10ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Ceres Solver - A fast non-linear least squares minimizer
20ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Copyright 2010, 2011, 2012 Google Inc. All rights reserved.
30ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// http://code.google.com/p/ceres-solver/
40ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
50ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Redistribution and use in source and binary forms, with or without
60ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// modification, are permitted provided that the following conditions are met:
70ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
80ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions of source code must retain the above copyright notice,
90ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//   this list of conditions and the following disclaimer.
100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Redistributions in binary form must reproduce the above copyright notice,
110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//   this list of conditions and the following disclaimer in the documentation
120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//   and/or other materials provided with the distribution.
130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// * Neither the name of Google Inc. nor the names of its contributors may be
140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//   used to endorse or promote products derived from this software without
150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//   specific prior written permission.
160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// POSSIBILITY OF SUCH DAMAGE.
280ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
290ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Author: keir@google.com (Keir Mierle)
300ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
310ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// A minimal, self-contained bundle adjuster using Ceres, that reads
320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// files from University of Washington' Bundle Adjustment in the Large dataset:
330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// http://grail.cs.washington.edu/projects/bal
340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong//
350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// This does not use the best configuration for solving; see the more involved
360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// bundle_adjuster.cc file for details.
370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include <cmath>
390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include <cstdio>
400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include <iostream>
410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/ceres.h"
430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong#include "ceres/rotation.h"
440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Read a Bundle Adjustment in the Large dataset.
460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongclass BALProblem {
470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong public:
480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  ~BALProblem() {
490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    delete[] point_index_;
500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    delete[] camera_index_;
510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    delete[] observations_;
520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    delete[] parameters_;
530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int num_observations()       const { return num_observations_;               }
560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  const double* observations() const { return observations_;                   }
570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* mutable_cameras()          { return parameters_;                     }
580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* mutable_points()           { return parameters_  + 9 * num_cameras_; }
590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* mutable_camera_for_observation(int i) {
610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return mutable_cameras() + camera_index_[i] * 9;
620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
630ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* mutable_point_for_observation(int i) {
640ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return mutable_points() + point_index_[i] * 3;
650ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
660ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
670ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  bool LoadFile(const char* filename) {
680ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    FILE* fptr = fopen(filename, "r");
690ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    if (fptr == NULL) {
700ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      return false;
710ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    };
720ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
730ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    FscanfOrDie(fptr, "%d", &num_cameras_);
740ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    FscanfOrDie(fptr, "%d", &num_points_);
750ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    FscanfOrDie(fptr, "%d", &num_observations_);
760ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
770ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    point_index_ = new int[num_observations_];
780ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    camera_index_ = new int[num_observations_];
790ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    observations_ = new double[2 * num_observations_];
800ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
810ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    num_parameters_ = 9 * num_cameras_ + 3 * num_points_;
820ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    parameters_ = new double[num_parameters_];
830ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
840ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    for (int i = 0; i < num_observations_; ++i) {
850ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      FscanfOrDie(fptr, "%d", camera_index_ + i);
860ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      FscanfOrDie(fptr, "%d", point_index_ + i);
870ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      for (int j = 0; j < 2; ++j) {
880ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong        FscanfOrDie(fptr, "%lf", observations_ + 2*i + j);
890ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      }
900ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    }
910ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
920ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    for (int i = 0; i < num_parameters_; ++i) {
930ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      FscanfOrDie(fptr, "%lf", parameters_ + i);
940ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    }
950ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return true;
960ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
970ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
980ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong private:
990ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  template<typename T>
1000ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  void FscanfOrDie(FILE *fptr, const char *format, T *value) {
1010ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    int num_scanned = fscanf(fptr, format, value);
1020ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    if (num_scanned != 1) {
1030ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      LOG(FATAL) << "Invalid UW data file.";
1040ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    }
1050ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
1060ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1070ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int num_cameras_;
1080ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int num_points_;
1090ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int num_observations_;
1100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int num_parameters_;
1110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int* point_index_;
1130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  int* camera_index_;
1140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* observations_;
1150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double* parameters_;
1160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong};
1170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// Templated pinhole camera model for used with Ceres.  The camera is
1190ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// parameterized using 9 parameters: 3 for rotation, 3 for translation, 1 for
1200ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// focal length and 2 for radial distortion. The principal point is not modeled
1210ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong// (i.e. it is assumed be located at the image center).
1220ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongstruct SnavelyReprojectionError {
1230ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  SnavelyReprojectionError(double observed_x, double observed_y)
1240ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong      : observed_x(observed_x), observed_y(observed_y) {}
1250ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1260ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  template <typename T>
1270ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  bool operator()(const T* const camera,
1280ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong                  const T* const point,
1290ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong                  T* residuals) const {
1300ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // camera[0,1,2] are the angle-axis rotation.
1310ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T p[3];
1320ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    ceres::AngleAxisRotatePoint(camera, point, p);
1330ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1340ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // camera[3,4,5] are the translation.
1350ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    p[0] += camera[3];
1360ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    p[1] += camera[4];
1370ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    p[2] += camera[5];
1380ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1390ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // Compute the center of distortion. The sign change comes from
1400ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // the camera model that Noah Snavely's Bundler assumes, whereby
1410ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // the camera coordinate system has a negative z axis.
1420ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T xp = - p[0] / p[2];
1430ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T yp = - p[1] / p[2];
1440ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1450ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // Apply second and fourth order radial distortion.
1460ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    const T& l1 = camera[7];
1470ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    const T& l2 = camera[8];
1480ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T r2 = xp*xp + yp*yp;
1490ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T distortion = T(1.0) + r2  * (l1 + l2  * r2);
1500ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1510ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // Compute final projected point position.
1520ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    const T& focal = camera[6];
1530ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T predicted_x = focal * distortion * xp;
1540ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    T predicted_y = focal * distortion * yp;
1550ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1560ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // The error is the difference between the predicted and observed position.
1570ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    residuals[0] = predicted_x - T(observed_x);
1580ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    residuals[1] = predicted_y - T(observed_y);
1590ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1600ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return true;
1610ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
1620ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1631d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling  // Factory to hide the construction of the CostFunction object from
1641d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling  // the client code.
1651d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling  static ceres::CostFunction* Create(const double observed_x,
1661d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling                                     const double observed_y) {
1671d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling    return (new ceres::AutoDiffCostFunction<SnavelyReprojectionError, 2, 9, 3>(
1681d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling                new SnavelyReprojectionError(observed_x, observed_y)));
1691d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling  }
1701d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling
1710ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double observed_x;
1720ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  double observed_y;
1730ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong};
1740ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1750ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kongint main(int argc, char** argv) {
1760ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  google::InitGoogleLogging(argv[0]);
1770ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  if (argc != 2) {
1780ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    std::cerr << "usage: simple_bundle_adjuster <bal_problem>\n";
1790ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return 1;
1800ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
1810ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1820ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  BALProblem bal_problem;
1830ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  if (!bal_problem.LoadFile(argv[1])) {
1840ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    std::cerr << "ERROR: unable to open file " << argv[1] << "\n";
1850ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    return 1;
1860ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
1870ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1881d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling  const double* observations = bal_problem.observations();
1891d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling
1900ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  // Create residuals for each observation in the bundle adjustment problem. The
1910ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  // parameters for cameras and points are added automatically.
1920ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  ceres::Problem problem;
1930ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  for (int i = 0; i < bal_problem.num_observations(); ++i) {
1940ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // Each Residual block takes a point and a camera as input and outputs a 2
1950ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // dimensional residual. Internally, the cost function stores the observed
1960ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    // image location and compares the reprojection against the observation.
1970ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
1981d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling    ceres::CostFunction* cost_function =
1991d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling        SnavelyReprojectionError::Create(observations[2 * i + 0],
2001d2624a10e2c559f8ba9ef89eaa30832c0a83a96Sascha Haeberling                                         observations[2 * i + 1]);
2010ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong    problem.AddResidualBlock(cost_function,
2020ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong                             NULL /* squared loss */,
2030ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong                             bal_problem.mutable_camera_for_observation(i),
2040ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong                             bal_problem.mutable_point_for_observation(i));
2050ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  }
2060ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
2070ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  // Make Ceres automatically detect the bundle structure. Note that the
2080ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  // standard solver, SPARSE_NORMAL_CHOLESKY, also works fine but it is slower
2090ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  // for standard bundle adjustment problems.
2100ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  ceres::Solver::Options options;
2110ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  options.linear_solver_type = ceres::DENSE_SCHUR;
2120ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  options.minimizer_progress_to_stdout = true;
2130ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong
2140ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  ceres::Solver::Summary summary;
2150ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  ceres::Solve(options, &problem, &summary);
2160ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  std::cout << summary.FullReport() << "\n";
2170ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong  return 0;
2180ae28bd5885b5daa526898fcf7c323dc2c3e1963Angus Kong}
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