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// Copyright (c) 2011 libmv authors.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to
// deal in the Software without restriction, including without limitation the
// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
// sell copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
// IN THE SOFTWARE.
#include "libmv/simple_pipeline/initialize_reconstruction.h"
#include "libmv/base/vector.h"
#include "libmv/logging/logging.h"
#include "libmv/multiview/fundamental.h"
#include "libmv/multiview/projection.h"
#include "libmv/numeric/levenberg_marquardt.h"
#include "libmv/numeric/numeric.h"
#include "libmv/simple_pipeline/reconstruction.h"
#include "libmv/simple_pipeline/tracks.h"
namespace libmv {
namespace {
void GetImagesInMarkers(const vector<Marker> &markers,
int *image1, int *image2) {
if (markers.size() < 2) {
return;
}
*image1 = markers[0].image;
for (int i = 1; i < markers.size(); ++i) {
if (markers[i].image != *image1) {
*image2 = markers[i].image;
return;
}
}
*image2 = -1;
LOG(FATAL) << "Only one image in the markers.";
}
} // namespace
bool EuclideanReconstructTwoFrames(const vector<Marker> &markers,
EuclideanReconstruction *reconstruction) {
if (markers.size() < 16) {
LG << "Not enough markers to initialize from two frames: " << markers.size();
return false;
}
int image1, image2;
GetImagesInMarkers(markers, &image1, &image2);
Mat x1, x2;
CoordinatesForMarkersInImage(markers, image1, &x1);
CoordinatesForMarkersInImage(markers, image2, &x2);
Mat3 F;
NormalizedEightPointSolver(x1, x2, &F);
// The F matrix should be an E matrix, but squash it just to be sure.
Mat3 E;
FundamentalToEssential(F, &E);
// Recover motion between the two images. Since this function assumes a
// calibrated camera, use the identity for K.
Mat3 R;
Vec3 t;
Mat3 K = Mat3::Identity();
if (!MotionFromEssentialAndCorrespondence(E,
K, x1.col(0),
K, x2.col(0),
&R, &t)) {
LG << "Failed to compute R and t from E and K.";
return false;
}
// Image 1 gets the reference frame, image 2 gets the relative motion.
reconstruction->InsertCamera(image1, Mat3::Identity(), Vec3::Zero());
reconstruction->InsertCamera(image2, R, t);
LG << "From two frame reconstruction got:\nR:\n" << R
<< "\nt:" << t.transpose();
return true;
}
namespace {
Mat3 DecodeF(const Vec9 &encoded_F) {
// Decode F and force it to be rank 2.
Map<const Mat3> full_rank_F(encoded_F.data(), 3, 3);
Eigen::JacobiSVD<Mat3> svd(full_rank_F,
Eigen::ComputeFullU | Eigen::ComputeFullV);
Vec3 diagonal = svd.singularValues();
diagonal(2) = 0;
Mat3 F = svd.matrixU() * diagonal.asDiagonal() * svd.matrixV().transpose();
return F;
}
// This is the stupidest way to refine F known to mankind, since it requires
// doing a full SVD of F at each iteration. This uses sampson error.
struct FundamentalSampsonCostFunction {
public:
typedef Vec FMatrixType;
typedef Vec9 XMatrixType;
// Assumes markers are ordered by track.
explicit FundamentalSampsonCostFunction(const vector<Marker> &markers)
: markers(markers) {}
Vec operator()(const Vec9 &encoded_F) const {
// Decode F and force it to be rank 2.
Mat3 F = DecodeF(encoded_F);
Vec residuals(markers.size() / 2);
residuals.setZero();
for (int i = 0; i < markers.size() / 2; ++i) {
const Marker &marker1 = markers[2*i + 0];
const Marker &marker2 = markers[2*i + 1];
CHECK_EQ(marker1.track, marker2.track);
Vec2 x1(marker1.x, marker1.y);
Vec2 x2(marker2.x, marker2.y);
residuals[i] = SampsonDistance(F, x1, x2);
}
return residuals;
}
const vector<Marker> &markers;
};
} // namespace
bool ProjectiveReconstructTwoFrames(const vector<Marker> &markers,
ProjectiveReconstruction *reconstruction) {
if (markers.size() < 16) {
return false;
}
int image1, image2;
GetImagesInMarkers(markers, &image1, &image2);
Mat x1, x2;
CoordinatesForMarkersInImage(markers, image1, &x1);
CoordinatesForMarkersInImage(markers, image2, &x2);
Mat3 F;
NormalizedEightPointSolver(x1, x2, &F);
// XXX Verify sampson distance.
#if 0
// Refine the resulting projection fundamental matrix using Sampson's
// approximation of geometric error. This avoids having to do a full bundle
// at the cost of some accuracy.
//
// TODO(keir): After switching to a better bundling library, use a proper
// full bundle adjust here instead of this lame bundle adjustment.
typedef LevenbergMarquardt<FundamentalSampsonCostFunction> Solver;
FundamentalSampsonCostFunction fundamental_cost(markers);
// Pack the initial P matrix into a size-12 vector..
Vec9 encoded_F = Map<Vec9>(F.data(), 3, 3);
Solver solver(fundamental_cost);
Solver::SolverParameters params;
Solver::Results results = solver.minimize(params, &encoded_F);
// TODO(keir): Check results to ensure clean termination.
// Recover F from the minimization.
F = DecodeF(encoded_F);
#endif
// Image 1 gets P = [I|0], image 2 gets arbitrary P.
Mat34 P1 = Mat34::Zero();
P1.block<3, 3>(0, 0) = Mat3::Identity();
Mat34 P2;
ProjectionsFromFundamental(F, &P1, &P2);
reconstruction->InsertCamera(image1, P1);
reconstruction->InsertCamera(image2, P2);
LG << "From two frame reconstruction got P2:\n" << P2;
return true;
}
} // namespace libmv
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