Ceres入门详解_公众号『机器感知』-CSDN博客

来自 : CSDN技术社区 发布时间：2021-03-24

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机器感知
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开源地址 点击该链接 Ceres用法总结 入门操作

定义CostFunctor(i.e.函数 f ),以 f(x) 10-x 为例

使用自动求导(当使用自动求导时, operator() 是一个模板函数)

struct AutoDiffCostFunctor { template typename T  bool operator()(const T* const x, T* residual) const { //修饰大括号的const必须有 residual[0] T(10.0) - x[0]; //10.0必须强制转换为T类型,否则会编译器会报无法实现运算操作的类型 return true;

使用数值求导

struct NumericDiffCostFunctor { bool operator()(const double* const x, double* residual) const { residual[0] 10.0 - x[0]; return true;

使用函数导数的解析式求导

class QuadraticCostFunction: public ceres::SizedCostFunction 1,1 {public: virtual ~QuadraticCostFunction() {} virtual bool Evaluate(double const* const* parameters,//二维参数块指针 double* residuals, //一维残差指针 double** jacobians) const { //二维jacobian矩阵元素指针,与parameters对应 residuals[0] 10.0 - parameters[0][0]; if(jacobians jacobians[0]) { jacobians[0][0] -1; return true;

主函数对最小二乘问题的实现

int main(int argc, char** argv) const double initial_x 0.2; double x initial_x;Problem problem; Solver::Options options; //control whether the log is output to STDOUT options.minimizer_progress_to_stdout false; Solver::Summary summary; //AutoDiff CostFunction* CostFunction  new AutoDiffCostFunction AutoDiffCostFunctor,1,1 ( new AutoDiffCostFunctor); problem.AddResidualBlock(CostFunction,NULL,  clock_t solve_start clock(); // summary must be non NULL Solve(options, problem, summary); clock_t solve_end clock(); std::cout AutoDiff time : solve_end-solve_start std::endl; std::cout x : initial_x - x std::endl; //NumericDiff CostFunction  new NumericDiffCostFunction NumericDiffCostFunctor,CENTRAL,1,1 ( new NumericDiffCostFunctor); x 0.2; problem.AddResidualBlock(CostFunction,NULL,  solve_start clock(); Solve(options, problem, summary); solve_end clock(); std::cout NumercDiff time : solve_end-solve_start std::endl; std::cout x : initial_x - x std::endl; //AnalyticDiff //QuadraticCostFunction继承自SizedCostFunction,而SizedCostFunction继承自 //CostFunction,因此此语句与上述两种对CostFunction的赋值操作略有不同 CostFunction new QuadraticCostFunction; x 0.2; problem.AddResidualBlock(CostFunction,NULL,  solve_start clock(); Solve(options, problem, summary); solve_end clock(); std::cout AnalyticDiff time : solve_end-solve_start std::endl; std::cout x : initial_x - x std::endl; return 0;

总结

定义CostFunctor,重载 operator() (i.e. f 所表示的运算过程)函数主函数中定义 Problem ,设置一些必要的配置,添加残差块, Solve 求解 Powell’s Function 第一种实现方法

struct CostFuntorF1 {template typename T  bool operator()(const T* const x1, const T* const x2, T* residuals) const { residuals[0] x1[0] T(10)*x2[0]; return true;struct CostFuntorF2 { template typename T  bool operator()(const T* const x3, const T* const x4, T* residuals) const { residuals[0] sqrt(5)*(x3[0] - x4[0]); return true;struct CostFuntorF3 { template typename T  bool operator()(const T* const x2, const T* const x3, T* residuals) const { residuals[0] (x2[0] - T(2)*x3[0])*(x2[0] - T(2)*x3[0]); return true;struct CostFuntorF4 { template typename T  bool operator()(const T* const x1, const T* const x4, T* residuals) const { residuals[0] sqrt(10)*(x1[0] - x4[0])*(x1[0] - x4[0]); return true;int main(int argc, char** argv) const double initial_x1 10, initial_x2 5, initial_x3 2, initial_x4  double x1 initial_x1, x2 initial_x2, x3 initial_x3, x4 initial_x4; Problem problem; Solver::Options options; //control whether the log is output to STDOUT options.minimizer_progress_to_stdout true; Solver::Summary summary; CostFunction* costfunction1  new AutoDiffCostFunction CostFuntorF1,1,1,1 (new CostFuntorF1); CostFunction* costfunction2  new AutoDiffCostFunction CostFuntorF2,1,1,1 (new CostFuntorF2); CostFunction* costfunction3  new AutoDiffCostFunction CostFuntorF3,1,1,1 (new CostFuntorF3); CostFunction* costfunction4  new AutoDiffCostFunction CostFuntorF4,1,1,1 (new CostFuntorF4); problem.AddResidualBlock(costfunction1,NULL, x1, x2); problem.AddResidualBlock(costfunction2,NULL, x3, x4); problem.AddResidualBlock(costfunction3,NULL, x2, x3); problem.AddResidualBlock(costfunction4,NULL, x1, x4); Solve(options, problem, summary); cout x1 : initial_x1 - x1 endl; cout x2 : initial_x2 - x2 endl; cout x3 : initial_x3 - x3 endl; cout x4 : initial_x4 - x4 endl; return 0;

第二种实现方法

struct CostFunctor { template typename T  bool operator()(const T* const x, T* residuals) const{ residuals[0] x[0] - T(10) * x[1]; residuals[1] T(sqrt(5)) * (x[2] - x[4]); residuals[2] (x[1] - T(2) * x[2]) * (x[1] - T(2) * x[2]); residuals[3] T(sqrt(10)) * (x[0] - x[3]) * (x[0] - x[3]); return true;int main(int argc, char** argv) const double initial_x1 10, initial_x2 5, initial_x3 2, initial_x4  Problem problem; Solver::Options options; //control whether the log is output to STDOUT options.minimizer_progress_to_stdout true; Solver::Summary summary; double x[4] {initial_x1, initial_x2, initial_x3, initial_x4}; CostFunction* costfunction new AutoDiffCostFunction CostFunctor, 4, 4 ( new CostFunctor); Problem pb; pb.AddResidualBlock(costfunction,NULL,x); Solve(options, pb, summary); cout x[0] : initial_x1 - x[0] endl; cout x[1] : initial_x2 - x[1] endl; cout x[2] : initial_x3 - x[2] endl; cout x[3] : initial_x4 - x[3] endl; return 0;

曲线拟合 y exp(0.3*x 0.1)

#include iostream #include vector #include random #include ceres/ceres.h using namespace std;using ceres::AutoDiffCostFunction;using ceres::Problem;using ceres::Solver;using ceres::CostFunction;using ceres::SizedCostFunction;struct CostFunctor { CostFunctor(double x, double y): _x(x), _y(y) {} template typename T  bool operator()(const T* const m, const T* const c, T* residual) const { residual[0] T(_y) - exp(m[0]*T(_x) c[0]); return true;private: double _x; double _y;class QuadraticCostFunctor: public SizedCostFunction 1,1,1 {public: QuadraticCostFunctor(double x, double y): _x(x), _y(y) {} virtual ~QuadraticCostFunctor() {} bool Evaluate(double const* const* parameters, double* residuals, double** jacobians) const {//const cant t be ignore! residuals[0] _y - exp(parameters[0][0]*_x parameters[1][0]); if(jacobians jacobians[0] jacobians[1]) { //we should provide Solver negtive gradient! //so that costfunction can decrese.  jacobians[0][0] -_x*exp(parameters[0][0]*_x parameters[1][0]); jacobians[1][0] -exp(parameters[0][0]*_x parameters[1][0]); return true;private: double _x, _y;struct point_data { point_data(): x(0), y(0) {} double x; double y;int main(int argc, char **argv)  //create data with Gaussian noise const int data_size 50; struct point_data data[data_size]; struct point_data point; default_random_engine generator; normal_distribution double distribution(0.0,0.5); //y exp(0.3*x 0.1) for(int i i data_size; i ) { point.x 0.1 * i; point.y exp(0.3*point.x 0.1) distribution(generator); data[i] point; double m 0.0, c 0.1; Problem problem; CostFunction* costfunction; for(int i i data_size; i ) { costfunction new AutoDiffCostFunction CostFunctor,1,1,1 ( new CostFunctor(data[i].x, data[i].y)); problem.AddResidualBlock(costfunction, NULL, m,  Solver::Options options; options.max_num_iterations 25; options.linear_solver_type ceres::DENSE_QR; options.minimizer_progress_to_stdout true; Solver::Summary summary; Solve(options, problem, summary); std::cout summary.BriefReport() \\n  std::cout Initial m: 0.0 c: 0.1 \\n  std::cout Final m: m c: c \\n  //Analytic m 3.0, c 1.1; for(int i i data_size; i ) { costfunction new QuadraticCostFunctor(data[i].x, data[i].y); problem.AddResidualBlock(costfunction, NULL, m,  options.max_num_iterations 100; Solve(options, problem, summary); std::cout summary.BriefReport() \\n  std::cout Initial m: 3.0 c: 1.1 \\n  std::cout Final m: m c: c \\n  return 0;