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+// 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/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+//   this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+//   this list of conditions and the following disclaimer in the documentation
+//   and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+//   used to endorse or promote products derived from this software without
+//   specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+//
+// Templated struct implementing the camera model and residual
+// computation for bundle adjustment used by Noah Snavely's Bundler
+// SfM system. This is also the camera model/residual for the bundle
+// adjustment problems in the BAL dataset. It is templated so that we
+// can use Ceres's automatic differentiation to compute analytic
+// jacobians.
+//
+// For details see: http://phototour.cs.washington.edu/bundler/
+// and http://grail.cs.washington.edu/projects/bal/
+
+#ifndef CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_
+#define CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_
+
+#include "ceres/rotation.h"
+
+namespace ceres {
+namespace examples {
+
+// Templated pinhole camera model for used with Ceres.  The camera is
+// parameterized using 9 parameters: 3 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 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] are the angle-axis rotation.
+    T p[3];
+    ceres::AngleAxisRotatePoint(camera, point, p);
+
+    // camera[3,4,5] are the translation.
+    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& focal = camera[6];
+    T xp = - focal * p[0] / p[2];
+    T yp = - focal * p[1] / p[2];
+
+    // Apply second and fourth order radial distortion.
+    const T& l1 = camera[7];
+    const T& l2 = camera[8];
+    T r2 = xp*xp + yp*yp;
+    T distortion = T(1.0) + r2  * (l1 + l2  * r2);
+
+    // Compute final projected point position.
+    T predicted_x = distortion * xp;
+    T predicted_y = 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;
+  }
+
+  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 SnavelyReprojectionErrorWitQuaternions {
+  // (u, v): the position of the observation with respect to the image
+  // center point.
+  SnavelyReprojectionErrorWitQuaternions(double observed_x, double observed_y)
+      : observed_x(observed_x), observed_y(observed_y) {}
+
+  template <typename T>
+  bool operator()(const T* const camera_rotation,
+                  const T* const camera_translation_and_intrinsics,
+                  const T* const point,
+                  T* residuals) const {
+    const T& focal = camera_translation_and_intrinsics[3];
+    const T& l1 = camera_translation_and_intrinsics[4];
+    const T& l2 = camera_translation_and_intrinsics[5];
+
+    // Use a quaternion rotation that doesn't assume the quaternion is
+    // normalized, since one of the ways to run the bundler is to let Ceres
+    // optimize all 4 quaternion parameters unconstrained.
+    T p[3];
+    QuaternionRotatePoint(camera_rotation, point, p);
+
+    p[0] += camera_translation_and_intrinsics[0];
+    p[1] += camera_translation_and_intrinsics[1];
+    p[2] += camera_translation_and_intrinsics[2];
+
+    // 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.
+    T xp = - focal * p[0] / p[2];
+    T yp = - focal * p[1] / p[2];
+
+    // Apply second and fourth order radial distortion.
+    T r2 = xp*xp + yp*yp;
+    T distortion = T(1.0) + r2  * (l1 + l2  * r2);
+
+    // Compute final projected point position.
+    T predicted_x = distortion * xp;
+    T predicted_y = 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;
+  }
+
+  double observed_x;
+  double observed_y;
+};
+
+}  // namespace examples
+}  // namespace ceres
+
+#endif  // CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_