Ceres-Solver学习笔记(3)

Ceres的一个主要目的是解决大尺度bundle adjustment 问题。多说无益,直接上代码:

// file bal_problem.h
#ifndef CERES_EXAMPLES_BAL_PROBLEM_H_
#define CERES_EXAMPLES_BAL_PROBLEM_H_
#include 

namespace ceres {
namespace examples {

class BALProblem {
 public:
  explicit BALProblem(const std::string& filename, bool use_quaternions);
  ~BALProblem();

  void WriteToFile(const std::string& filename) const;
  void WriteToPLYFile(const std::string& filename) const;


  // 将重建的“中心”移到原点,中心是通过计算点的marginal median来确定的。
  // 然后对重构进行缩放,以便从原点处得到的点的 median absolute deviation 是100.0
  //
  // 问题的重投影误差保持不变
  void Normalize();

  // 用特定标准差的随机正态分布值扰乱相机姿态和几何结构
  void Perturb(const double rotation_sigma,
               const double translation_sigma,
               const double point_sigma);

    //相机参数的个数
  int camera_block_size()      const { return use_quaternions_ ? 10 : 9; }
  // 点参数的个数
  int point_block_size()       const { return 3;                         }
  int num_cameras()            const { return num_cameras_;              }
  int num_points()             const { return num_points_;               }
  int num_observations()       const { return num_observations_;         }
  int num_parameters()         const { return num_parameters_;           }
  const int* point_index()     const { return point_index_;              }
  const int* camera_index()    const { return camera_index_;             }
  const double* observations() const { return observations_;             }
  const double* parameters()   const { return parameters_;               }
  const double* cameras()      const { return parameters_;               }
  double* mutable_cameras()          { return parameters_;               }
  double* mutable_points() {
    return parameters_  + camera_block_size() * num_cameras_;
  }

 private:
  void CameraToAngleAxisAndCenter(const double* camera,
                                  double* angle_axis,
                                  double* center) const;

  void AngleAxisAndCenterToCamera(const double* angle_axis,
                                  const double* center,
                                  double* camera) const;
  int num_cameras_;
  int num_points_;
  int num_observations_;
  int num_parameters_;
  bool use_quaternions_;

  int* point_index_;
  int* camera_index_;
  double* observations_;
  // The parameter vector is laid out as follows
  // [camera_1, ..., camera_n, point_1, ..., point_m]
  double* parameters_;
};

}  // namespace examples
}  // namespace ceres

#endif  // CERES_EXAMPLES_BAL_PROBLEM_H_
// file bundle_adjuster.cc

#include 
#include 
#include 
#include 
#include 
#include 

#include "bal_problem.h"
#include "ceres/ceres.h"
#include "gflags/gflags.h"
#include "glog/logging.h"
#include "snavely_reprojection_error.h"


namespace ceres {
namespace examples {

void SetLinearSolver(Solver::Options* options) {
  // 设置LinearSolver,可选项为:"sparse_schur, dense_schur, iterative_schur,   
  // sparse_normal_cholesky, ""dense_qr, dense_normal_cholesky and cgnr."
  CHECK(StringToLinearSolverType(FLAGS_linear_solver,
                                 &options->linear_solver_type));
  // 设置PreconditionerType,可选项为:"identity, jacobi, 
  // schur_jacobi, cluster_jacobi, ""cluster_tridiagonal."
  CHECK(StringToPreconditionerType(FLAGS_preconditioner,
                                   &options->preconditioner_type));
  // 设置VisibilityClusteringType,可选项为:"single_linkage, 
  // canonical_views"
  CHECK(StringToVisibilityClusteringType(FLAGS_visibility_clustering,
                                         &options->visibility_clustering_type));
  // 设置SparseLinearAlgebraLibraryType,可选项为:"suite_sparse,
  // cx_sparse"
  CHECK(StringToSparseLinearAlgebraLibraryType(
            FLAGS_sparse_linear_algebra_library,
            &options->sparse_linear_algebra_library_type));
  // 设置DenseLinearAlgebraLibraryType,可选项为:"eigen,
  // lapack."
  CHECK(StringToDenseLinearAlgebraLibraryType(
            FLAGS_dense_linear_algebra_library,
            &options->dense_linear_algebra_library_type));
  // 线程数
  options->num_linear_solver_threads = FLAGS_num_threads;
  // 是否使用舍尔补
  options->use_explicit_schur_complement = FLAGS_explicit_schur_complement;
}

void SetOrdering(BALProblem* bal_problem, Solver::Options* options) {
  // 3D点数量
  const int num_points = bal_problem->num_points();
  // 点的维度(3维)
  const int point_block_size = bal_problem->point_block_size();
  // 点数据起始地址
  double* points = bal_problem->mutable_points();

  // 相机姿态数
  const int num_cameras = bal_problem->num_cameras();
  // 相机参数数(9/10)
  const int camera_block_size = bal_problem->camera_block_size();
  // 相机参数起始地址
  double* cameras = bal_problem->mutable_cameras();
  // true(使用内迭代对非线性进行)
  // false(细化每个成功的信任区域步骤)
  if (options->use_inner_iterations) {
    // 可选参数类型automatic, cameras, points,(points,cameras),(cameras,points)
    if (FLAGS_blocks_for_inner_iterations == "cameras") {
      LOG(INFO) << "Camera blocks for inner iterations";
      options->inner_iteration_ordering.reset(new ParameterBlockOrdering);
      for (int i = 0; i < num_cameras; ++i) {
        // 添加元素到一个组
        options->inner_iteration_ordering->AddElementToGroup(cameras + camera_block_size * i, 0);
      }
    } else if (FLAGS_blocks_for_inner_iterations == "points") {
      LOG(INFO) << "Point blocks for inner iterations";
      options->inner_iteration_ordering.reset(new ParameterBlockOrdering);
      for (int i = 0; i < num_points; ++i) {
        options->inner_iteration_ordering->AddElementToGroup(points + point_block_size * i, 0);
      }
    } else if (FLAGS_blocks_for_inner_iterations == "cameras,points") {
      LOG(INFO) << "Camera followed by point blocks for inner iterations";
      options->inner_iteration_ordering.reset(new ParameterBlockOrdering);
      for (int i = 0; i < num_cameras; ++i) {
        options->inner_iteration_ordering->AddElementToGroup(cameras + camera_block_size * i, 0);
      }
      for (int i = 0; i < num_points; ++i) {
        options->inner_iteration_ordering->AddElementToGroup(points + point_block_size * i, 1);
      }
    } else if (FLAGS_blocks_for_inner_iterations == "points,cameras") {
      LOG(INFO) << "Point followed by camera blocks for inner iterations";
      options->inner_iteration_ordering.reset(new ParameterBlockOrdering);
      for (int i = 0; i < num_cameras; ++i) {
        options->inner_iteration_ordering->AddElementToGroup(cameras + camera_block_size * i, 1);
      }
      for (int i = 0; i < num_points; ++i) {
        options->inner_iteration_ordering->AddElementToGroup(points + point_block_size * i, 0);
      }
    } else if (FLAGS_blocks_for_inner_iterations == "automatic") {
      LOG(INFO) << "Choosing automatic blocks for inner iterations";
    } else {
      LOG(FATAL) << "Unknown block type for inner iterations: "
                 << FLAGS_blocks_for_inner_iterations;
    }
  }

  // BA问题有一个稀疏的结构,使它们能够适应更专业、更高效的解决方案策略。斯帕塞舒尔、登斯舒尔和迭代器的解决者利用了这种特殊的结构。
  //
  // 这可以通过指定Options::orderingtype=ceres::SCHUR,
  // 在这种情况下,Ceres将自动确定正确的参数块排序,
  // 或者手动指定一个合适的排序向量,定义Options::num_eliminate_blocks。
  if (FLAGS_ordering == "automatic") {
    return;
  }

  ceres::ParameterBlockOrdering* ordering =
      new ceres::ParameterBlockOrdering;

  // The points come before the cameras.
  for (int i = 0; i < num_points; ++i) {
    ordering->AddElementToGroup(points + point_block_size * i, 0);
  }

  for (int i = 0; i < num_cameras; ++i) {
    // When using axis-angle, there is a single parameter block for
    // the entire camera.
    ordering->AddElementToGroup(cameras + camera_block_size * i, 1);
  }

  options->linear_solver_ordering.reset(ordering);
}

void SetMinimizerOptions(Solver::Options* options) {
  // 最大迭代次数
  options->max_num_iterations = FLAGS_num_iterations;
  // 迭代过程是否输出
  options->minimizer_progress_to_stdout = true;
  // 线程数
  options->num_threads = FLAGS_num_threads;
  // 每次迭代的精度
  options->eta = FLAGS_eta;
  // 求解时间
  options->max_solver_time_in_seconds = FLAGS_max_solver_time;
  // 信任区间算法/nonmonotic
  options->use_nonmonotonic_steps = FLAGS_nonmonotonic_steps;
  if (FLAGS_line_search) {
    options->minimizer_type = ceres::LINE_SEARCH;
  }   
  CHECK(StringToTrustRegionStrategyType(FLAGS_trust_region_strategy,
                                        &options->trust_region_strategy_type));
  // 可选项:raditional_dogleg,subspace_dogleg
  CHECK(StringToDoglegType(FLAGS_dogleg, &options->dogleg_type));
  options->use_inner_iterations = FLAGS_inner_iterations;
}

void SetSolverOptionsFromFlags(BALProblem* bal_problem,
                               Solver::Options* options) {
  SetMinimizerOptions(options);
  SetLinearSolver(options);
  SetOrdering(bal_problem, options);
}

void BuildProblem(BALProblem* bal_problem, Problem* problem) {
  const int point_block_size = bal_problem->point_block_size();
  const int camera_block_size = bal_problem->camera_block_size();
  double* points = bal_problem->mutable_points();
  double* cameras = bal_problem->mutable_cameras();

  // Observations是特征的坐标 u v
  const double* observations = bal_problem->observations();
  for (int i = 0; i < bal_problem->num_observations(); ++i) {
       CostFunction* cost_function;
    // Each Residual block takes a point and a camera as input and
    // outputs a 2 dimensional residual.
    // 加入约束 特征位置
    cost_function =
        (FLAGS_use_quaternions)
        ? SnavelyReprojectionErrorWithQuaternions::Create(
            observations[2 * i + 0],
            observations[2 * i + 1])
        : SnavelyReprojectionError::Create(
            observations[2 * i + 0],
            observations[2 * i + 1]);

    // If enabled use Huber's loss function.
    LossFunction* loss_function = FLAGS_robustify ? new HuberLoss(1.0) : NULL;

    // 没一个特征对应这一个相机姿态和一个三维点
    // 加入点 和 相机
    double* camera =
        cameras + camera_block_size * bal_problem->camera_index()[i];
    double* point = points + point_block_size * bal_problem->point_index()[i];
    problem->AddResidualBlock(cost_function, loss_function, camera, point);
  }

  if (FLAGS_use_quaternions && FLAGS_use_local_parameterization) {
    LocalParameterization* camera_parameterization =
        new ProductParameterization(
            new QuaternionParameterization(),
            new IdentityParameterization(6));
    for (int i = 0; i < bal_problem->num_cameras(); ++i) {
      // ????
      problem->SetParameterization(cameras + camera_block_size * i,
                                   camera_parameterization);
    }
  }
}


void SolveProblem(const char* filename) {
  // 实例化BALProblem 导入文件信息
  BALProblem bal_problem(filename, FLAGS_use_quaternions);

  if (!FLAGS_initial_ply.empty()) {
    bal_problem.WriteToPLYFile(FLAGS_initial_ply);
  }

  Problem problem;

  srand(FLAGS_random_seed);
  bal_problem.Normalize();
  // 添加噪声
  bal_problem.Perturb(FLAGS_rotation_sigma,
                      FLAGS_translation_sigma,
                      FLAGS_point_sigma);
  // 添加约束
  BuildProblem(&bal_problem, &problem);
  Solver::Options options;
  // 设置优化选项
  SetSolverOptionsFromFlags(&bal_problem, &options);
  options.gradient_tolerance = 1e-16;
  options.function_tolerance = 1e-16;
  Solver::Summary summary;
  //求解
  Solve(options, &problem, &summary);
  std::cout << summary.FullReport() << "\n";

  if (!FLAGS_final_ply.empty()) {
    bal_problem.WriteToPLYFile(FLAGS_final_ply);
  }
}

}  // namespace examples
} 

// main
int main(int argc, char** argv) {
  CERES_GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true);
  google::InitGoogleLogging(argv[0]);
  if (FLAGS_input.empty()) {
    LOG(ERROR) << "Usage: bundle_adjuster --input=bal_problem";
    return 1;
  }

  CHECK(FLAGS_use_quaternions || !FLAGS_use_local_parameterization)
      << "--use_local_parameterization can only be used with "
      << "--use_quaternions.";
  ceres::examples::SolveProblem(FLAGS_input.c_str());
  return 0;
}
// file snavely_reprojection_error.h
#include "ceres/rotation.h"

namespace ceres {
namespace examples {

// 小孔相机模型.  camera用9个参数表示, 3 个表示旋转, 3 个表示平移, 1个焦距,2个径向畸变
// 中心点没有建模,假设为图片中心
struct SnavelyReprojectionError {
  SnavelyReprojectionError(double observed_x, double observed_y)
      : observed_x(observed_x), observed_y(observed_y) {}

  template <typename T>
  bool operator()(const T* const camera,
                  const T* const point,
                  T* residuals) const {
    // camera[0,1,2] 是angle-axis 旋转.
    T p[3];
    AngleAxisRotatePoint(camera, point, p);

    // camera[3,4,5] are the translation.
    // 点转换到相机坐标系
    p[0] += camera[3];
    p[1] += camera[4];
    p[2] += camera[5];

    // Compute the center of distortion. The sign change comes from
    // the camera model that Noah Snavely's Bundler assumes, whereby
    // the camera coordinate system has a negative z axis.
    const T xp = - p[0] / p[2];
    const T yp = - p[1] / p[2];

    // Apply second and fourth order radial distortion.
    const T& l1 = camera[7];
    const T& l2 = camera[8];
    const T r2 = xp*xp + yp*yp;
    const T distortion = T(1.0) + r2  * (l1 + l2  * r2);


    // Compute final projected point position.
    const T& focal = camera[6];
    // 得到3D点投影到图像上的位置
    const T predicted_x = focal * distortion * xp;
    const T predicted_y = focal * distortion * yp;

    // 特征位置与3D点计算位置的差
    residuals[0] = predicted_x - T(observed_x);
    residuals[1] = predicted_y - T(observed_y);

    return true;
  }

  // Factory to hide the construction of the CostFunction object from
  // the client code.
  static ceres::CostFunction* Create(const double observed_x,
                                     const double observed_y) {
    // 使用AutoDiffCostFunction,2个残差,参数1有9维,参数2有3维
    return (new ceres::AutoDiffCostFunction2, 9, 3>(
                new SnavelyReprojectionError(observed_x, observed_y)));
  }

  double observed_x;
  double observed_y;
};

// Templated pinhole camera model for used with Ceres.  The camera is
// parameterized using 10 parameters. 4 for rotation, 3 for
// translation, 1 for focal length and 2 for radial distortion. The
// principal point is not modeled (i.e. it is assumed be located at
// the image center).
struct SnavelyReprojectionErrorWithQuaternions {
  // (u, v): the position of the observation with respect to the image
  // center point.
  SnavelyReprojectionErrorWithQuaternions(double observed_x, double observed_y)
      : observed_x(observed_x), observed_y(observed_y) {}

  template <typename T>
  bool operator()(const T* const camera,
                  const T* const point,
                  T* residuals) const {
    // camera[0,1,2,3] is are the rotation of the camera as a quaternion.
    //
    // We use QuaternionRotatePoint as it does not assume that the
    // quaternion is normalized, since one of the ways to run the
    // bundle adjuster is to let Ceres optimize all 4 quaternion
    // parameters without a local parameterization.
    T p[3];
    QuaternionRotatePoint(camera, point, p);

    p[0] += camera[4];
    p[1] += camera[5];
    p[2] += camera[6];

    // Compute the center of distortion. The sign change comes from
    // the camera model that Noah Snavely's Bundler assumes, whereby
    // the camera coordinate system has a negative z axis.
    const T xp = - p[0] / p[2];
    const T yp = - p[1] / p[2];

    // Apply second and fourth order radial distortion.
    const T& l1 = camera[8];
    const T& l2 = camera[9];

    const T r2 = xp*xp + yp*yp;
    const T distortion = T(1.0) + r2  * (l1 + l2  * r2);

    // Compute final projected point position.
    const T& focal = camera[7];
    const T predicted_x = focal * distortion * xp;
    const T predicted_y = focal * distortion * yp;

    // The error is the difference between the predicted and observed position.
    residuals[0] = predicted_x - T(observed_x);
    residuals[1] = predicted_y - T(observed_y);

    return true;
  }

  // Factory to hide the construction of the CostFunction object from
  // the client code.
  static ceres::CostFunction* Create(const double observed_x,
                                     const double observed_y) {
    return (new ceres::AutoDiffCostFunction<
            SnavelyReprojectionErrorWithQuaternions, 2, 10, 3>(
                new SnavelyReprojectionErrorWithQuaternions(observed_x,
                                                            observed_y)));
  }

  double observed_x;
  double observed_y;
};

这个例程比较长,看起来很复杂,但是实际上只是将options的一些选项,列举了出来,具体的使用也没有很好的介绍,本质上并没有什么太难的。options的可设置参数非常之多,具体可以看solver.h文件。

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