// Ceres Solver - A fast non-linear least squares minimizer
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// 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];
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 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 = 1.0 + r2 * (l1 + l2 * r2);
// Compute final projected point position.
const T& focal = camera[6];
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 - observed_x;
residuals[1] = predicted_y - 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<SnavelyReprojectionError, 2, 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 = 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 - observed_x;
residuals[1] = predicted_y - 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;
};
} // namespace examples
} // namespace ceres
#endif // CERES_EXAMPLES_SNAVELY_REPROJECTION_ERROR_H_