ba_full.cpp

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/* +------------------------------------------------------------------------+
   |                     Mobile Robot Programming Toolkit (MRPT)            |
   |                          http://www.mrpt.org/                          |
   |                                                                        |
   | Copyright (c) 2005-2017, Individual contributors, see AUTHORS file     |
   | See: http://www.mrpt.org/Authors - All rights reserved.                |
   | Released under BSD License. See details in http://www.mrpt.org/License |
   +------------------------------------------------------------------------+ */

#include "vision-precomp.h"  // Precompiled headers

#include <mrpt/vision/bundle_adjustment.h>
#include <mrpt/utils/CTimeLogger.h>
#include <mrpt/math/CSparseMatrix.h>
#include <mrpt/math/ops_containers.h>

#include <memory>  // unique_ptr

#include "ba_internals.h"

using namespace std;
using namespace mrpt;
using namespace mrpt::vision;
using namespace mrpt::utils;
using namespace mrpt::math;

using mrpt::aligned_containers;

// Define -> estimate the inverse of poses; Undefined -> estimate the camera
// poses (read the doc of mrpt::vision::bundle_adj_full)
#define USE_INVERSE_POSES

#ifdef USE_INVERSE_POSES
#define INV_POSES_BOOL true
#else
#define INV_POSES_BOOL false
#endif

/* ----------------------------------------------------------
                                        bundle_adj_full

        See bundle_adjustment.h for docs.

  This implementation is almost entirely an adapted version from
  RobotVision (at OpenSLAM.org) (C) by Hauke Strasdat (Imperial
  College London), licensed under GNU LGPL.
  See the related paper:  H. Strasdat, J.M.M. Montiel,
  A.J. Davison: "Scale Drift-Aware Large Scale Monocular SLAM",
  RSS2010, http://www.roboticsproceedings.org/rss06/p10.html

   ---------------------------------------------------------- */
double mrpt::vision::bundle_adj_full(
        const TSequenceFeatureObservations& observations,
        const TCamera& camera_params, TFramePosesVec& frame_poses,
        TLandmarkLocationsVec& landmark_points,
        const mrpt::utils::TParametersDouble& extra_params,
        const TBundleAdjustmentFeedbackFunctor user_feedback)
{
        MRPT_START

        // Generic BA problem dimension numbers:
        static const unsigned int FrameDof = 6;  // Poses: x y z yaw pitch roll
        static const unsigned int PointDof = 3;  // Landmarks: x y z
        static const unsigned int ObsDim = 2;  // Obs: x y (pixels)

        // Typedefs for this specific BA problem:
        typedef JacData<FrameDof, PointDof, ObsDim> MyJacData;
        typedef aligned_containers<MyJacData>::vector_t MyJacDataVec;

        typedef std::array<double, ObsDim> Array_O;
        typedef CArrayDouble<FrameDof> Array_F;
        typedef CArrayDouble<PointDof> Array_P;
        typedef CMatrixFixedNumeric<double, FrameDof, FrameDof> Matrix_FxF;
        typedef CMatrixFixedNumeric<double, PointDof, PointDof> Matrix_PxP;
        typedef CMatrixFixedNumeric<double, FrameDof, PointDof> Matrix_FxP;

        // Extra params:
        const bool use_robust_kernel =
                0 != extra_params.getWithDefaultVal("robust_kernel", 1);
        const bool verbose = 0 != extra_params.getWithDefaultVal("verbose", 0);
        const double initial_mu = extra_params.getWithDefaultVal("mu", -1);
        const size_t max_iters =
                extra_params.getWithDefaultVal("max_iterations", 50);
        const size_t num_fix_frames =
                extra_params.getWithDefaultVal("num_fix_frames", 1);
        const size_t num_fix_points =
                extra_params.getWithDefaultVal("num_fix_points", 0);
        const double kernel_param =
                extra_params.getWithDefaultVal("kernel_param", 3.0);

        const bool enable_profiler =
                0 != extra_params.getWithDefaultVal("profiler", 0);

        mrpt::utils::CTimeLogger profiler(enable_profiler);

        profiler.enter("bundle_adj_full (complete run)");

        // Input data sizes:
        const size_t num_points = landmark_points.size();
        const size_t num_frames = frame_poses.size();
        const size_t num_obs = observations.size();

        ASSERT_ABOVE_(num_frames, 0)
        ASSERT_ABOVE_(num_points, 0)
        ASSERT_(num_fix_frames >= 1)
        ASSERT_ABOVEEQ_(num_frames, num_fix_frames);
        ASSERT_ABOVEEQ_(num_points, num_fix_points);

#ifdef USE_INVERSE_POSES
        // *Warning*: This implementation assumes inverse camera poses: inverse them
        // at the entrance and at exit:
        profiler.enter("invert_poses");
        for (size_t i = 0; i < num_frames; i++) frame_poses[i].inverse();
        profiler.leave("invert_poses");
#endif

        MyJacDataVec jac_data_vec(num_obs);
        vector<Array_O> residual_vec(num_obs);
        vector<double> kernel_1st_deriv(num_obs);

        // prepare structure of sparse Jacobians:
        for (size_t i = 0; i < num_obs; i++)
        {
                jac_data_vec[i].frame_id = observations[i].id_frame;
                jac_data_vec[i].point_id = observations[i].id_feature;
        }

        // Compute sparse Jacobians:
        profiler.enter("compute_Jacobians");
        ba_compute_Jacobians<INV_POSES_BOOL>(
                frame_poses, landmark_points, camera_params, jac_data_vec,
                num_fix_frames, num_fix_points);
        profiler.leave("compute_Jacobians");

        profiler.enter("reprojectionResiduals");
        double res = mrpt::vision::reprojectionResiduals(
                observations, camera_params, frame_poses, landmark_points, residual_vec,
                INV_POSES_BOOL,  // are poses inverse?
                use_robust_kernel, kernel_param,
                use_robust_kernel ? &kernel_1st_deriv : nullptr);
        profiler.leave("reprojectionResiduals");

        MRPT_CHECK_NORMAL_NUMBER(res)

        VERBOSE_COUT << "res: " << res << endl;

        // Auxiliary vars:
        Array_F arrF_zeros;
        arrF_zeros.assign(0);
        Array_P arrP_zeros;
        arrP_zeros.assign(0);

        const size_t num_free_frames = num_frames - num_fix_frames;
        const size_t num_free_points = num_points - num_fix_points;
        const size_t len_free_frames = FrameDof * num_free_frames;
        const size_t len_free_points = PointDof * num_free_points;

        aligned_containers<Matrix_FxF>::vector_t H_f(num_free_frames);
        aligned_containers<Array_F>::vector_t eps_frame(
                num_free_frames, arrF_zeros);
        aligned_containers<Matrix_PxP>::vector_t H_p(num_free_points);
        aligned_containers<Array_P>::vector_t eps_point(
                num_free_points, arrP_zeros);

        profiler.enter("build_gradient_Hessians");
        ba_build_gradient_Hessians(
                observations, residual_vec, jac_data_vec, H_f, eps_frame, H_p,
                eps_point, num_fix_frames, num_fix_points,
                use_robust_kernel ? &kernel_1st_deriv : nullptr);
        profiler.leave("build_gradient_Hessians");

        double nu = 2;
        double eps = 1e-16;  // 0.000000000000001;
        bool stop = false;
        double mu = initial_mu;

        // Automatic guess of "mu":
        if (mu < 0)
        {
                double norm_max_A = 0;
                for (size_t j = 0; j < num_free_frames; ++j)
                        for (size_t dim = 0; dim < FrameDof; dim++)
                                keep_max(norm_max_A, H_f[j](dim, dim));

                for (size_t i = 0; i < num_free_points; ++i)
                        for (size_t dim = 0; dim < PointDof; dim++)
                                keep_max(norm_max_A, H_p[i](dim, dim));
                double tau = 1e-3;
                mu = tau * norm_max_A;
        }

        Matrix_FxF I_muFrame(UNINITIALIZED_MATRIX);
        Matrix_PxP I_muPoint(UNINITIALIZED_MATRIX);

        // Cholesky object, as a pointer to reuse it between iterations:
        typedef std::unique_ptr<CSparseMatrix::CholeskyDecomp> SparseCholDecompPtr;

        SparseCholDecompPtr ptrCh;

        for (size_t iter = 0; iter < max_iters; iter++)
        {
                VERBOSE_COUT << "iteration: " << iter << endl;

                // provide feedback to the user:
                if (user_feedback)
                        user_feedback(
                                iter, res, max_iters, observations, frame_poses,
                                landmark_points);

                bool has_improved = false;
                do
                {
                        profiler.enter("COMPLETE_ITER");

                        VERBOSE_COUT << "mu: " << mu << endl;

                        I_muFrame.unit(FrameDof, mu);
                        I_muPoint.unit(PointDof, mu);

                        aligned_containers<Matrix_FxF>::vector_t U_star(
                                num_free_frames, I_muFrame);
                        aligned_containers<Matrix_PxP>::vector_t V_inv(num_free_points);

                        for (size_t i = 0; i < U_star.size(); ++i) U_star[i] += H_f[i];

                        for (size_t i = 0; i < H_p.size(); ++i)
                                (H_p[i] + I_muPoint).inv_fast(V_inv[i]);

                        typedef aligned_containers<pair<TCameraPoseID, TLandmarkID>,
                                                                           Matrix_FxP>::map_t WMap;
                        WMap W, Y;

                        // For quick look-up of entries in W affecting a given point ID:
                        vector<vector<WMap::iterator>> W_entries(
                                num_points);  // Index is "TLandmarkID"

                        MyJacDataVec::const_iterator jac_iter = jac_data_vec.begin();
                        for (TSequenceFeatureObservations::const_iterator it_obs =
                                         observations.begin();
                                 it_obs != observations.end(); ++it_obs)
                        {
                                const TFeatureID feat_id = it_obs->id_feature;
                                const TCameraPoseID frame_id = it_obs->id_frame;

                                if (jac_iter->J_frame_valid && jac_iter->J_point_valid)
                                {
                                        const CMatrixFixedNumeric<double, ObsDim, FrameDof>&
                                                J_frame = jac_iter->J_frame;
                                        const CMatrixFixedNumeric<double, ObsDim, PointDof>&
                                                J_point = jac_iter->J_point;
                                        const pair<TCameraPoseID, TLandmarkID> id_pair =
                                                make_pair(frame_id, feat_id);

                                        Matrix_FxP tmp(UNINITIALIZED_MATRIX);
                                        tmp.multiply_AtB(J_frame, J_point);

                                        // W[ids] = J_f^T * J_p
                                        // Was: W[id_pair] = tmp;
                                        const pair<WMap::iterator, bool>& retInsert =
                                                W.insert(make_pair(id_pair, tmp));
                                        ASSERT_(retInsert.second == true)
                                        W_entries[feat_id].push_back(
                                                retInsert.first);  // Keep the iterator

                                        // Y[ids] = W[ids] * H_p^{-1}
                                        Y[id_pair].multiply_AB(
                                                tmp, V_inv[feat_id - num_fix_points]);
                                }
                                ++jac_iter;
                        }

                        aligned_containers<pair<TCameraPoseID, TLandmarkID>,
                                                           Matrix_FxF>::map_t YW_map;
                        for (size_t i = 0; i < H_f.size(); ++i)
                                YW_map[std::pair<TCameraPoseID, TLandmarkID>(i, i)] = U_star[i];

                        CVectorDouble delta(
                                len_free_frames + len_free_points);  // The optimal step
                        CVectorDouble e(len_free_frames);

                        profiler.enter("Schur.build.reduced.frames");
                        for (size_t j = 0; j < num_free_frames; ++j)
                                ::memcpy(
                                        &e[j * FrameDof], &eps_frame[j][0],
                                        sizeof(e[0]) * FrameDof);  // e.slice(j*FrameDof,FrameDof) =
                        // AT(eps_frame,j);

                        for (WMap::iterator Y_ij = Y.begin(); Y_ij != Y.end(); ++Y_ij)
                        {
                                const TLandmarkID point_id = Y_ij->first.second;
                                const size_t i =
                                        Y_ij->first.second - num_fix_points;  // point index
                                const size_t j =
                                        Y_ij->first.first - num_fix_frames;  // frame index

                                const vector<WMap::iterator>& iters =
                                        W_entries[point_id];  //->second;

                                for (size_t itIdx = 0; itIdx < iters.size(); itIdx++)
                                // for (size_t k=0; k<num_free_frames; ++k)
                                {
                                        const WMap::iterator& W_ik = iters[itIdx];
                                        const TLandmarkID k = W_ik->first.first - num_fix_frames;

                                        Matrix_FxF YWt(UNINITIALIZED_MATRIX);  //-(Y_ij->second) *
                                        //(W_ik->second).T();
                                        YWt.multiply_ABt(Y_ij->second, W_ik->second);
                                        // YWt*=-1.0; // The "-" sign is taken into account below:

                                        const pair<TCameraPoseID, TLandmarkID> ids_jk =
                                                pair<TCameraPoseID, TLandmarkID>(j, k);

                                        aligned_containers<pair<TCameraPoseID, TLandmarkID>,
                                                                           Matrix_FxF>::map_t::iterator it =
                                                YW_map.find(ids_jk);
                                        if (it != YW_map.end())
                                                it->second -= YWt;  // += (-YWt);
                                        else
                                                YW_map[ids_jk] = YWt * (-1.0);
                                }

                                CArrayDouble<FrameDof> r;
                                Y_ij->second.multiply_Ab(eps_point[i], r);
                                for (size_t k = 0; k < FrameDof; k++)
                                        e[j * FrameDof + k] -= r[k];
                        }
                        profiler.leave("Schur.build.reduced.frames");

                        profiler.enter("sS:ALL");
                        profiler.enter("sS:fill");

                        VERBOSE_COUT << "Entries in YW_map:" << YW_map.size() << endl;

                        CSparseMatrix sS(len_free_frames, len_free_frames);

                        for (aligned_containers<pair<TCameraPoseID, TLandmarkID>,
                                                                        Matrix_FxF>::map_t::const_iterator it =
                                         YW_map.begin();
                                 it != YW_map.end(); ++it)
                        {
                                const pair<TCameraPoseID, TLandmarkID>& ids = it->first;
                                const Matrix_FxF& YW = it->second;
                                sS.insert_submatrix(
                                        ids.first * FrameDof, ids.second * FrameDof, YW);
                        }
                        profiler.leave("sS:fill");

                        // Compress the sparse matrix:
                        profiler.enter("sS:compress");
                        sS.compressFromTriplet();
                        profiler.leave("sS:compress");

                        try
                        {
                                profiler.enter("sS:chol");
                                if (!ptrCh.get())
                                        ptrCh.reset(new CSparseMatrix::CholeskyDecomp(sS));
                                else
                                        ptrCh.get()->update(sS);
                                profiler.leave("sS:chol");

                                profiler.enter("sS:backsub");
                                CVectorDouble bck_res;
                                ptrCh->backsub(e, bck_res);  // Ax = b -->  delta= x*
                                ::memcpy(
                                        &delta[0], &bck_res[0],
                                        bck_res.size() * sizeof(bck_res[0]));  // delta.slice(0,...)
                                // = Ch.backsub(e);
                                profiler.leave("sS:backsub");
                                profiler.leave("sS:ALL");
                        }
                        catch (CExceptionNotDefPos&)
                        {
                                profiler.leave("sS:ALL");
                                // not positive definite so increase mu and try again
                                mu *= nu;
                                nu *= 2.;
                                stop = (mu > 999999999.f);
                                continue;
                        }

                        profiler.enter("PostSchur.landmarks");

                        CVectorDouble g(len_free_frames + len_free_points);
                        ::memcpy(
                                &g[0], &e[0],
                                len_free_frames *
                                        sizeof(
                                                g[0]));  // g.slice(0,FrameDof*(num_frames-num_fix_frames))
                        // = e;

                        for (size_t i = 0; i < num_free_points; ++i)
                        {
                                Array_P tmp =
                                        eps_point[i];  // eps_point.slice(PointDof*i,PointDof);

                                for (size_t j = 0; j < num_free_frames; ++j)
                                {
                                        WMap::iterator W_ij;
                                        W_ij = W.find(
                                                make_pair(
                                                        TCameraPoseID(j + num_fix_frames),
                                                        TLandmarkID(i + num_fix_points)));

                                        if (W_ij != W.end())
                                        {
                                                // tmp -= W_ij->second.T() *
                                                // delta.slice(j*FrameDof,FrameDof);
                                                const Array_F v(&delta[j * FrameDof]);
                                                Array_P r;
                                                W_ij->second.multiply_Atb(v, r);  // r= A^t * v
                                                tmp -= r;
                                        }
                                }
                                Array_P Vi_tmp;
                                V_inv[i].multiply_Ab(tmp, Vi_tmp);  // Vi_tmp = V_inv[i] * tmp

                                ::memcpy(
                                        &delta[len_free_frames + i * PointDof], &Vi_tmp[0],
                                        sizeof(Vi_tmp[0]) * PointDof);
                                ::memcpy(
                                        &g[len_free_frames + i * PointDof], &eps_point[i][0],
                                        sizeof(eps_point[0][0]) * PointDof);
                        }
                        profiler.leave("PostSchur.landmarks");

                        // Vars for temptative new estimates:
                        TFramePosesVec new_frame_poses;
                        TLandmarkLocationsVec new_landmark_points;

                        profiler.enter("add_se3_deltas_to_frames");
                        add_se3_deltas_to_frames(
                                frame_poses, delta, 0, len_free_frames, new_frame_poses,
                                num_fix_frames);
                        profiler.leave("add_se3_deltas_to_frames");

                        profiler.enter("add_3d_deltas_to_points");
                        add_3d_deltas_to_points(
                                landmark_points, delta, len_free_frames, len_free_points,
                                new_landmark_points, num_fix_points);
                        profiler.leave("add_3d_deltas_to_points");

                        vector<Array_O> new_residual_vec(num_obs);
                        vector<double> new_kernel_1st_deriv(num_obs);

                        profiler.enter("reprojectionResiduals");
                        double res_new = mrpt::vision::reprojectionResiduals(
                                observations, camera_params, new_frame_poses,
                                new_landmark_points, new_residual_vec,
                                INV_POSES_BOOL,  // are poses inverse?
                                use_robust_kernel, kernel_param,
                                use_robust_kernel ? &new_kernel_1st_deriv : nullptr);
                        profiler.leave("reprojectionResiduals");

                        MRPT_CHECK_NORMAL_NUMBER(res_new)

                        has_improved = (res_new < res);

                        if (has_improved)
                        {
                                // rho = (res-)/ (delta.array()*(mu*delta + g).array() ).sum();
                                // Good: Accept new values
                                VERBOSE_COUT << "new total sqr.err=" << res_new
                                                         << " avr.err(px):" << std::sqrt(res / num_obs)
                                                         << "->" << std::sqrt(res_new / num_obs) << endl;

                                // swap is faster than "="
                                frame_poses.swap(new_frame_poses);
                                landmark_points.swap(new_landmark_points);
                                residual_vec.swap(new_residual_vec);
                                kernel_1st_deriv.swap(new_kernel_1st_deriv);

                                res = res_new;

                                profiler.enter("compute_Jacobians");
                                ba_compute_Jacobians<INV_POSES_BOOL>(
                                        frame_poses, landmark_points, camera_params, jac_data_vec,
                                        num_fix_frames, num_fix_points);
                                profiler.leave("compute_Jacobians");

                                // Reset to zeros:
                                H_f.assign(num_free_frames, Matrix_FxF());
                                H_p.assign(num_free_points, Matrix_PxP());
                                eps_frame.assign(num_free_frames, arrF_zeros);
                                eps_point.assign(num_free_points, arrP_zeros);

                                profiler.enter("build_gradient_Hessians");
                                ba_build_gradient_Hessians(
                                        observations, residual_vec, jac_data_vec, H_f, eps_frame,
                                        H_p, eps_point, num_fix_frames, num_fix_points,
                                        use_robust_kernel ? &kernel_1st_deriv : nullptr);
                                profiler.leave("build_gradient_Hessians");

                                stop = norm_inf(g) <= eps;
                                // mu *= max(1.0/3.0, 1-std::pow(2*rho-1,3.0) );
                                mu *= 0.1;
                                mu = std::max(mu, 1e-100);
                                nu = 2.0;
                        }
                        else
                        {
                                VERBOSE_COUT << "no update: res vs.res_new " << res << " vs. "
                                                         << res_new << endl;
                                mu *= nu;
                                nu *= 2.0;
                                stop = (mu > 1e9);
                        }

                        profiler.leave("COMPLETE_ITER");
                } while (!has_improved && !stop);

                if (stop) break;

        }  // end for each "iter"

// *Warning*: This implementation assumes inverse camera poses: inverse them at
// the entrance and at exit:
#ifdef USE_INVERSE_POSES
        profiler.enter("invert_poses");
        for (size_t i = 0; i < num_frames; i++) frame_poses[i].inverse();
        profiler.leave("invert_poses");
#endif

        profiler.leave("bundle_adj_full (complete run)");

        return res;
        MRPT_END
}