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								/* ----------------------------------------------------------------------------
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								 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
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								 * Atlanta, Georgia 30332-0415
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								 * All Rights Reserved
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								 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)
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								 * See LICENSE for the license information
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								 * -------------------------------------------------------------------------- */
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								/**
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								 * @file    SFMExampleExpressions_bal.cpp
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								 * @brief   A structure-from-motion example done with Expressions
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								 * @author  Frank Dellaert
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								 * @date    January 2015
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								 */
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								/**
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								 * This is the Expression version of SFMExample
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								 * See detailed description of headers there, this focuses on explaining the AD part
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								 */
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								// The two new headers that allow using our Automatic Differentiation Expression framework
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								#include <gtsam/slam/expressions.h>
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								#include <gtsam/nonlinear/ExpressionFactorGraph.h>
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								// Header order is close to far
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								#include <gtsam/inference/Symbol.h>
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								#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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								#include <gtsam/slam/dataset.h> // for loading BAL datasets !
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								#include <vector>
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								using namespace std;
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								using namespace gtsam;
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								using namespace noiseModel;
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								using symbol_shorthand::C;
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								using symbol_shorthand::P;
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								// An SfM_Camera is defined in datase.h as a camera with unknown Cal3Bundler calibration
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								// and has a total of 9 free parameters
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								/* ************************************************************************* */
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								int main(int argc, char* argv[]) {
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								  // Find default file, but if an argument is given, try loading a file
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								  string filename = findExampleDataFile("dubrovnik-3-7-pre");
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								  if (argc > 1)
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								    filename = string(argv[1]);
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								  // Load the SfM data from file
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								  SfM_data mydata;
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								  readBAL(filename, mydata);
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								  cout
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								      << boost::format("read %1% tracks on %2% cameras\n")
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								          % mydata.number_tracks() % mydata.number_cameras();
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								  // Create a factor graph
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								  ExpressionFactorGraph graph;
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								  // Here we don't use a PriorFactor but directly the ExpressionFactor class
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								  // First, we create an expression to the pose from the first camera
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								  Expression<SfM_Camera> camera0_(C(0));
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								  // Then, to get its pose:
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								  Pose3_ pose0_(&SfM_Camera::getPose, camera0_);
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								  // Finally, we say it should be equal to first guess
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								  graph.addExpressionFactor(pose0_, mydata.cameras[0].pose(),
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								      noiseModel::Isotropic::Sigma(6, 0.1));
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								  // similarly, we create a prior on the first point
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								  Point3_ point0_(P(0));
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								  graph.addExpressionFactor(point0_, mydata.tracks[0].p,
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								      noiseModel::Isotropic::Sigma(3, 0.1));
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								  // We share *one* noiseModel between all projection factors
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								  noiseModel::Isotropic::shared_ptr noise = noiseModel::Isotropic::Sigma(2,
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								      1.0); // one pixel in u and v
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								  // Simulated measurements from each camera pose, adding them to the factor graph
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								  size_t j = 0;
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								  for(const SfM_Track& track: mydata.tracks) {
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								    // Leaf expression for j^th point
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								    Point3_ point_('p', j);
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								    for(const SfM_Measurement& m: track.measurements) {
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								      size_t i = m.first;
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								      Point2 uv = m.second;
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								      // Leaf expression for i^th camera
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								      Expression<SfM_Camera> camera_(C(i));
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								      // Below an expression for the prediction of the measurement:
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								      Point2_ predict_ = project2<SfM_Camera>(camera_, point_);
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								      // Again, here we use an ExpressionFactor
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								      graph.addExpressionFactor(predict_, uv, noise);
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								    }
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								    j += 1;
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								  }
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								  // Create initial estimate
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								  Values initial;
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								  size_t i = 0;
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								  j = 0;
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								  for(const SfM_Camera& camera: mydata.cameras)
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								    initial.insert(C(i++), camera);
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								  for(const SfM_Track& track: mydata.tracks)
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								    initial.insert(P(j++), track.p);
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								  /* Optimize the graph and print results */
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								  Values result;
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								  try {
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								    LevenbergMarquardtParams params;
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								    params.setVerbosity("ERROR");
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								    LevenbergMarquardtOptimizer lm(graph, initial, params);
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								    result = lm.optimize();
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								  } catch (exception& e) {
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								    cout << e.what();
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								  }
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								  cout << "final error: " << graph.error(result) << endl;
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								  return 0;
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								}
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								/* ************************************************************************* */
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