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Ceres入门详解

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Ceres入门详解
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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 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( new AutoDiffCostFunctor); problem.AddResidualBlock(CostFunction,NULL,&x); 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( new NumericDiffCostFunctor); x = 0.2; problem.AddResidualBlock(CostFunction,NULL,&x); 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,&x); 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; };

  • 【Ceres入门详解】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 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 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 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 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 = 1; 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(new CostFuntorF1); CostFunction* costfunction2 = new AutoDiffCostFunction(new CostFuntorF2); CostFunction* costfunction3 = new AutoDiffCostFunction(new CostFuntorF3); CostFunction* costfunction4 = new AutoDiffCostFunction(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 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 = 1; 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( 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 #include #include #include 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 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 distribution(0.0,0.5); //y = exp(0.3*x + 0.1) for(int i=0; i( new CostFunctor(data[i].x, data[i].y)); problem.AddResidualBlock(costfunction, NULL, &m, &c); }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 << "Finalm: " << m << " c: " << c << "\n"; //Analytic m = 3.0, c = 1.1; for(int i=0; i

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