ceres优化库的一点总结（问题构建总结和求导方式的分析）

1.Ceres中求解一个优化问题的结构

背景：在SLAM中，很多问题都是在求解Translation（包含旋转和平移量），因此这里以其为代表，来分析使用ceres如何对其近求导。

void Calibrator::Optimize(Eigen::Matrix4d& tf)
{
   
   
    //待优化参数分别为rotation和t
    Eigen::Matrix3d rot = T_.topLeftCorner(3,3);
    Eigen::Quaterniond q (rot);
    Eigen::Vector3d p = T_.topRightCorner(3,1);

    ceres::Problem problem;
    ceres::Solver::Summary summary;
    ceres::Solver::Options options;
    ceres::LossFunction* loss_function_edge (new ceres::SoftLOneLoss(1));

    ceres::LocalParameterization* quaternion_local_parameterization =
        new ceres::EigenQuaternionParameterization;

    for(const auto& ply : polygons_)
    {
   
   
        // add edge 误差来源：每一条3D点云边上的点，到2D平面的直线的距离
        for(uint32_t i=0; i<size_; i++)
        {
   
   
            if(ply.pc->edges[i].points.cols() == 0)
            {
   
   
                continue;
            }
            ceres::CostFunction* cost = new ceres::AutoDiffCostFunction<Edge2EdgeError, 1,4,3>(new Edge2EdgeError( K_, ply.pc->edges[i].points, ply.img->edges[ply.ids[i]].coef ));//
            problem.AddResidualBlock(cost, loss_function_edge,q.coeffs().data(), p.data());
        }
    }
    problem.SetParameterization(q.coeffs().data(), quaternion_local_parameterization);
    options.linear_solver_type = ceres::SPARSE_NORMAL_CHOLESKY;
    options.max_num_iterations = 5000;
    options.num_threads= boost::thread::hardware_concurrency() - 1;
    options.num_linear_solver_threads = options.num_threads;

    ceres::Solve(options, &problem,