Checked evaluation and calculation
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@ -6,27 +6,30 @@
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*/
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#include <gtsam/slam/EssentialMatrixFactor.h>
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#include <gtsam/geometry/SimpleCamera.h>
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#include <gtsam/base/LieScalar.h>
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namespace gtsam {
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/**
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* Binary factor that optimizes for E and inverse depth: assumes measurement
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* in image 1 is perfect, and returns re-projection error in image 2
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* in image 2 is perfect, and returns re-projection error in image 1
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*/
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class EssentialMatrixFactor2: public NoiseModelFactor2<EssentialMatrix,
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LieScalar> {
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Point2 pA_, pB_; ///< Measurements in image A and B
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Cal3_S2 K_; ///< Calibration
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typedef NoiseModelFactor2<EssentialMatrix, LieScalar> Base;
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typedef EssentialMatrixFactor2 This;
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public:
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/// Constructor
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EssentialMatrixFactor2(Key key1, Key key2, const Point2& pA, const Point2& pB,
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const SharedNoiseModel& model) :
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Base(model, key1, key2), pA_(pA), pB_(pB) {
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const Cal3_S2& K, const SharedNoiseModel& model) :
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Base(model, key1, key2), pA_(pA), pB_(pB), K_(K) {
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}
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/// print
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@ -42,16 +45,32 @@ public:
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Vector evaluateError(const EssentialMatrix& E, const LieScalar& d,
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boost::optional<Matrix&> H1 = boost::none, boost::optional<Matrix&> H2 =
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boost::none) const {
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// We have point x,y in image 1
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// Given a depth Z, the corresponding 3D point P1 = Z*(x,y,1) = (x,y,1)/d
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// We then convert to first camera by 2P = 1R2Õ*(P1-1T2)
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// The homogeneous coordinates of can be written as
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// 2R1*(P1-1T2) == 2R1*d*(P1-1T2) == 2R1*((x,y,1)-d*1T2)
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// Note that this is just a homography for d==0
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Point3 dP1(pA_.x(), pA_.y(), 1);
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Point3 P2 = E.rotation().unrotate(dP1 - d * E.direction().point3());
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// Project to normalized image coordinates, then uncalibrate
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const Point2 pn = SimpleCamera::project_to_camera(P2);
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const Point2 pi = K_.uncalibrate(pn);
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Point2 reprojectionError(pi - pB_);
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if (H1)
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*H1 = zeros(2, 5);
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if (H2)
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*H2 = zeros(2, 1);
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return (Vector(2) << 0,0);
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return reprojectionError.vector();
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}
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};
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} // gtsam
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}
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// gtsam
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#include <gtsam/slam/dataset.h>
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#include <gtsam/nonlinear/NonlinearFactorGraph.h>
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@ -187,31 +206,47 @@ TEST (EssentialMatrixFactor, fromConstraints) {
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//*************************************************************************
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TEST (EssentialMatrixFactor2, factor) {
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EssentialMatrix trueE(aRb, aTb);
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LieScalar d(5);
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EssentialMatrix E(aRb, aTb);
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noiseModel::Unit::shared_ptr model = noiseModel::Unit::Create(1);
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for (size_t i = 0; i < 5; i++) {
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EssentialMatrixFactor2 factor(100, i, pA(i), pB(i), model);
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Cal3_S2 K;
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EssentialMatrixFactor2 factor(100, i, pA(i), pB(i), K, model);
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// Check evaluation
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Vector expected(1);
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expected << 0;
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Point3 P1 = data.tracks[i].p, P2 = E.transform_to(P1);
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LieScalar d(1.0 / P1.z());
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const Point2 pn = SimpleCamera::project_to_camera(P2);
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const Point2 pi = K.uncalibrate(pn);
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Point2 reprojectionError(pi - pB(i));
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Vector expected = reprojectionError.vector();
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{
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// Check calculations
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Point3 dP1(pA(i).x(), pA(i).y(), 1);
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EXPECT_DOUBLES_EQUAL(pA(i).x(), P1.x()/P1.z(), 1e-8);
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EXPECT_DOUBLES_EQUAL(pA(i).y(), P1.y()/P1.z(), 1e-8);
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EXPECT(assert_equal(P1,dP1/d));
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Point3 otherP2 = E.rotation().unrotate(
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d * P1 - d * E.direction().point3());
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EXPECT(assert_equal(P2,otherP2/d));
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}
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Matrix Hactual1, Hactual2;
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Vector actual = factor.evaluateError(trueE, d, Hactual1, Hactual2);
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Vector actual = factor.evaluateError(E, d, Hactual1, Hactual2);
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EXPECT(assert_equal(expected, actual, 1e-7));
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// Use numerical derivatives to calculate the expected Jacobian
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Matrix Hexpected1, Hexpected2;
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boost::function<Vector(const EssentialMatrix&, const LieScalar&)> f =
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boost::bind(&EssentialMatrixFactor2::evaluateError, &factor, _1, _2,
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boost::none, boost::none);
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Hexpected1 = numericalDerivative21<EssentialMatrix>(f, trueE, d);
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Hexpected2 = numericalDerivative22<EssentialMatrix>(f, trueE, d);
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// Verify the Jacobian is correct
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EXPECT(assert_equal(Hexpected1, Hactual1, 1e-8));
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EXPECT(assert_equal(Hexpected2, Hactual2, 1e-8));
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// // Use numerical derivatives to calculate the expected Jacobian
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// Matrix Hexpected1, Hexpected2;
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// boost::function<Vector(const EssentialMatrix&, const LieScalar&)> f =
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// boost::bind(&EssentialMatrixFactor2::evaluateError, &factor, _1, _2,
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// boost::none, boost::none);
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// Hexpected1 = numericalDerivative21<EssentialMatrix>(f, E, d);
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// Hexpected2 = numericalDerivative22<EssentialMatrix>(f, E, d);
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//
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// // Verify the Jacobian is correct
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// EXPECT(assert_equal(Hexpected1, Hactual1, 1e-8));
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// EXPECT(assert_equal(Hexpected2, Hactual2, 1e-8));
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}
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}
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