examples/bal_problem.cc

// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
// http://code.google.com/p/ceres-solver/
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// Author: sameeragarwal@google.com (Sameer Agarwal)

#include "bal_problem.h"

#include <cstdio>
#include <cstdlib>
#include <string>
#include <vector>
#include "Eigen/Core"
#include "ceres/rotation.h"
#include "glog/logging.h"

namespace ceres {
namespace examples {
namespace {
typedef Eigen::Map<Eigen::VectorXd> VectorRef;
typedef Eigen::Map<const Eigen::VectorXd> ConstVectorRef;

inline double RandDouble() {
  double r = static_cast<double>(rand());
  return r / RAND_MAX;
}

// Box-Muller algorithm for normal random number generation.
// http://en.wikipedia.org/wiki/Box-Muller_transform
inline double RandNormal() {
  double x1, x2, w;
  do {
    x1 = 2.0 * RandDouble() - 1.0;
    x2 = 2.0 * RandDouble() - 1.0;
    w = x1 * x1 + x2 * x2;
  } while ( w >= 1.0 || w == 0.0 );

  w = sqrt((-2.0 * log(w)) / w);
  return x1 * w;
}

template<typename T>
void FscanfOrDie(FILE* fptr, const char* format, T* value) {
  int num_scanned = fscanf(fptr, format, value);
  if (num_scanned != 1) {
    LOG(FATAL) << "Invalid UW data file.";
  }
}

void PerturbPoint3(const double sigma, double* point) {
  for (int i = 0; i < 3; ++i) {
    point[i] += RandNormal() * sigma;
  }
}

double Median(std::vector<double>* data) {
  int n = data->size();
  std::vector<double>::iterator mid_point = data->begin() + n / 2;
  std::nth_element(data->begin(), mid_point, data->end());
  return *mid_point;
}

}  // namespace

BALProblem::BALProblem(const std::string& filename, bool use_quaternions) {
  FILE* fptr = fopen(filename.c_str(), "r");

  if (fptr == NULL) {
    LOG(FATAL) << "Error: unable to open file " << filename;
    return;
  };

  // This wil die horribly on invalid files. Them's the breaks.
  FscanfOrDie(fptr, "%d", &num_cameras_);
  FscanfOrDie(fptr, "%d", &num_points_);
  FscanfOrDie(fptr, "%d", &num_observations_);

  VLOG(1) << "Header: " << num_cameras_
          << " " << num_points_
          << " " << num_observations_;

  point_index_ = new int[num_observations_];
  camera_index_ = new int[num_observations_];
  observations_ = new double[2 * num_observations_];

  num_parameters_ = 9 * num_cameras_ + 3 * num_points_;
  parameters_ = new double[num_parameters_];

  for (int i = 0; i < num_observations_; ++i) {
    FscanfOrDie(fptr, "%d", camera_index_ + i);
    FscanfOrDie(fptr, "%d", point_index_ + i);
    for (int j = 0; j < 2; ++j) {
      FscanfOrDie(fptr, "%lf", observations_ + 2*i + j);
    }
  }

  for (int i = 0; i < num_parameters_; ++i) {
    FscanfOrDie(fptr, "%lf", parameters_ + i);
  }

  fclose(fptr);

  use_quaternions_ = use_quaternions;
  if (use_quaternions) {
    // Switch the angle-axis rotations to quaternions.
    num_parameters_ = 10 * num_cameras_ + 3 * num_points_;
    double* quaternion_parameters = new double[num_parameters_];
    double* original_cursor = parameters_;
    double* quaternion_cursor = quaternion_parameters;
    for (int i = 0; i < num_cameras_; ++i) {
      AngleAxisToQuaternion(original_cursor, quaternion_cursor);
      quaternion_cursor += 4;
      original_cursor += 3;
      for (int j = 4; j < 10; ++j) {
       *quaternion_cursor++ = *original_cursor++;
      }
    }
    // Copy the rest of the points.
    for (int i = 0; i < 3 * num_points_; ++i) {
      *quaternion_cursor++ = *original_cursor++;
    }
    // Swap in the quaternion parameters.
    delete []parameters_;
    parameters_ = quaternion_parameters;
  }
}

// This function writes the problem to a file in the same format that
// is read by the constructor.
void BALProblem::WriteToFile(const std::string& filename) const {
  FILE* fptr = fopen(filename.c_str(), "w");

  if (fptr == NULL) {
    LOG(FATAL) << "Error: unable to open file " << filename;
    return;
  };

  fprintf(fptr, "%d %d %d\n", num_cameras_, num_points_, num_observations_);

  for (int i = 0; i < num_observations_; ++i) {
    fprintf(fptr, "%d %d", camera_index_[i], point_index_[i]);
    for (int j = 0; j < 2; ++j) {
      fprintf(fptr, " %g", observations_[2 * i + j]);
    }
    fprintf(fptr, "\n");
  }

  for (int i = 0; i < num_cameras(); ++i) {
    double angleaxis[9];
    if (use_quaternions_) {
      // Output in angle-axis format.
      QuaternionToAngleAxis(parameters_ + 10 * i, angleaxis);
      memcpy(angleaxis + 3, parameters_ + 10 * i + 4, 6 * sizeof(double));
    } else {
      memcpy(angleaxis, parameters_ + 9 * i, 9 * sizeof(double));
    }
    for (int j = 0; j < 9; ++j) {
      fprintf(fptr, "%.16g\n", angleaxis[j]);
    }
  }

  const double* points = parameters_ + camera_block_size() * num_cameras_;
  for (int i = 0; i < num_points(); ++i) {
    const double* point = points + i * point_block_size();
    for (int j = 0; j < point_block_size(); ++j) {
      fprintf(fptr, "%.16g\n", point[j]);
    }
  }

  fclose(fptr);
}

void BALProblem::CameraToAngleAxisAndCenter(const double* camera,
                                            double* angle_axis,
                                            double* center) {
  VectorRef angle_axis_ref(angle_axis, 3);
  if (use_quaternions_) {
    QuaternionToAngleAxis(camera, angle_axis);
  } else {
    angle_axis_ref = ConstVectorRef(camera, 3);
  }

  // c = -R't
  Eigen::VectorXd inverse_rotation = -angle_axis_ref;
  AngleAxisRotatePoint(inverse_rotation.data(),
                       camera + camera_block_size() - 6,
                       center);
  VectorRef(center, 3) *= -1.0;
}

void BALProblem::AngleAxisAndCenterToCamera(const double* angle_axis,
                                            const double* center,
                                            double* camera) {
  ConstVectorRef angle_axis_ref(angle_axis, 3);
  if (use_quaternions_) {
    AngleAxisToQuaternion(angle_axis, camera);
  } else {
    VectorRef(camera, 3) = angle_axis_ref;
  }

  // t = -R * c
  AngleAxisRotatePoint(angle_axis,
                       center,
                       camera + camera_block_size() - 6);
  VectorRef(camera + camera_block_size() - 6, 3) *= -1.0;
}


void BALProblem::Normalize() {
  // Compute the marginal median of the geometry.
  std::vector<double> tmp(num_points_);
  Eigen::Vector3d median;
  double* points = mutable_points();
  for (int i = 0; i < 3; ++i) {
    for (int j = 0; j < num_points_; ++j) {
      tmp[j] = points[3 * j + i];
    }
    median(i) = Median(&tmp);
  }

  for (int i = 0; i < num_points_; ++i) {
    VectorRef point(points + 3 * i, 3);
    tmp[i] = (point - median).lpNorm<1>();
  }

  const double median_absolute_deviation = Median(&tmp);

  // Scale so that the median absolute deviation of the resulting
  // reconstruction is 100.
  const double scale = 100.0 / median_absolute_deviation;

  VLOG(2) << "median: " << median.transpose();
  VLOG(2) << "median absolute deviation: " << median_absolute_deviation;
  VLOG(2) << "scale: " << scale;

  // X = scale * (X - median)
  for (int i = 0; i < num_points_; ++i) {
    VectorRef point(points + 3 * i, 3);
    point = scale * (point - median);
  }

  double* cameras = mutable_cameras();
  double angle_axis[3];
  double center[3];
  for (int i = 0; i < num_cameras_; ++i) {
    double* camera = cameras + camera_block_size() * i;
    CameraToAngleAxisAndCenter(camera, angle_axis, center);
    // center = scale * (center - median)
    VectorRef(center, 3) = scale * (VectorRef(center, 3) - median);
    AngleAxisAndCenterToCamera(angle_axis, center, camera);
  }
}

void BALProblem::Perturb(const double rotation_sigma,
                         const double translation_sigma,
                         const double point_sigma) {
  CHECK_GE(point_sigma, 0.0);
  CHECK_GE(rotation_sigma, 0.0);
  CHECK_GE(translation_sigma, 0.0);

  double* points = mutable_points();
  if (point_sigma > 0) {
    for (int i = 0; i < num_points_; ++i) {
      PerturbPoint3(point_sigma, points + 3 * i);
    }
  }

  for (int i = 0; i < num_cameras_; ++i) {
    double* camera = mutable_cameras() + camera_block_size() * i;

    double angle_axis[3];
    double center[3];
    // Perturb in the rotation of the camera in the angle-axis
    // representation.
    CameraToAngleAxisAndCenter(camera, angle_axis, center);
    if (rotation_sigma > 0.0) {
      PerturbPoint3(rotation_sigma, angle_axis);
    }
    AngleAxisAndCenterToCamera(angle_axis, center, camera);

    if (translation_sigma > 0.0) {
      PerturbPoint3(translation_sigma, camera + camera_block_size() - 6);
    }
  }
}

BALProblem::~BALProblem() {
  delete []point_index_;
  delete []camera_index_;
  delete []observations_;
  delete []parameters_;
}

}  // namespace examples
}  // namespace ceres