第6讲 非线性优化
6.3 实践Ceres
环境配置
https://blog.csdn.net/qq_39236499/article/details/122547508
代码详解
#include <iostream>
#include <opencv2/core/core.hpp>
#include <ceres/ceres.h>
#include <chrono>
using namespace std;
// 代价函数的计算模型
struct CURVE_FITTING_COST
{
CURVE_FITTING_COST (double x, double y) : _x(x), _y(y) {}
// 残差的计算
template <typename T>
bool operator() (
const T* const abc, // 模型参数，有3维
T* residual ) const // 残差
{
residual[0]=T(_y)-ceres::exp(abc[0]*T(_x)*T(_x)+abc[1]*T (_x)+abc[2]);
// y-exp(ax^2+bx+c)
return true;
}
const double _x, _y; // x,y数据
};
int main ( int argc, char** argv )
{
double a=1.0, b=2.0, c=1.0; // 真实参数值
int N=100; // 数据点 100个样本
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
//生成数据
cout << "生成数据: " << 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;
}
cout << endl;
// 构建最小二乘问题
ceres::Problem problem;
for (int i=0; i<N; i++){
problem.AddResidualBlock ( // 向问题中添加误差项
// 使用自动求导，模板参数：误差类型，输出维度，输入维度，维数要与前面struct中一致
new ceres::AutoDiffCostFunction<CURVE_FITTING_COST, 1, 3> (
new CURVE_FITTING_COST ( x_data[i], y_data[i] )
),
nullptr, // 核函数，这里不使用，为空
abc // 待估计参数
);
}
// 配置求解器
ceres::Solver::Options options; // 这里有很多配置项可以填
options.linear_solver_type = ceres::DENSE_QR; // 增量方程如何求解
options.minimizer_progress_to_stdout = true; // 输出到cout
ceres::Solver::Summary summary; // 优化信息
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
ceres::Solve ( options, &problem, &summary ); // 开始优化
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>( t2-t1 );
cout << endl;
cout << "solve time cost = " << time_used.count() << " seconds. " << endl;
// 输出结果
cout << summary.BriefReport() << endl;
cout << "estimated a,b,c = ";
for (auto i : abc){
cout << i << " ";
}
cout << endl;
return 0;
}
6.4 实践：g2o
环境配置
还没安装成功，之后来补
代码详解
#include <iostream>
#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_MAKE_ALIGNED_OPERATOR_NEW
virtual void setToOriginImpl() { // 顶点重置
_estimate << 0,0,0;
}
virtual void oplusImpl( const double* update ) { // 顶点更新
_estimate += Eigen::Vector3d(update);
}
// 存盘和读盘：留空
virtual bool read( istream& in ) {}
virtual bool write( ostream& out ) const {}
};
// 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 ) {}
virtual bool write( ostream& out ) const {}
public:
double _x; // x 值， y 值为 _measurement
};
int main( int argc, char** argv )
{
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;
}
cout << endl;
// 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) );
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
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
cout << endl;
cout << "开始优化：" << endl;
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
optimizer.initializeOptimization();
optimizer.optimize(100);
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "solve time cost = " << time_used.count() << " seconds. " << endl;
// 输出优化值
Eigen::Vector3d abc_estimate = v->estimate();
cout << "estimated model: " << abc_estimate.transpose() << endl;
return 0;
}