Akshay Krishnan
GitHub
commit
7c53235fdb
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010-2020, 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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#pragma once
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/**
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* @file TranslationFactor.h
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* @author Frank Dellaert
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* @date March 2020
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* @brief Binary factor for a relative translation direction measurement.
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*/
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#include <gtsam/geometry/Point3.h>
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#include <gtsam/geometry/Unit3.h>
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#include <gtsam/linear/NoiseModel.h>
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#include <gtsam/nonlinear/NonlinearFactor.h>
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namespace gtsam {
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/**
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* Binary factor for a relative translation direction measurement
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* w_aZb. The measurement equation is
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* w_aZb = Unit3(Tb - Ta)
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* i.e., w_aZb is the translation direction from frame A to B, in world
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* coordinates. Although Unit3 instances live on a manifold, following
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* Wilson14eccv_1DSfM.pdf error we compute the *chordal distance* in the
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* ambient world coordinate frame:
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* normalized(Tb - Ta) - w_aZb.point3()
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*
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* @addtogroup SFM
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*/
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class TranslationFactor : public NoiseModelFactor2<Point3, Point3> {
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private:
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typedef NoiseModelFactor2<Point3, Point3> Base;
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Point3 measured_w_aZb_;
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public:
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/// default constructor
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TranslationFactor() {}
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TranslationFactor(Key a, Key b, const Unit3& w_aZb,
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const SharedNoiseModel& noiseModel)
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: Base(noiseModel, a, b), measured_w_aZb_(w_aZb.point3()) {}
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/**
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* @brief Caclulate error: (norm(Tb - Ta) - measurement)
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* where Tb and Ta are Point3 translations and measurement is
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* the Unit3 translation direction from a to b.
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*
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* @param Ta translation for key a
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* @param Tb translation for key b
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* @param H1 optional jacobian in Ta
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* @param H2 optional jacobian in Tb
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* @return * Vector
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*/
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Vector evaluateError(
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const Point3& Ta, const Point3& Tb,
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boost::optional<Matrix&> H1 = boost::none,
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boost::optional<Matrix&> H2 = boost::none) const override {
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const Point3 dir = Tb - Ta;
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Matrix33 H_predicted_dir;
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const Point3 predicted =
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dir.normalized(H1 || H2 ? &H_predicted_dir : nullptr);
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if (H1) *H1 = -H_predicted_dir;
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if (H2) *H2 = H_predicted_dir;
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return predicted - measured_w_aZb_;
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}
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private:
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friend class boost::serialization::access;
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template <class ARCHIVE>
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void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
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ar& boost::serialization::make_nvp(
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"Base", boost::serialization::base_object<Base>(*this));
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}
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}; // \ TranslationFactor
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} // namespace gtsam
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010-2020, 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 TranslationRecovery.h
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* @author Frank Dellaert
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* @date March 2020
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* @brief test recovering translations when rotations are given.
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*/
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#include <gtsam/sfm/TranslationRecovery.h>
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#include <gtsam/geometry/Point3.h>
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#include <gtsam/geometry/Pose3.h>
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#include <gtsam/geometry/Unit3.h>
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#include <gtsam/linear/NoiseModel.h>
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#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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#include <gtsam/nonlinear/NonlinearFactor.h>
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#include <gtsam/nonlinear/NonlinearFactorGraph.h>
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#include <gtsam/nonlinear/Values.h>
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#include <gtsam/sfm/TranslationFactor.h>
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#include <gtsam/slam/PriorFactor.h>
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using namespace gtsam;
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using namespace std;
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NonlinearFactorGraph TranslationRecovery::buildGraph() const {
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auto noiseModel = noiseModel::Isotropic::Sigma(3, 0.01);
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NonlinearFactorGraph graph;
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// Add all relative translation edges
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for (auto edge : relativeTranslations_) {
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Key a, b;
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tie(a, b) = edge.first;
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const Unit3 w_aZb = edge.second;
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graph.emplace_shared<TranslationFactor>(a, b, w_aZb, noiseModel);
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}
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return graph;
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}
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void TranslationRecovery::addPrior(const double scale,
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NonlinearFactorGraph* graph) const {
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auto noiseModel = noiseModel::Isotropic::Sigma(3, 0.01);
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auto edge = relativeTranslations_.begin();
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Key a, b;
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tie(a, b) = edge->first;
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const Unit3 w_aZb = edge->second;
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graph->emplace_shared<PriorFactor<Point3> >(a, Point3(0, 0, 0), noiseModel);
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graph->emplace_shared<PriorFactor<Point3> >(b, scale * w_aZb.point3(),
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noiseModel);
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}
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Values TranslationRecovery::initalizeRandomly() const {
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// Create a lambda expression that checks whether value exists and randomly
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// initializes if not.
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Values initial;
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auto insert = [&initial](Key j) {
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if (!initial.exists(j)) {
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initial.insert<Point3>(j, Vector3::Random());
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}
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};
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// Loop over measurements and add a random translation
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for (auto edge : relativeTranslations_) {
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Key a, b;
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tie(a, b) = edge.first;
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insert(a);
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insert(b);
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}
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return initial;
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}
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Values TranslationRecovery::run(const double scale) const {
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auto graph = buildGraph();
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addPrior(scale, &graph);
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const Values initial = initalizeRandomly();
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LevenbergMarquardtOptimizer lm(graph, initial, params_);
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Values result = lm.optimize();
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return result;
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}
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TranslationRecovery::TranslationEdges TranslationRecovery::SimulateMeasurements(
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const Values& poses, const vector<KeyPair>& edges) {
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TranslationEdges relativeTranslations;
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for (auto edge : edges) {
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Key a, b;
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tie(a, b) = edge;
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const Pose3 wTa = poses.at<Pose3>(a), wTb = poses.at<Pose3>(b);
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const Point3 Ta = wTa.translation(), Tb = wTb.translation();
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const Unit3 w_aZb(Tb - Ta);
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relativeTranslations[edge] = w_aZb;
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}
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return relativeTranslations;
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}
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010-2020, 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 TranslationRecovery.h
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* @author Frank Dellaert
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* @date March 2020
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* @brief test recovering translations when rotations are given.
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*/
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#include <gtsam/geometry/Unit3.h>
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#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
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#include <gtsam/nonlinear/Values.h>
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#include <map>
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#include <utility>
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namespace gtsam {
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// Set up an optimization problem for the unknown translations Ti in the world
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// coordinate frame, given the known camera attitudes wRi with respect to the
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// world frame, and a set of (noisy) translation directions of type Unit3,
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// w_aZb. The measurement equation is
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// w_aZb = Unit3(Tb - Ta) (1)
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// i.e., w_aZb is the translation direction from frame A to B, in world
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// coordinates. Although Unit3 instances live on a manifold, following
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// Wilson14eccv_1DSfM.pdf error we compute the *chordal distance* in the
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// ambient world coordinate frame.
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//
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// It is clear that we cannot recover the scale, nor the absolute position,
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// so the gauge freedom in this case is 3 + 1 = 4. We fix these by taking fixing
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// the translations Ta and Tb associated with the first measurement w_aZb,
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// clamping them to their initial values as given to this method. If no initial
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// values are given, we use the origin for Tb and set Tb to make (1) come
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// through, i.e.,
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// Tb = s * wRa * Point3(w_aZb) (2)
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// where s is an arbitrary scale that can be supplied, default 1.0. Hence, two
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// versions are supplied below corresponding to whether we have initial values
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// or not.
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class TranslationRecovery {
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public:
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using KeyPair = std::pair<Key, Key>;
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using TranslationEdges = std::map<KeyPair, Unit3>;
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private:
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TranslationEdges relativeTranslations_;
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LevenbergMarquardtParams params_;
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public:
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/**
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* @brief Construct a new Translation Recovery object
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*
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* @param relativeTranslations the relative translations, in world coordinate
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* frames, indexed in a map by a pair of Pose keys.
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* @param lmParams (optional) gtsam::LavenbergMarquardtParams that can be
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* used to modify the parameters for the LM optimizer. By default, uses the
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* default LM parameters.
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*/
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TranslationRecovery(const TranslationEdges& relativeTranslations,
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const LevenbergMarquardtParams& lmParams = LevenbergMarquardtParams())
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: relativeTranslations_(relativeTranslations), params_(lmParams) {
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params_.setVerbosityLM("Summary");
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}
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/**
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* @brief Build the factor graph to do the optimization.
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*
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* @return NonlinearFactorGraph
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*/
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NonlinearFactorGraph buildGraph() const;
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/**
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* @brief Add priors on ednpoints of first measurement edge.
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*
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* @param scale scale for first relative translation which fixes gauge.
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* @param graph factor graph to which prior is added.
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*/
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void addPrior(const double scale, NonlinearFactorGraph* graph) const;
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/**
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* @brief Create random initial translations.
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*
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* @return Values
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*/
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Values initalizeRandomly() const;
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/**
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* @brief Build and optimize factor graph.
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*
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* @param scale scale for first relative translation which fixes gauge.
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* @return Values
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*/
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Values run(const double scale = 1.0) const;
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/**
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* @brief Simulate translation direction measurements
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*
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* @param poses SE(3) ground truth poses stored as Values
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* @param edges pairs (a,b) for which a measurement w_aZb will be generated.
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* @return TranslationEdges map from a KeyPair to the simulated Unit3
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* translation direction measurement between the cameras in KeyPair.
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*/
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static TranslationEdges SimulateMeasurements(
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const Values& poses, const std::vector<KeyPair>& edges);
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};
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} // namespace gtsam
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010-2020, 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 testTranslationFactor.cpp
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* @brief Unit tests for TranslationFactor Class
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* @author Frank dellaert
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* @date March 2020
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*/
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#include <gtsam/base/numericalDerivative.h>
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#include <gtsam/geometry/Point3.h>
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#include <gtsam/sfm/TranslationFactor.h>
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#include <CppUnitLite/TestHarness.h>
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using namespace std;
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using namespace gtsam;
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// Create a noise model for the chordal error
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static SharedNoiseModel model(noiseModel::Isotropic::Sigma(3, 0.05));
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// Keys are deliberately *not* in sorted order to test that case.
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static const Key kKey1(2), kKey2(1);
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static const Unit3 kMeasured(1, 0, 0);
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/* ************************************************************************* */
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TEST(TranslationFactor, Constructor) {
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TranslationFactor factor(kKey1, kKey2, kMeasured, model);
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}
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/* ************************************************************************* */
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TEST(TranslationFactor, ZeroError) {
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// Create a factor
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TranslationFactor factor(kKey1, kKey2, kMeasured, model);
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// Set the linearization
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Point3 T1(1, 0, 0), T2(2, 0, 0);
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// Use the factor to calculate the error
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Vector actualError(factor.evaluateError(T1, T2));
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// Verify we get the expected error
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Vector expected = (Vector3() << 0, 0, 0).finished();
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EXPECT(assert_equal(expected, actualError, 1e-9));
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}
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/* ************************************************************************* */
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TEST(TranslationFactor, NonZeroError) {
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// create a factor
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TranslationFactor factor(kKey1, kKey2, kMeasured, model);
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// set the linearization
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Point3 T1(0, 1, 1), T2(0, 2, 2);
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// use the factor to calculate the error
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Vector actualError(factor.evaluateError(T1, T2));
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// verify we get the expected error
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Vector expected = (Vector3() << -1, 1/sqrt(2), 1/sqrt(2)).finished();
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EXPECT(assert_equal(expected, actualError, 1e-9));
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}
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/* ************************************************************************* */
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Vector factorError(const Point3& T1, const Point3& T2,
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const TranslationFactor& factor) {
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return factor.evaluateError(T1, T2);
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}
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TEST(TranslationFactor, Jacobian) {
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// Create a factor
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TranslationFactor factor(kKey1, kKey2, kMeasured, model);
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// Set the linearization
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Point3 T1(1, 0, 0), T2(2, 0, 0);
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// Use the factor to calculate the Jacobians
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Matrix H1Actual, H2Actual;
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factor.evaluateError(T1, T2, H1Actual, H2Actual);
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// Use numerical derivatives to calculate the Jacobians
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Matrix H1Expected, H2Expected;
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H1Expected = numericalDerivative11<Vector, Point3>(
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boost::bind(&factorError, _1, T2, factor), T1);
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H2Expected = numericalDerivative11<Vector, Point3>(
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boost::bind(&factorError, T1, _1, factor), T2);
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// Verify the Jacobians are correct
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EXPECT(assert_equal(H1Expected, H1Actual, 1e-9));
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EXPECT(assert_equal(H2Expected, H2Actual, 1e-9));
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}
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/* ************************************************************************* */
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int main() {
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TestResult tr;
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return TestRegistry::runAllTests(tr);
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}
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/* ************************************************************************* */
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@ -0,0 +1,87 @@
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/* ----------------------------------------------------------------------------
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* GTSAM Copyright 2010-2020, Georgia Tech Research Corporation,
|
||||
* Atlanta, Georgia 30332-0415
|
||||
* All Rights Reserved
|
||||
* Authors: Frank Dellaert, et al. (see THANKS for the full author list)
|
||||
|
||||
* See LICENSE for the license information
|
||||
|
||||
* -------------------------------------------------------------------------- */
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/**
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* @file testTranslationRecovery.cpp
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* @author Frank Dellaert
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* @date March 2020
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* @brief test recovering translations when rotations are given.
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*/
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#include <gtsam/sfm/TranslationRecovery.h>
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#include <CppUnitLite/TestHarness.h>
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#include <gtsam/slam/dataset.h>
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using namespace std;
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using namespace gtsam;
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/* ************************************************************************* */
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// We read the BAL file, which has 3 cameras in it, with poses. We then assume
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// the rotations are correct, but translations have to be estimated from
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// translation directions only. Since we have 3 cameras, A, B, and C, we can at
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// most create three relative measurements, let's call them w_aZb, w_aZc, and
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// bZc. These will be of type Unit3. We then call `recoverTranslations` which
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// sets up an optimization problem for the three unknown translations.
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TEST(TranslationRecovery, BAL) {
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const string filename = findExampleDataFile("dubrovnik-3-7-pre");
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SfmData db;
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bool success = readBAL(filename, db);
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if (!success) throw runtime_error("Could not access file!");
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// Get camera poses, as Values
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size_t j = 0;
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Values poses;
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for (auto camera : db.cameras) {
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poses.insert(j++, camera.pose());
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}
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// Simulate measurements
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const auto relativeTranslations = TranslationRecovery::SimulateMeasurements(
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poses, {{0, 1}, {0, 2}, {1, 2}});
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// Check
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const Pose3 wTa = poses.at<Pose3>(0), wTb = poses.at<Pose3>(1),
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wTc = poses.at<Pose3>(2);
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const Point3 Ta = wTa.translation(), Tb = wTb.translation(),
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Tc = wTc.translation();
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const Rot3 aRw = wTa.rotation().inverse();
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const Unit3 w_aZb = relativeTranslations.at({0, 1});
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EXPECT(assert_equal(Unit3(Tb - Ta), w_aZb));
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const Unit3 w_aZc = relativeTranslations.at({0, 2});
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EXPECT(assert_equal(Unit3(Tc - Ta), w_aZc));
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TranslationRecovery algorithm(relativeTranslations);
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const auto graph = algorithm.buildGraph();
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EXPECT_LONGS_EQUAL(3, graph.size());
|
||||
|
||||
// Translation recovery, version 1
|
||||
const double scale = 2.0;
|
||||
const auto result = algorithm.run(scale);
|
||||
|
||||
// Check result for first two translations, determined by prior
|
||||
EXPECT(assert_equal(Point3(0, 0, 0), result.at<Point3>(0)));
|
||||
EXPECT(assert_equal(Point3(2 * w_aZb.point3()), result.at<Point3>(1)));
|
||||
|
||||
// Check that the third translations is correct
|
||||
Point3 expected = (Tc - Ta) * (scale / (Tb - Ta).norm());
|
||||
EXPECT(assert_equal(expected, result.at<Point3>(2), 1e-4));
|
||||
|
||||
// TODO(frank): how to get stats back?
|
||||
// EXPECT_DOUBLES_EQUAL(0.0199833, actualError, 1e-5);
|
||||
}
|
||||
|
||||
/* ************************************************************************* */
|
||||
int main() {
|
||||
TestResult tr;
|
||||
return TestRegistry::runAllTests(tr);
|
||||
}
|
||||
/* ************************************************************************* */
|
||||
Loading…
Reference in New Issue