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gtsam/gtsam/geometry/CameraSet.h

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/* ----------------------------------------------------------------------------
* GTSAM Copyright 2010, 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
* -------------------------------------------------------------------------- */
/**
* @file CameraSet.h
* @brief Base class to create smart factors on poses or cameras
* @author Frank Dellaert
* @date Feb 19, 2015
*/
#pragma once
#include <gtsam/base/FastMap.h>
#include <gtsam/base/SymmetricBlockMatrix.h>
#include <gtsam/base/Testable.h>
#include <gtsam/geometry/CalibratedCamera.h> // for Cheirality exception
#include <gtsam/geometry/Point3.h>
#include <gtsam/inference/Key.h>
#include <vector>
namespace gtsam {
/**
* @brief A set of cameras, all with their own calibration
*/
template <class CAMERA>
class CameraSet : public std::vector<CAMERA, Eigen::aligned_allocator<CAMERA>> {
protected:
using Base = std::vector<CAMERA, typename Eigen::aligned_allocator<CAMERA>>;
/**
* 2D measurement and noise model for each of the m views
* The order is kept the same as the keys that we use to create the factor.
*/
typedef typename CAMERA::Measurement Z;
typedef typename CAMERA::MeasurementVector ZVector;
static const int D = traits<CAMERA>::dimension; ///< Camera dimension
static const int ZDim = traits<Z>::dimension; ///< Measurement dimension
/// Make a vector of re-projection errors
static Vector ErrorVector(const ZVector& predicted, const ZVector& measured) {
// Check size
size_t m = predicted.size();
if (measured.size() != m)
throw std::runtime_error("CameraSet::errors: size mismatch");
// Project and fill error vector
Vector b(ZDim * m);
for (size_t i = 0, row = 0; i < m; i++, row += ZDim) {
Vector bi = traits<Z>::Local(measured[i], predicted[i]);
if (ZDim == 3 && std::isnan(bi(1))) { // if it is a stereo point and the
// right pixel is missing (nan)
bi(1) = 0;
}
b.segment<ZDim>(row) = bi;
}
return b;
}
public:
using Base::Base; // Inherit the vector constructors
/// Destructor
virtual ~CameraSet() = default;
/// Definitions for blocks of F
using MatrixZD = Eigen::Matrix<double, ZDim, D>;
using FBlocks = std::vector<MatrixZD, Eigen::aligned_allocator<MatrixZD>>;
/**
* print
* @param s optional string naming the factor
* @param keyFormatter optional formatter useful for printing Symbols
*/
virtual void print(const std::string& s = "") const {
std::cout << s << "CameraSet, cameras = \n";
for (size_t k = 0; k < this->size(); ++k) this->at(k).print(s);
}
/// equals
bool equals(const CameraSet& p, double tol = 1e-9) const {
if (this->size() != p.size()) return false;
bool camerasAreEqual = true;
for (size_t i = 0; i < this->size(); i++) {
if (this->at(i).equals(p.at(i), tol) == false) camerasAreEqual = false;
break;
}
return camerasAreEqual;
}
/**
* Project a point (possibly Unit3 at infinity), with derivatives
* Note that F is a sparse block-diagonal matrix, so instead of a large dense
* matrix this function returns the diagonal blocks.
* throws CheiralityException
*/
template <class POINT>
ZVector project2(const POINT& point, //
boost::optional<FBlocks&> Fs = boost::none, //
boost::optional<Matrix&> E = boost::none) const {
static const int N = FixedDimension<POINT>::value;
// Allocate result
size_t m = this->size();
ZVector z;
z.reserve(m);
// Allocate derivatives
if (E) E->resize(ZDim * m, N);
if (Fs) Fs->resize(m);
// Project and fill derivatives
for (size_t i = 0; i < m; i++) {
MatrixZD Fi;
Eigen::Matrix<double, ZDim, N> Ei;
z.emplace_back(this->at(i).project2(point, Fs ? &Fi : 0, E ? &Ei : 0));
if (Fs) (*Fs)[i] = Fi;
if (E) E->block<ZDim, N>(ZDim * i, 0) = Ei;
}
return z;
}
/// Calculate vector [project2(point)-z] of re-projection errors
template <class POINT>
Vector reprojectionError(const POINT& point, const ZVector& measured,
boost::optional<FBlocks&> Fs = boost::none, //
boost::optional<Matrix&> E = boost::none) const {
return ErrorVector(project2(point, Fs, E), measured);
}
/**
* Do Schur complement, given Jacobian as Fs,E,P, return SymmetricBlockMatrix
* G = F' * F - F' * E * P * E' * F
* g = F' * (b - E * P * E' * b)
* Fixed size version
*/
template <int N,
int ND> // N = 2 or 3 (point dimension), ND is the camera dimension
static SymmetricBlockMatrix SchurComplement(
const std::vector<
Eigen::Matrix<double, ZDim, ND>,
Eigen::aligned_allocator<Eigen::Matrix<double, ZDim, ND>>>& Fs,
const Matrix& E, const Eigen::Matrix<double, N, N>& P, const Vector& b) {
// a single point is observed in m cameras
size_t m = Fs.size();
// Create a SymmetricBlockMatrix (augmented hessian, with extra row/column
// with info vector)
size_t M1 = ND * m + 1;
std::vector<DenseIndex> dims(m + 1); // this also includes the b term
std::fill(dims.begin(), dims.end() - 1, ND);
dims.back() = 1;
SymmetricBlockMatrix augmentedHessian(dims, Matrix::Zero(M1, M1));
// Blockwise Schur complement
for (size_t i = 0; i < m; i++) { // for each camera
const Eigen::Matrix<double, ZDim, ND>& Fi = Fs[i];
const auto FiT = Fi.transpose();
const Eigen::Matrix<double, ZDim, N> Ei_P = //
E.block(ZDim * i, 0, ZDim, N) * P;
// D = (Dx2) * ZDim
augmentedHessian.setOffDiagonalBlock(
i, m,
FiT * b.segment<ZDim>(ZDim * i) // F' * b
-
FiT *
(Ei_P *
(E.transpose() *
b))); // D = (DxZDim) * (ZDimx3) * (N*ZDimm) * (ZDimm x 1)
// (DxD) = (DxZDim) * ( (ZDimxD) - (ZDimx3) * (3xZDim) * (ZDimxD) )
augmentedHessian.setDiagonalBlock(
i,
FiT * (Fi - Ei_P * E.block(ZDim * i, 0, ZDim, N).transpose() * Fi));
// upper triangular part of the hessian
for (size_t j = i + 1; j < m; j++) { // for each camera
const Eigen::Matrix<double, ZDim, ND>& Fj = Fs[j];
// (DxD) = (Dx2) * ( (2x2) * (2xD) )
augmentedHessian.setOffDiagonalBlock(
i, j,
-FiT * (Ei_P * E.block(ZDim * j, 0, ZDim, N).transpose() * Fj));
}
} // end of for over cameras
augmentedHessian.diagonalBlock(m)(0, 0) += b.squaredNorm();
return augmentedHessian;
}
/**
* Do Schur complement, given Jacobian as Fs,E,P, return SymmetricBlockMatrix
* G = F' * F - F' * E * P * E' * F
* g = F' * (b - E * P * E' * b)
* In this version, we allow for the case where the keys in the Jacobian are
* organized differently from the keys in the output SymmetricBlockMatrix In
* particular: each diagonal block of the Jacobian F captures 2 poses (useful
* for rolling shutter and extrinsic calibration) such that F keeps the block
* structure that makes the Schur complement trick fast.
*
* N = 2 or 3 (point dimension), ND is the Jacobian block dimension, NDD is
* the Hessian block dimension
*/
template <int N, int ND, int NDD>
static SymmetricBlockMatrix SchurComplementAndRearrangeBlocks(
const std::vector<
Eigen::Matrix<double, ZDim, ND>,
Eigen::aligned_allocator<Eigen::Matrix<double, ZDim, ND>>>& Fs,
const Matrix& E, const Eigen::Matrix<double, N, N>& P, const Vector& b,
const KeyVector& jacobianKeys, const KeyVector& hessianKeys) {
size_t nrNonuniqueKeys = jacobianKeys.size();
size_t nrUniqueKeys = hessianKeys.size();
// Marginalize point: note - we reuse the standard SchurComplement function.
SymmetricBlockMatrix augmentedHessian = SchurComplement<N, ND>(Fs, E, P, b);
// Pack into an Hessian factor, allow space for b term.
std::vector<DenseIndex> dims(nrUniqueKeys + 1);
std::fill(dims.begin(), dims.end() - 1, NDD);
dims.back() = 1;
SymmetricBlockMatrix augmentedHessianUniqueKeys;
// Deal with the fact that some blocks may share the same keys.
if (nrUniqueKeys == nrNonuniqueKeys) {
// Case when there is 1 calibration key per camera:
augmentedHessianUniqueKeys = SymmetricBlockMatrix(
dims, Matrix(augmentedHessian.selfadjointView()));
} else {
// When multiple cameras share a calibration we have to rearrange
// the results of the Schur complement matrix.
std::vector<DenseIndex> nonuniqueDims(nrNonuniqueKeys + 1); // includes b
std::fill(nonuniqueDims.begin(), nonuniqueDims.end() - 1, NDD);
nonuniqueDims.back() = 1;
augmentedHessian = SymmetricBlockMatrix(
nonuniqueDims, Matrix(augmentedHessian.selfadjointView()));
// Get map from key to location in the new augmented Hessian matrix (the
// one including only unique keys).
std::map<Key, size_t> keyToSlotMap;
for (size_t k = 0; k < nrUniqueKeys; k++) {
keyToSlotMap[hessianKeys[k]] = k;
}
// Initialize matrix to zero.
augmentedHessianUniqueKeys = SymmetricBlockMatrix(
dims, Matrix::Zero(NDD * nrUniqueKeys + 1, NDD * nrUniqueKeys + 1));
// Add contributions for each key: note this loops over the hessian with
// nonUnique keys (augmentedHessian) and populates an Hessian that only
// includes the unique keys (that is what we want to return).
for (size_t i = 0; i < nrNonuniqueKeys; i++) { // rows
Key key_i = jacobianKeys.at(i);
// Update information vector.
augmentedHessianUniqueKeys.updateOffDiagonalBlock(
keyToSlotMap[key_i], nrUniqueKeys,
augmentedHessian.aboveDiagonalBlock(i, nrNonuniqueKeys));
// Update blocks.
for (size_t j = i; j < nrNonuniqueKeys; j++) { // cols
Key key_j = jacobianKeys.at(j);
if (i == j) {
augmentedHessianUniqueKeys.updateDiagonalBlock(
keyToSlotMap[key_i], augmentedHessian.diagonalBlock(i));
} else { // (i < j)
if (keyToSlotMap[key_i] != keyToSlotMap[key_j]) {
augmentedHessianUniqueKeys.updateOffDiagonalBlock(
keyToSlotMap[key_i], keyToSlotMap[key_j],
augmentedHessian.aboveDiagonalBlock(i, j));
} else {
augmentedHessianUniqueKeys.updateDiagonalBlock(
keyToSlotMap[key_i],
augmentedHessian.aboveDiagonalBlock(i, j) +
augmentedHessian.aboveDiagonalBlock(i, j).transpose());
}
}
}
}
// Update bottom right element of the matrix.
augmentedHessianUniqueKeys.updateDiagonalBlock(
nrUniqueKeys, augmentedHessian.diagonalBlock(nrNonuniqueKeys));
}
return augmentedHessianUniqueKeys;
}
/**
* Do Schur complement, given Jacobian as Fs,E,P, return SymmetricBlockMatrix
* G = F' * F - F' * E * P * E' * F
* g = F' * (b - E * P * E' * b)
* Fixed size version
*/
template <int N> // N = 2 or 3
static SymmetricBlockMatrix SchurComplement(
const FBlocks& Fs, const Matrix& E, const Eigen::Matrix<double, N, N>& P,
const Vector& b) {
return SchurComplement<N, D>(Fs, E, P, b);
}
/// Computes Point Covariance P, with lambda parameter
template <int N> // N = 2 or 3 (point dimension)
static void ComputePointCovariance(Eigen::Matrix<double, N, N>& P,
const Matrix& E, double lambda,
bool diagonalDamping = false) {
Matrix EtE = E.transpose() * E;
if (diagonalDamping) { // diagonal of the hessian
EtE.diagonal() += lambda * EtE.diagonal();
} else {
DenseIndex n = E.cols();
EtE += lambda * Eigen::MatrixXd::Identity(n, n);
}
P = (EtE).inverse();
}
/// Computes Point Covariance P, with lambda parameter, dynamic version
static Matrix PointCov(const Matrix& E, const double lambda = 0.0,
bool diagonalDamping = false) {
if (E.cols() == 2) {
Matrix2 P2;
ComputePointCovariance<2>(P2, E, lambda, diagonalDamping);
return P2;
} else {
Matrix3 P3;
ComputePointCovariance<3>(P3, E, lambda, diagonalDamping);
return P3;
}
}
/**
* Do Schur complement, given Jacobian as Fs,E,P, return SymmetricBlockMatrix
* Dynamic version
*/
static SymmetricBlockMatrix SchurComplement(const FBlocks& Fblocks,
const Matrix& E, const Vector& b,
const double lambda = 0.0,
bool diagonalDamping = false) {
if (E.cols() == 2) {
Matrix2 P;
ComputePointCovariance<2>(P, E, lambda, diagonalDamping);
return SchurComplement<2>(Fblocks, E, P, b);
} else {
Matrix3 P;
ComputePointCovariance<3>(P, E, lambda, diagonalDamping);
return SchurComplement<3>(Fblocks, E, P, b);
}
}
/**
* Applies Schur complement (exploiting block structure) to get a smart factor
* on cameras, and adds the contribution of the smart factor to a
* pre-allocated augmented Hessian.
*/
template <int N> // N = 2 or 3 (point dimension)
static void UpdateSchurComplement(
const FBlocks& Fs, const Matrix& E, const Eigen::Matrix<double, N, N>& P,
const Vector& b, const KeyVector& allKeys, const KeyVector& keys,
/*output ->*/ SymmetricBlockMatrix& augmentedHessian) {
assert(keys.size() == Fs.size());
assert(keys.size() <= allKeys.size());
FastMap<Key, size_t> KeySlotMap;
for (size_t slot = 0; slot < allKeys.size(); slot++)
KeySlotMap.insert(std::make_pair(allKeys[slot], slot));
// Schur complement trick
// G = F' * F - F' * E * P * E' * F
// g = F' * (b - E * P * E' * b)
// a single point is observed in m cameras
size_t m = Fs.size(); // cameras observing current point
size_t M = (augmentedHessian.rows() - 1) / D; // all cameras in the group
assert(allKeys.size() == M);
// Blockwise Schur complement
for (size_t i = 0; i < m; i++) { // for each camera in the current factor
const MatrixZD& Fi = Fs[i];
const auto FiT = Fi.transpose();
const Eigen::Matrix<double, 2, N> Ei_P =
E.template block<ZDim, N>(ZDim * i, 0) * P;
// D = (DxZDim) * (ZDim)
// allKeys are the list of all camera keys in the group, e.g, (1,3,4,5,7)
// we should map those to a slot in the local (grouped) hessian
// (0,1,2,3,4) Key cameraKey_i = this->keys_[i];
DenseIndex aug_i = KeySlotMap.at(keys[i]);
// information vector - store previous vector
// vectorBlock = augmentedHessian(aug_i, aug_m).knownOffDiagonal();
// add contribution of current factor
augmentedHessian.updateOffDiagonalBlock(
aug_i, M,
FiT * b.segment<ZDim>(ZDim * i) // F' * b
-
FiT *
(Ei_P *
(E.transpose() *
b))); // D = (DxZDim) * (ZDimx3) * (N*ZDimm) * (ZDimm x 1)
// (DxD) += (DxZDim) * ( (ZDimxD) - (ZDimx3) * (3xZDim) * (ZDimxD) )
// add contribution of current factor
// TODO(gareth): Eigen doesn't let us pass the expression. Call eval() for
// now...
augmentedHessian.updateDiagonalBlock(
aug_i,
((FiT *
(Fi -
Ei_P * E.template block<ZDim, N>(ZDim * i, 0).transpose() * Fi)))
.eval());
// upper triangular part of the hessian
for (size_t j = i + 1; j < m; j++) { // for each camera
const MatrixZD& Fj = Fs[j];
DenseIndex aug_j = KeySlotMap.at(keys[j]);
// (DxD) = (DxZDim) * ( (ZDimxZDim) * (ZDimxD) )
// off diagonal block - store previous block
// matrixBlock = augmentedHessian(aug_i, aug_j).knownOffDiagonal();
// add contribution of current factor
augmentedHessian.updateOffDiagonalBlock(
aug_i, aug_j,
-FiT * (Ei_P * E.template block<ZDim, N>(ZDim * j, 0).transpose() *
Fj));
}
} // end of for over cameras
augmentedHessian.diagonalBlock(M)(0, 0) += b.squaredNorm();
}
private:
/// Serialization function
friend class boost::serialization::access;
template <class ARCHIVE>
void serialize(ARCHIVE& ar, const unsigned int /*version*/) {
ar&(*this);
}
public:
GTSAM_MAKE_ALIGNED_OPERATOR_NEW
};
template <class CAMERA>
const int CameraSet<CAMERA>::D;
template <class CAMERA>
const int CameraSet<CAMERA>::ZDim;
template <class CAMERA>
struct traits<CameraSet<CAMERA>> : public Testable<CameraSet<CAMERA>> {};
template <class CAMERA>
struct traits<const CameraSet<CAMERA>> : public Testable<CameraSet<CAMERA>> {};
} // namespace gtsam
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