1// Ceres Solver - A fast non-linear least squares minimizer
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3// http://code.google.com/p/ceres-solver/
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28//
29// Author: sameeragarwal@google.com (Sameer Agarwal)
30//
31// Templated struct implementing the camera model and residual
32// computation for bundle adjustment used by Noah Snavely's Bundler
33// SfM system. This is also the camera model/residual for the bundle
34// adjustment problems in the BAL dataset. It is templated so that we
35// can use Ceres's automatic differentiation to compute analytic
36// jacobians.
37//
38// For details see: http://phototour.cs.washington.edu/bundler/
39// and http://grail.cs.washington.edu/projects/bal/
40
41#ifndef CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_
42#define CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_
43
44#include "ceres/rotation.h"
45
46namespace ceres {
47namespace examples {
48
49// Templated pinhole camera model for used with Ceres.  The camera is
50// parameterized using 9 parameters: 3 for rotation, 3 for translation, 1 for
51// focal length and 2 for radial distortion. The principal point is not modeled
52// (i.e. it is assumed be located at the image center).
53struct SnavelyReprojectionError {
54  SnavelyReprojectionError(double observed_x, double observed_y)
55      : observed_x(observed_x), observed_y(observed_y) {}
56
57  template <typename T>
58  bool operator()(const T* const camera,
59                  const T* const point,
60                  T* residuals) const {
61    // camera[0,1,2] are the angle-axis rotation.
62    T p[3];
63    ceres::AngleAxisRotatePoint(camera, point, p);
64
65    // camera[3,4,5] are the translation.
66    p[0] += camera[3];
67    p[1] += camera[4];
68    p[2] += camera[5];
69
70    // Compute the center of distortion. The sign change comes from
71    // the camera model that Noah Snavely's Bundler assumes, whereby
72    // the camera coordinate system has a negative z axis.
73    const T& focal = camera[6];
74    T xp = - p[0] / p[2];
75    T yp = - p[1] / p[2];
76
77    // Apply second and fourth order radial distortion.
78    const T& l1 = camera[7];
79    const T& l2 = camera[8];
80    T r2 = xp*xp + yp*yp;
81    T distortion = T(1.0) + r2  * (l1 + l2  * r2);
82
83    // Compute final projected point position.
84    T predicted_x = focal * distortion * xp;
85    T predicted_y = focal * distortion * yp;
86
87    // The error is the difference between the predicted and observed position.
88    residuals[0] = predicted_x - T(observed_x);
89    residuals[1] = predicted_y - T(observed_y);
90
91    return true;
92  }
93
94  // Factory to hide the construction of the CostFunction object from
95  // the client code.
96  static ceres::CostFunction* Create(const double observed_x,
97                                     const double observed_y) {
98    return (new ceres::AutoDiffCostFunction<SnavelyReprojectionError, 2, 9, 3>(
99                new SnavelyReprojectionError(observed_x, observed_y)));
100  }
101
102  double observed_x;
103  double observed_y;
104};
105
106// Templated pinhole camera model for used with Ceres.  The camera is
107// parameterized using 10 parameters. 4 for rotation, 3 for
108// translation, 1 for focal length and 2 for radial distortion. The
109// principal point is not modeled (i.e. it is assumed be located at
110// the image center).
111struct SnavelyReprojectionErrorWithQuaternions {
112  // (u, v): the position of the observation with respect to the image
113  // center point.
114  SnavelyReprojectionErrorWithQuaternions(double observed_x, double observed_y)
115      : observed_x(observed_x), observed_y(observed_y) {}
116
117  template <typename T>
118  bool operator()(const T* const camera_rotation,
119                  const T* const camera_translation_and_intrinsics,
120                  const T* const point,
121                  T* residuals) const {
122    const T& focal = camera_translation_and_intrinsics[3];
123    const T& l1 = camera_translation_and_intrinsics[4];
124    const T& l2 = camera_translation_and_intrinsics[5];
125
126    // Use a quaternion rotation that doesn't assume the quaternion is
127    // normalized, since one of the ways to run the bundler is to let Ceres
128    // optimize all 4 quaternion parameters unconstrained.
129    T p[3];
130    QuaternionRotatePoint(camera_rotation, point, p);
131
132    p[0] += camera_translation_and_intrinsics[0];
133    p[1] += camera_translation_and_intrinsics[1];
134    p[2] += camera_translation_and_intrinsics[2];
135
136    // Compute the center of distortion. The sign change comes from
137    // the camera model that Noah Snavely's Bundler assumes, whereby
138    // the camera coordinate system has a negative z axis.
139    T xp = - p[0] / p[2];
140    T yp = - p[1] / p[2];
141
142    // Apply second and fourth order radial distortion.
143    T r2 = xp*xp + yp*yp;
144    T distortion = T(1.0) + r2  * (l1 + l2  * r2);
145
146    // Compute final projected point position.
147    T predicted_x = focal * distortion * xp;
148    T predicted_y = focal * distortion * yp;
149
150    // The error is the difference between the predicted and observed position.
151    residuals[0] = predicted_x - T(observed_x);
152    residuals[1] = predicted_y - T(observed_y);
153
154    return true;
155  }
156
157  // Factory to hide the construction of the CostFunction object from
158  // the client code.
159  static ceres::CostFunction* Create(const double observed_x,
160                                     const double observed_y) {
161    return (new ceres::AutoDiffCostFunction<
162            SnavelyReprojectionErrorWithQuaternions, 2, 4, 6, 3>(
163                new SnavelyReprojectionErrorWithQuaternions(observed_x,
164                                                            observed_y)));
165  }
166
167  double observed_x;
168  double observed_y;
169};
170
171}  // namespace examples
172}  // namespace ceres
173
174#endif  // CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_
175