G2O曲线拟合1

用G2O来拟合曲线，拟合模型：y = exp(a*x*x + b*x + c);

首先利用opencv产生随机数，x_data， y_data；同时我们把随机数写入txt，通过matlab来拟合检验

#include <iostream>
#include<fstream>
#include<iomanip>

#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/optimization_algorithm_levenberg.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/core/optimization_algorithm_dogleg.h>
#include <g2o/solvers/dense/linear_solver_dense.h>
#include <Eigen/Core>
#include <opencv2/core/core.hpp>
#include <cmath>
#include <chrono>

using namespace std; 

// 曲线模型的顶点，模板参数：优化变量维度和数据类型
class CurveFittingVertex: public g2o::BaseVertex<3, Eigen::Vector3d>
{
public:
    // Eigen库为了使用SSE加速，所以内存分配上使用了128位的指针
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW// 参考 https://blog.csdn.net/rs_huangzs/article/details/50574141

    virtual void setToOriginImpl() // 顶点重置
    {
        _estimate << 0,0,0;
    }
    
    virtual void oplusImpl( const double* update ) // 顶点更新，X_k+1 = X_k + X_delta
    {
        _estimate += Eigen::Vector3d(update);
    }
    // 存盘和读盘：留空
    virtual bool read(istream& in) { return 0; }
    virtual bool write( ostream& out ) const { return 0; }
};

// 误差模型 模板参数：观测值维度，类型，连接顶点类型
class CurveFittingEdge: public g2o::BaseUnaryEdge<1,double,CurveFittingVertex>
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW
    CurveFittingEdge( double x ): BaseUnaryEdge(), _x(x) {}
    // 计算曲线模型误差
    void computeError()
    {
        const CurveFittingVertex* v = static_cast<const CurveFittingVertex*> (_vertices[0]);
        const Eigen::Vector3d abc = v->estimate();
        _error(0,0) = _measurement - std::exp( abc(0,0)*_x*_x + abc(1,0)*_x + abc(2,0) );
    }
    virtual bool read( istream& in ) { return 0; }
    virtual bool write( ostream& out ) const { return 0; }
public:
    double _x;  // x 值， y 值为 _measurement
};

int main( int argc, char** argv )
{
    // 产生带噪声的数据
    double a=1.0, b=2.0, c=1.0;         // 真实参数值
    int N=100;                          // 数据点
    double w_sigma=1.0;                 // 噪声Sigma值
    cv::RNG rng;                        // OpenCV随机数产生器
    double abc[3] = {0,0,0};            // abc参数的估计值

    vector<double> x_data, y_data;      // 数据
    
    cout<<"generating data: "<<endl;
    for ( int i=0; i<N; i++ )
    {
        double x = i/100.0;
        x_data.push_back ( x );
        y_data.push_back (
            exp ( a*x*x + b*x + c ) + rng.gaussian ( w_sigma ) 
        );
        cout<<x_data[i]<<" "<<y_data[i]<<endl;
    }
    
    //将数据写入文本
    //创建文件
    fstream f("file_1.txt", ios::out);
    if (f.bad())
    {
        cout << "打开文件出错" << endl;
        return 0;
    }
    //写入x
    for (size_t i = 0; i < x_data.size(); i++)
    {
        f << x_data[i] << "  ";
    }
    f << endl;//换行
    //写入y
    for (size_t i = 0; i < y_data.size(); i++)
    {
        f << y_data[i] << " ";
    }
    //关闭文件
    f.close();


    // 构建图优化，先设定g2o
    typedef g2o::BlockSolver< g2o::BlockSolverTraits<3,1> > Block;  // 每个误差项优化变量维度为3，误差值维度为1
    Block::LinearSolverType* linearSolver = new g2o::LinearSolverDense<Block::PoseMatrixType>(); // 线性方程求解器
    Block* solver_ptr = new Block( linearSolver );      // 矩阵块求解器
    // 梯度下降方法，从GN, LM, DogLeg 中选
    g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg( solver_ptr );
    //g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(solver_ptr);
    //g2o::OptimizationAlgorithmDogleg* solver = new g2o::OptimizationAlgorithmDogleg(solver_ptr);

    g2o::SparseOptimizer optimizer;     // 图模型
    optimizer.setAlgorithm( solver );   // 设置求解器
    optimizer.setVerbose( true );       // 打开调试输出
    
    // 往图中增加顶点
    CurveFittingVertex* v = new CurveFittingVertex();
    v->setEstimate( Eigen::Vector3d(0,0,0) );//猜想初始值
    v->setId(0);
    optimizer.addVertex( v );
    
    // 往图中增加边
    for ( int i=0; i<N; i++ )
    {
        CurveFittingEdge* edge = new CurveFittingEdge( x_data[i] );
        edge->setId(i);
        edge->setVertex( 0, v );                // 设置连接的顶点 //  set the ith vertex on the hyper-edge to the pointer supplied
        edge->setMeasurement( y_data[i] );      // 观测数值
        edge->setInformation( Eigen::Matrix<double,1,1>::Identity()*1/(w_sigma*w_sigma) ); // 信息矩阵：协方差矩阵之逆
        optimizer.addEdge( edge );
    }
    
    // 执行优化
    optimizer.initializeOptimization();
    optimizer.optimize(100);
    // 输出优化值
    Eigen::Vector3d abc_estimate = v->estimate();
    cout<<"estimated model: "<<abc_estimate.transpose()<<endl;
    
    return 0;
}

g2o拟合结果： 

a = 0.890911;
b = 2.1719;
c = 0.943629;

我们基于此，利用如下matlab代码，将随机数和G2O拟合结果可视化

%%clear all
close all
clc
load file_1.txt
%% 待拟合数据
temp = file_1;
x1 = temp(1,:);
y1 = temp(2,:);

plot(x1,y1,'*'); hold on;

%% plot the results of G2O
syms x;
a = 0.890911;
b = 2.1719;
c = 0.943629;
x = 0:0.01:0.99;
y = zeros(1,100);
[m,n] = size(x);
for i = 1:1:n
   y(i) = exp( a*x(i)*x(i) + b*x(i) + c );
end
plot(x,y);

最后，再看看matlab拟合工具箱拟合结果（其实工具箱强得一笔，随便用其他模型也能达到完美得置信区间和残差）：