double N[3] = { sum_x2y, sum_xy, sum_y };
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// <20><>˹<EFBFBD><CBB9>Ԫ<EFBFBD><D4AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Է<EFBFBD><D4B7><EFBFBD><EFBFBD>飨3Ԫһ<D4AA>η<EFBFBD><CEB7><EFBFBD><EFBFBD>飩
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// <20><><EFBFBD><EFBFBD>1<EFBFBD><31><EFBFBD><EFBFBD>Mת<4D><D7AA>Ϊ<EFBFBD><CEAA><EFBFBD><EFBFBD><EFBFBD>Ǿ<EFBFBD><C7BE><EFBFBD>
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for (int i = 0; i < 3; i++) {
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// ѡ<><D1A1>Ԫ<EFBFBD><D4AA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ0<CEAA><30>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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std::swap(M[i], M[pivot]);
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std::swap(N[i], N[pivot]);
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// <20><>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>Ԫ<EFBFBD><D4AA>
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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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// <20><>ȥ<EFBFBD>·<EFBFBD><C2B7><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD>2<EFBFBD><32><EFBFBD>ش<EFBFBD><D8B4><EFBFBD><EFBFBD><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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; // <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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return true;
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}
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#endif
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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD> 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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// <20><><EFBFBD><EFBFBD>ϵ<EFBFBD><CFB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>A<EFBFBD><41>Ŀ<EFBFBD><C4BF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>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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// <20><>С<EFBFBD><D0A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>⣺Ax = B<><42>ֱ<EFBFBD>ӵ<EFBFBD><D3B5><EFBFBD>Eigen<65><6E><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>: 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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//<2F><>С<EFBFBD><D0A1><EFBFBD>˷<EFBFBD><CBB7><EFBFBD><EFBFBD><EFBFBD>ƽ<EFBFBD><C6BD>
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//<2F><>ȡcv::Mat<61><74><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ϵ<EFBFBD><CFB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊx<CEAA>ᣬ<EFBFBD><E1A3AC><EFBFBD><EFBFBD>Ϊy<CEAA>ᣬ<EFBFBD><E1A3AC>cvPoint<6E><74><EFBFBD><EFBFBD><EFBFBD>෴
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//ϵ<><CFB5><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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//<2F><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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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//<2F><><EFBFBD><EFBFBD>ƽ<EFBFBD><C6BD>ϵ<EFBFBD><CFB5>
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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<><5A>ϵ<EFBFBD><CFB5>Ϊ-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 <EFBFBD>ռ<EFBFBD>ֱ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>С<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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* @param points <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ά<EFBFBD>㼯<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>2<EFBFBD><EFBFBD><EFBFBD>㣬<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>壩
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* @param center <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֱ<EFBFBD>ߵ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>P0<EFBFBD><EFBFBD>
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* @param direction <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֱ<EFBFBD>ߵķ<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>v<EFBFBD><EFBFBD><EFBFBD><EFBFBD>λ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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* @return <EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ƿ<EFBFBD><EFBFBD>ɹ<EFBFBD><EFBFBD><EFBFBD><EFBFBD>㼯<EFBFBD><EFBFBD>Ч<EFBFBD><EFBFBD><EFBFBD><EFBFBD>true<EFBFBD><EFBFBD>
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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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// <20><><EFBFBD><EFBFBD><EFBFBD>㼯<EFBFBD><E3BCAF>Ч<EFBFBD><D0A7>
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if (points.size() < 2) {
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std::cerr << "Error: <20>㼯<EFBFBD><E3BCAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ڵ<EFBFBD><DAB5><EFBFBD>2<EFBFBD><32>" << 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); // <20>㼯<EFBFBD><E3BCAF><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ÿ<EFBFBD><C3BF>һ<EFBFBD><D2BB><EFBFBD><EFBFBD><EFBFBD><EFBFBD>(x,y,z)
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// 1. <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ģ<EFBFBD>center<65><72>
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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; // <20><><EFBFBD><EFBFBD><EFBFBD>㼯<EFBFBD><E3BCAF><EFBFBD><EFBFBD>
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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. <20><><EFBFBD><EFBFBD>ȥ<EFBFBD><C8A5><EFBFBD>Ļ<EFBFBD><C4BB><EFBFBD>Э<EFBFBD><D0AD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>3x3<78><33>
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// <20>ؼ<EFBFBD><D8BC><EFBFBD><DEB8><EFBFBD>ʹ<EFBFBD><CAB9>RowVector3d<33><64><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>rowwise<73><65><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ƥ<EFBFBD><C6A5>ά<EFBFBD><CEAC>
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Eigen::RowVector3d centroid_row(cx, cy, cz);
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Eigen::MatrixXd centered = A.rowwise() - centroid_row; // ά<><CEAC>ƥ<EFBFBD>䣬<EFBFBD>ޱ<EFBFBD><DEB1><EFBFBD>
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// Э<><D0AD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>㣨n-1Ϊ<31><CEAA>ƫ<EFBFBD><C6AB><EFBFBD>ƣ<EFBFBD><C6A3><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ҳ<EFBFBD><D2B2>ֱ<EFBFBD><D6B1><EFBFBD><EFBFBD>n<EFBFBD><6E>
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Eigen::Matrix3d cov = centered.transpose() * centered; // / (points.size() - 1);
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// 3. <20><><EFBFBD><EFBFBD>ֵ<EFBFBD>ֽ⣺<D6BD><E2A3BA>Э<EFBFBD><D0AD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>
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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: <20><><EFBFBD><EFBFBD>ֵ<EFBFBD>ֽ<EFBFBD>ʧ<EFBFBD>ܣ<EFBFBD>" << std::endl;
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return false;
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}
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// <20><><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><D6B5>Ӧ<EFBFBD><D3A6><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>Ϊ<EFBFBD><CEAA><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>EigenĬ<6E>ϰ<EFBFBD><CFB0><EFBFBD><EFBFBD><EFBFBD>ֵ<EFBFBD><D6B5><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>У<EFBFBD>ȡ<EFBFBD><C8A1><EFBFBD><EFBFBD>һ<EFBFBD><D2BB><EFBFBD><EFBFBD>
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Eigen::Vector3d dir = eigensolver.eigenvectors().col(2);
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// <20><>λ<EFBFBD><CEBB><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ѡ<EFBFBD><D1A1><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>ͨ<EFBFBD><CDA8><EFBFBD><EFBFBD><EFBFBD><D7BC><EFBFBD><EFBFBD>
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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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