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#ifndef FRICP_H
#define FRICP_H
#include "ICP.h"
#include <AndersonAcceleration.h>
#include <eigen/unsupported/Eigen/MatrixFunctions>
#include "median.h"
#include <limits>
#define SAME_THRESHOLD 1e-6
#include <type_traits>
template<class T>
typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type
almost_equal(T x, T y, int ulp)
{
// the machine epsilon has to be scaled to the magnitude of the values used
// and multiplied by the desired precision in ULPs (units in the last place)
return std::fabs(x-y) <= std::numeric_limits<T>::epsilon() * std::fabs(x+y) * ulp
// unless the result is subnormal
|| std::fabs(x-y) < std::numeric_limits<T>::min();
}
template<int N>
class FRICP
{
public:
typedef double Scalar;
typedef Eigen::Matrix<Scalar, N, Eigen::Dynamic> MatrixNX;
typedef Eigen::Matrix<Scalar, N, N> MatrixNN;
typedef Eigen::Matrix<Scalar, N+1, N+1> AffineMatrixN;
typedef Eigen::Transform<Scalar, N, Eigen::Affine> AffineNd;
typedef Eigen::Matrix<Scalar, N, 1> VectorN;
typedef nanoflann::KDTreeAdaptor<MatrixNX, N, nanoflann::metric_L2_Simple> KDtree;
typedef Eigen::Matrix<Scalar, 6, 1> Vector6;
double test_total_construct_time=.0;
double test_total_solve_time=.0;
int test_total_iters=0;
FRICP(){};
~FRICP(){};
private:
AffineMatrixN LogMatrix(const AffineMatrixN& T)
{
Eigen::RealSchur<AffineMatrixN> schur(T);
AffineMatrixN U = schur.matrixU();
AffineMatrixN R = schur.matrixT();
std::vector<bool> selected(N, true);
MatrixNN mat_B = MatrixNN::Zero(N, N);
MatrixNN mat_V = MatrixNN::Identity(N, N);
for (int i = 0; i < N; i++)
{
if (selected[i] && fabs(R(i, i) - 1)> SAME_THRESHOLD)
{
int pair_second = -1;
for (int j = i + 1; j <N; j++)
{
if (fabs(R(j, j) - R(i, i)) < SAME_THRESHOLD)
{
pair_second = j;
selected[j] = false;
break;
}
}
if (pair_second > 0)
{
selected[i] = false;
R(i, i) = R(i, i) < -1 ? -1 : R(i, i);
double theta = acos(R(i, i));
if (R(i, pair_second) < 0)
{
theta = -theta;
}
mat_B(i, pair_second) += theta;
mat_B(pair_second, i) += -theta;
mat_V(i, pair_second) += -theta / 2;
mat_V(pair_second, i) += theta / 2;
double coeff = 1 - (theta * R(i, pair_second)) / (2 * (1 - R(i, i)));
mat_V(i, i) += -coeff;
mat_V(pair_second, pair_second) += -coeff;
}
}
}
AffineMatrixN LogTrim = AffineMatrixN::Zero();
LogTrim.block(0, 0, N, N) = mat_B;
LogTrim.block(0, N, N, 1) = mat_V * R.block(0, N, N, 1);
AffineMatrixN res = U * LogTrim * U.transpose();
return res;
}
inline Vector6 RotToEuler(const AffineNd& T)
{
Vector6 res;
res.head(3) = T.rotation().eulerAngles(0,1,2);
res.tail(3) = T.translation();
return res;
}
inline AffineMatrixN EulerToRot(const Vector6& v)
{
MatrixNN s (Eigen::AngleAxis<Scalar>(v(0), Vector3::UnitX())
* Eigen::AngleAxis<Scalar>(v(1), Vector3::UnitY())
* Eigen::AngleAxis<Scalar>(v(2), Vector3::UnitZ()));
AffineMatrixN m = AffineMatrixN::Zero();
m.block(0,0,3,3) = s;
m(3,3) = 1;
m.col(3).head(3) = v.tail(3);
return m;
}
inline Vector6 LogToVec(const Eigen::Matrix4d& LogT)
{
Vector6 res;
res[0] = -LogT(1, 2);
res[1] = LogT(0, 2);
res[2] = -LogT(0, 1);
res[3] = LogT(0, 3);
res[4] = LogT(1, 3);
res[5] = LogT(2, 3);
return res;
}
inline AffineMatrixN VecToLog(const Vector6& v)
{
AffineMatrixN m = AffineMatrixN::Zero();
m << 0, -v[2], v[1], v[3],
v[2], 0, -v[0], v[4],
-v[1], v[0], 0, v[5],
0, 0, 0, 0;
return m;
}
double FindKnearestMed(const KDtree& kdtree,
const MatrixNX& X, int nk)
{
Eigen::VectorXd X_nearest(X.cols());
#pragma omp parallel for
for(int i = 0; i<X.cols(); i++)
{
int* id = new int[nk];
double *dist = new double[nk];
kdtree.query(X.col(i).data(), nk, id, dist);
Eigen::VectorXd k_dist = Eigen::Map<Eigen::VectorXd>(dist, nk);
igl::median(k_dist.tail(nk-1), X_nearest[i]);
delete[]id;
delete[]dist;
}
double med;
igl::median(X_nearest, med);
return sqrt(med);
}
/// Find self normal edge median of point cloud
double FindKnearestNormMed(const KDtree& kdtree, const Eigen::Matrix3Xd & X, int nk, const Eigen::Matrix3Xd & norm_x)
{
Eigen::VectorXd X_nearest(X.cols());
#pragma omp parallel for
for(int i = 0; i<X.cols(); i++)
{
int* id = new int[nk];
double *dist = new double[nk];
kdtree.query(X.col(i).data(), nk, id, dist);
Eigen::VectorXd k_dist = Eigen::Map<Eigen::VectorXd>(dist, nk);
for(int s = 1; s<nk; s++)
{
k_dist[s] = std::abs((X.col(id[s]) - X.col(id[0])).dot(norm_x.col(id[0])));
}
igl::median(k_dist.tail(nk-1), X_nearest[i]);
delete[]id;
delete[]dist;
}
double med;
igl::median(X_nearest, med);
return med;
}
template <typename Derived1, typename Derived2, typename Derived3>
AffineNd point_to_point(Eigen::MatrixBase<Derived1>& X,
Eigen::MatrixBase<Derived2>& Y,
const Eigen::MatrixBase<Derived3>& w) {
int dim = X.rows();
/// Normalize weight vector
Eigen::VectorXd w_normalized = w / w.sum();
/// De-mean
Eigen::VectorXd X_mean(dim), Y_mean(dim);
for (int i = 0; i<dim; ++i) {
X_mean(i) = (X.row(i).array()*w_normalized.transpose().array()).sum();
Y_mean(i) = (Y.row(i).array()*w_normalized.transpose().array()).sum();
}
X.colwise() -= X_mean;
Y.colwise() -= Y_mean;
/// Compute transformation
AffineNd transformation;
MatrixXX sigma = X * w_normalized.asDiagonal() * Y.transpose();
Eigen::JacobiSVD<MatrixXX> svd(sigma, Eigen::ComputeFullU | Eigen::ComputeFullV);
if (svd.matrixU().determinant()*svd.matrixV().determinant() < 0.0) {
VectorN S = VectorN::Ones(dim); S(dim-1) = -1.0;
transformation.linear() = svd.matrixV()*S.asDiagonal()*svd.matrixU().transpose();
}
else {
transformation.linear() = svd.matrixV()*svd.matrixU().transpose();
}
transformation.translation() = Y_mean - transformation.linear()*X_mean;
/// Re-apply mean
X.colwise() += X_mean;
Y.colwise() += Y_mean;
/// Return transformation
return transformation;
}
template <typename Derived1, typename Derived2, typename Derived3, typename Derived4, typename Derived5>
Eigen::Affine3d point_to_plane(Eigen::MatrixBase<Derived1>& X,
Eigen::MatrixBase<Derived2>& Y,
const Eigen::MatrixBase<Derived3>& Norm,
const Eigen::MatrixBase<Derived4>& w,
const Eigen::MatrixBase<Derived5>& u) {
typedef Eigen::Matrix<double, 6, 6> Matrix66;
typedef Eigen::Matrix<double, 6, 1> Vector6;
typedef Eigen::Block<Matrix66, 3, 3> Block33;
/// Normalize weight vector
Eigen::VectorXd w_normalized = w / w.sum();
/// De-mean
Eigen::Vector3d X_mean;
for (int i = 0; i<3; ++i)
X_mean(i) = (X.row(i).array()*w_normalized.transpose().array()).sum();
X.colwise() -= X_mean;
Y.colwise() -= X_mean;
/// Prepare LHS and RHS
Matrix66 LHS = Matrix66::Zero();
Vector6 RHS = Vector6::Zero();
Block33 TL = LHS.topLeftCorner<3, 3>();
Block33 TR = LHS.topRightCorner<3, 3>();
Block33 BR = LHS.bottomRightCorner<3, 3>();
Eigen::MatrixXd C = Eigen::MatrixXd::Zero(3, X.cols());
#pragma omp parallel
{
#pragma omp for
for (int i = 0; i<X.cols(); i++) {
C.col(i) = X.col(i).cross(Norm.col(i));
}
#pragma omp sections nowait
{
#pragma omp section
for (int i = 0; i<X.cols(); i++) TL.selfadjointView<Eigen::Upper>().rankUpdate(C.col(i), w(i));
#pragma omp section
for (int i = 0; i<X.cols(); i++) TR += (C.col(i)*Norm.col(i).transpose())*w(i);
#pragma omp section
for (int i = 0; i<X.cols(); i++) BR.selfadjointView<Eigen::Upper>().rankUpdate(Norm.col(i), w(i));
#pragma omp section
for (int i = 0; i<C.cols(); i++) {
double dist_to_plane = -((X.col(i) - Y.col(i)).dot(Norm.col(i)) - u(i))*w(i);
RHS.head<3>() += C.col(i)*dist_to_plane;
RHS.tail<3>() += Norm.col(i)*dist_to_plane;
}
}
}
LHS = LHS.selfadjointView<Eigen::Upper>();
/// Compute transformation
Eigen::Affine3d transformation;
Eigen::LDLT<Matrix66> ldlt(LHS);
RHS = ldlt.solve(RHS);
transformation = Eigen::AngleAxisd(RHS(0), Eigen::Vector3d::UnitX()) *
Eigen::AngleAxisd(RHS(1), Eigen::Vector3d::UnitY()) *
Eigen::AngleAxisd(RHS(2), Eigen::Vector3d::UnitZ());
transformation.translation() = RHS.tail<3>();
/// Apply transformation
/// Re-apply mean
X.colwise() += X_mean;
Y.colwise() += X_mean;
transformation.translation() += X_mean - transformation.linear()*X_mean;
/// Return transformation
return transformation;
}
template <typename Derived1, typename Derived2, typename Derived3, typename Derived4>
double point_to_plane_gaussnewton(const Eigen::MatrixBase<Derived1>& X,
const Eigen::MatrixBase<Derived2>& Y,
const Eigen::MatrixBase<Derived3>& norm_y,
const Eigen::MatrixBase<Derived4>& w,
Matrix44 Tk, Vector6& dir) {
typedef Eigen::Matrix<double, 6, 6> Matrix66;
typedef Eigen::Matrix<double, 12, 6> Matrix126;
typedef Eigen::Matrix<double, 9, 3> Matrix93;
typedef Eigen::Block<Matrix126, 9, 3> Block93;
typedef Eigen::Block<Matrix126, 3, 3> Block33;
typedef Eigen::Matrix<double, 12, 1> Vector12;
typedef Eigen::Matrix<double, 9, 1> Vector9;
typedef Eigen::Matrix<double, 4, 2> Matrix42;
/// Normalize weight vector
Eigen::VectorXd w_normalized = w / w.sum();
/// Prepare LHS and RHS
Matrix66 LHS = Matrix66::Zero();
Vector6 RHS = Vector6::Zero();
Vector6 log_T = LogToVec(LogMatrix(Tk));
Matrix33 B = VecToLog(log_T).block(0, 0, 3, 3);
double a = log_T[0];
double b = log_T[1];
double c = log_T[2];
Matrix33 R = Tk.block(0, 0, 3, 3);
Vector3 t = Tk.block(0, 3, 3, 1);
Vector3 u = log_T.tail(3);
Matrix93 dbdw = Matrix93::Zero();
dbdw(1, 2) = dbdw(5, 0) = dbdw(6, 1) = -1;
dbdw(2, 1) = dbdw(3, 2) = dbdw(7, 0) = 1;
Matrix93 db2dw = Matrix93::Zero();
db2dw(3, 1) = db2dw(4, 0) = db2dw(6, 2) = db2dw(8, 0) = a;
db2dw(0, 1) = db2dw(1, 0) = db2dw(7, 2) = db2dw(8, 1) = b;
db2dw(0, 2) = db2dw(2, 0) = db2dw(4, 2) = db2dw(5, 1) = c;
db2dw(1, 1) = db2dw(2, 2) = -2 * a;
db2dw(3, 0) = db2dw(5, 2) = -2 * b;
db2dw(6, 0) = db2dw(7, 1) = -2 * c;
double theta = std::sqrt(a*a + b*b + c*c);
double st = sin(theta), ct = cos(theta);
Matrix42 coeff = Matrix42::Zero();
if (theta>SAME_THRESHOLD)
{
coeff << st / theta, (1 - ct) / (theta*theta),
(theta*ct - st) / (theta*theta*theta), (theta*st - 2 * (1 - ct)) / pow(theta, 4),
(1 - ct) / (theta*theta), (theta - st) / pow(theta, 3),
(theta*st - 2 * (1 - ct)) / pow(theta, 4), (theta*(1 - ct) - 3 * (theta - st)) / pow(theta, 5);
}
else
coeff(0, 0) = 1;
Matrix93 tempB3;
tempB3.block<3, 3>(0, 0) = a*B;
tempB3.block<3, 3>(3, 0) = b*B;
tempB3.block<3, 3>(6, 0) = c*B;
Matrix33 B2 = B*B;
Matrix93 temp2B3;
temp2B3.block<3, 3>(0, 0) = a*B2;
temp2B3.block<3, 3>(3, 0) = b*B2;
temp2B3.block<3, 3>(6, 0) = c*B2;
Matrix93 dRdw = coeff(0, 0)*dbdw + coeff(1, 0)*tempB3
+ coeff(2, 0)*db2dw + coeff(3, 0)*temp2B3;
Vector9 dtdw = coeff(0, 1) * dbdw*u + coeff(1, 1) * tempB3*u
+ coeff(2, 1) * db2dw*u + coeff(3, 1)*temp2B3*u;
Matrix33 dtdu = Matrix33::Identity() + coeff(2, 0)*B + coeff(2, 1) * B2;
Eigen::VectorXd rk(X.cols());
Eigen::MatrixXd Jk(X.cols(), 6);
#pragma omp for
for (int i = 0; i < X.cols(); i++)
{
Vector3 xi = X.col(i);
Vector3 yi = Y.col(i);
Vector3 ni = norm_y.col(i);
double wi = sqrt(w_normalized[i]);
Matrix33 dedR = wi*ni * xi.transpose();
Vector3 dedt = wi*ni;
Vector6 dedx;
dedx(0) = (dedR.cwiseProduct(dRdw.block(0, 0, 3, 3))).sum()
+ dedt.dot(dtdw.head<3>());
dedx(1) = (dedR.cwiseProduct(dRdw.block(3, 0, 3, 3))).sum()
+ dedt.dot(dtdw.segment<3>(3));
dedx(2) = (dedR.cwiseProduct(dRdw.block(6, 0, 3, 3))).sum()
+ dedt.dot(dtdw.tail<3>());
dedx(3) = dedt.dot(dtdu.col(0));
dedx(4) = dedt.dot(dtdu.col(1));
dedx(5) = dedt.dot(dtdu.col(2));
Jk.row(i) = dedx.transpose();
rk[i] = wi * ni.dot(R*xi-yi+t);
}
LHS = Jk.transpose() * Jk;
RHS = -Jk.transpose() * rk;
Eigen::CompleteOrthogonalDecomposition<Matrix66> cod_(LHS);
dir = cod_.solve(RHS);
double gTd = -RHS.dot(dir);
return gTd;
}
public:
void point_to_point(MatrixNX& X, MatrixNX& Y, VectorN& source_mean,
VectorN& target_mean, ICP::Parameters& par){
/// Build kd-tree
KDtree kdtree(Y);
/// Buffers
MatrixNX Q = MatrixNX::Zero(N, X.cols());
VectorX W = VectorX::Zero(X.cols());
AffineNd T;
if (par.use_init) T.matrix() = par.init_trans;
else T = AffineNd::Identity();
MatrixXX To1 = T.matrix();
MatrixXX To2 = T.matrix();
int nPoints = X.cols();
//Anderson Acc para
AndersonAcceleration accelerator_;
AffineNd SVD_T = T;
double energy = .0, last_energy = std::numeric_limits<double>::max();
//ground truth point clouds
MatrixNX X_gt = X;
if(par.has_groundtruth)
{
VectorN temp_trans = par.gt_trans.col(N).head(N);
X_gt.colwise() += source_mean;
X_gt = par.gt_trans.block(0, 0, N, N) * X_gt;
X_gt.colwise() += temp_trans - target_mean;
}
//output para
std::string file_out = par.out_path;
std::vector<double> times, energys, gt_mses;
double begin_time, end_time, run_time;
double gt_mse = 0.0;
// dynamic welsch paras
double nu1 = 1, nu2 = 1;
double begin_init = omp_get_wtime();
//Find initial closest point
#pragma omp parallel for
for (int i = 0; i<nPoints; ++i) {
VectorN cur_p = T * X.col(i);
Q.col(i) = Y.col(kdtree.closest(cur_p.data()));
W[i] = (cur_p - Q.col(i)).norm();
}
if(par.f == ICP::WELSCH)
{
//dynamic welsch, calc k-nearest points with itself;
nu2 = par.nu_end_k * FindKnearestMed(kdtree, Y, 7);
double med1;
igl::median(W, med1);
nu1 = par.nu_begin_k * med1;
nu1 = nu1>nu2? nu1:nu2;
}
double end_init = omp_get_wtime();
double init_time = end_init - begin_init;
//AA init
accelerator_.init(par.anderson_m, (N + 1) * (N + 1), LogMatrix(T.matrix()).data());
begin_time = omp_get_wtime();
bool stop1 = false;
while(!stop1)
{
/// run ICP
int icp = 0;
for (; icp<par.max_icp; ++icp)
{
bool accept_aa = false;
energy = get_energy(par.f, W, nu1);
if (par.use_AA)
{
if (energy < last_energy) {
last_energy = energy;
accept_aa = true;
}
else{
accelerator_.replace(LogMatrix(SVD_T.matrix()).data());
//Re-find the closest point
#pragma omp parallel for
for (int i = 0; i<nPoints; ++i) {
VectorN cur_p = SVD_T * X.col(i);
Q.col(i) = Y.col(kdtree.closest(cur_p.data()));
W[i] = (cur_p - Q.col(i)).norm();
}
last_energy = get_energy(par.f, W, nu1);
}
}
else
last_energy = energy;
end_time = omp_get_wtime();
run_time = end_time - begin_time;
if(par.has_groundtruth)
{
gt_mse = (T*X - X_gt).squaredNorm()/nPoints;
}
// save results
energys.push_back(last_energy);
times.push_back(run_time);
gt_mses.push_back(gt_mse);
if (par.print_energy)
std::cout << "icp iter = " << icp << ", Energy = " << last_energy
<< ", time = " << run_time << std::endl;
robust_weight(par.f, W, nu1);
// Rotation and translation update
T = point_to_point(X, Q, W);
//Anderson Acc
SVD_T = T;
if (par.use_AA)
{
AffineMatrixN Trans = (Eigen::Map<const AffineMatrixN>(accelerator_.compute(LogMatrix(T.matrix()).data()).data(), N+1, N+1)).exp();
T.linear() = Trans.block(0,0,N,N);
T.translation() = Trans.block(0,N,N,1);
}
// Find closest point
#pragma omp parallel for
for (int i = 0; i<nPoints; ++i) {
VectorN cur_p = T * X.col(i) ;
Q.col(i) = Y.col(kdtree.closest(cur_p.data()));
W[i] = (cur_p - Q.col(i)).norm();
}
/// Stopping criteria
double stop2 = (T.matrix() - To2).norm();
To2 = T.matrix();
if(stop2 < par.stop)
{
break;
}
}
if(par.f!= ICP::WELSCH)
stop1 = true;
else
{
stop1 = fabs(nu1 - nu2)<SAME_THRESHOLD? true: false;
nu1 = nu1*par.nu_alpha > nu2? nu1*par.nu_alpha : nu2;
if(par.use_AA)
{
accelerator_.reset(LogMatrix(T.matrix()).data());
last_energy = std::numeric_limits<double>::max();
}
}
}
///calc convergence energy
last_energy = get_energy(par.f, W, nu1);
X = T * X;
gt_mse = (X-X_gt).squaredNorm()/nPoints;
T.translation() += - T.rotation() * source_mean + target_mean;
X.colwise() += target_mean;
///save convergence result
par.convergence_energy = last_energy;
par.convergence_gt_mse = gt_mse;
par.res_trans = T.matrix();
///output
if (par.print_output)
{
std::ofstream out_res(par.out_path);
if (!out_res.is_open())
{
std::cout << "Can't open out file " << par.out_path << std::endl;
}
//output time and energy
out_res.precision(16);
for (int i = 0; i<times.size(); i++)
{
out_res << times[i] << " "<< energys[i] << " " << gt_mses[i] << std::endl;
}
out_res.close();
std::cout << " write res to " << par.out_path << std::endl;
}
}
/// Reweighted ICP with point to plane
/// @param Source (one 3D point per column)
/// @param Target (one 3D point per column)
/// @param Target normals (one 3D normal per column)
/// @param Parameters
// template <typename Derived1, typename Derived2, typename Derived3>
void point_to_plane(Eigen::Matrix3Xd& X,
Eigen::Matrix3Xd& Y, Eigen::Matrix3Xd& norm_x, Eigen::Matrix3Xd& norm_y,
Eigen::Vector3d& source_mean, Eigen::Vector3d& target_mean,
ICP::Parameters &par) {
/// Build kd-tree
KDtree kdtree(Y);
/// Buffers
Eigen::Matrix3Xd Qp = Eigen::Matrix3Xd::Zero(3, X.cols());
Eigen::Matrix3Xd Qn = Eigen::Matrix3Xd::Zero(3, X.cols());
Eigen::VectorXd W = Eigen::VectorXd::Zero(X.cols());
Eigen::Matrix3Xd ori_X = X;
AffineNd T;
if (par.use_init) T.matrix() = par.init_trans;
else T = AffineNd::Identity();
AffineMatrixN To1 = T.matrix();
X = T*X;
Eigen::Matrix3Xd X_gt = X;
if(par.has_groundtruth)
{
Eigen::Vector3d temp_trans = par.gt_trans.block(0, 3, 3, 1);
X_gt = ori_X;
X_gt.colwise() += source_mean;
X_gt = par.gt_trans.block(0, 0, 3, 3) * X_gt;
X_gt.colwise() += temp_trans - target_mean;
}
std::vector<double> times, energys, gt_mses;
double begin_time, end_time, run_time;
double gt_mse = 0.0;
///dynamic welsch, calc k-nearest points with itself;
double begin_init = omp_get_wtime();
//Anderson Acc para
AndersonAcceleration accelerator_;
AffineNd LG_T = T;
double energy = 0.0, prev_res = std::numeric_limits<double>::max(), res = 0.0;
// Find closest point
#pragma omp parallel for
for (int i = 0; i<X.cols(); ++i) {
int id = kdtree.closest(X.col(i).data());
Qp.col(i) = Y.col(id);
Qn.col(i) = norm_y.col(id);
W[i] = std::abs(Qn.col(i).transpose() * (X.col(i) - Qp.col(i)));
}
double end_init = omp_get_wtime();
double init_time = end_init - begin_init;
begin_time = omp_get_wtime();
int total_iter = 0;
double test_total_time = 0.0;
bool stop1 = false;
while(!stop1)
{
/// ICP
for(int icp=0; icp<par.max_icp; ++icp) {
total_iter++;
bool accept_aa = false;
energy = get_energy(par.f, W, par.p);
end_time = omp_get_wtime();
run_time = end_time - begin_time;
energys.push_back(energy);
times.push_back(run_time);
Eigen::VectorXd test_w = (X-Qp).colwise().norm();
if(par.has_groundtruth)
{
gt_mse = (X - X_gt).squaredNorm()/X.cols();
}
gt_mses.push_back(gt_mse);
/// Compute weights
robust_weight(par.f, W, par.p);
/// Rotation and translation update
T = point_to_plane(X, Qp, Qn, W, Eigen::VectorXd::Zero(X.cols()))*T;
/// Find closest point
#pragma omp parallel for
for(int i=0; i<X.cols(); i++) {
X.col(i) = T * ori_X.col(i);
int id = kdtree.closest(X.col(i).data());
Qp.col(i) = Y.col(id);
Qn.col(i) = norm_y.col(id);
W[i] = std::abs(Qn.col(i).transpose() * (X.col(i) - Qp.col(i)));
}
if(par.print_energy)
std::cout << "icp iter = " << total_iter << ", gt_mse = " << gt_mse
<< ", energy = " << energy << std::endl;
/// Stopping criteria
double stop2 = (T.matrix() - To1).norm();
To1 = T.matrix();
if(stop2 < par.stop) break;
}
stop1 = true;
}
par.res_trans = T.matrix();
///calc convergence energy
W = (Qn.array()*(X - Qp).array()).colwise().sum().abs().transpose();
energy = get_energy(par.f, W, par.p);
gt_mse = (X - X_gt).squaredNorm() / X.cols();
T.translation().noalias() += -T.rotation()*source_mean + target_mean;
X.colwise() += target_mean;
norm_x = T.rotation()*norm_x;
///save convergence result
par.convergence_energy = energy;
par.convergence_gt_mse = gt_mse;
par.res_trans = T.matrix();
///output
if (par.print_output)
{
std::ofstream out_res(par.out_path);
if (!out_res.is_open())
{
std::cout << "Can't open out file " << par.out_path << std::endl;
}
///output time and energy
out_res.precision(16);
for (int i = 0; i<total_iter; i++)
{
out_res << times[i] << " "<< energys[i] << " " << gt_mses[i] << std::endl;
}
out_res.close();
std::cout << " write res to " << par.out_path << std::endl;
}
}
/// Reweighted ICP with point to plane
/// @param Source (one 3D point per column)
/// @param Target (one 3D point per column)
/// @param Target normals (one 3D normal per column)
/// @param Parameters
// template <typename Derived1, typename Derived2, typename Derived3>
void point_to_plane_GN(Eigen::Matrix3Xd& X,
Eigen::Matrix3Xd& Y, Eigen::Matrix3Xd& norm_x, Eigen::Matrix3Xd& norm_y,
Eigen::Vector3d& source_mean, Eigen::Vector3d& target_mean,
ICP::Parameters &par) {
/// Build kd-tree
KDtree kdtree(Y);
/// Buffers
Eigen::Matrix3Xd Qp = Eigen::Matrix3Xd::Zero(3, X.cols());
Eigen::Matrix3Xd Qn = Eigen::Matrix3Xd::Zero(3, X.cols());
Eigen::VectorXd W = Eigen::VectorXd::Zero(X.cols());
Eigen::Matrix3Xd ori_X = X;
AffineNd T;
if (par.use_init) T.matrix() = par.init_trans;
else T = AffineNd::Identity();
AffineMatrixN To1 = T.matrix();
X = T*X;
Eigen::Matrix3Xd X_gt = X;
if(par.has_groundtruth)
{
Eigen::Vector3d temp_trans = par.gt_trans.block(0, 3, 3, 1);
X_gt = ori_X;
X_gt.colwise() += source_mean;
X_gt = par.gt_trans.block(0, 0, 3, 3) * X_gt;
X_gt.colwise() += temp_trans - target_mean;
}
std::vector<double> times, energys, gt_mses;
double begin_time, end_time, run_time;
double gt_mse;
///dynamic welsch, calc k-nearest points with itself;
double nu1 = 1, nu2 = 1;
double begin_init = omp_get_wtime();
//Anderson Acc para
AndersonAcceleration accelerator_;
Vector6 LG_T;
Vector6 Dir;
//add time test
double energy = 0.0, prev_energy = std::numeric_limits<double>::max();
if(par.use_AA)
{
Eigen::Matrix4d log_T = LogMatrix(T.matrix());
LG_T = LogToVec(log_T);
accelerator_.init(par.anderson_m, 6, LG_T.data());
}
// Find closest point
#pragma omp parallel for
for (int i = 0; i<X.cols(); ++i) {
int id = kdtree.closest(X.col(i).data());
Qp.col(i) = Y.col(id);
Qn.col(i) = norm_y.col(id);
W[i] = std::abs(Qn.col(i).transpose() * (X.col(i) - Qp.col(i)));
}
if(par.f == ICP::WELSCH)
{
double med1;
igl::median(W, med1);
nu1 =par.nu_begin_k * med1;
nu2 = par.nu_end_k * FindKnearestNormMed(kdtree, Y, 7, norm_y);
nu1 = nu1>nu2? nu1:nu2;
}
double end_init = omp_get_wtime();
double init_time = end_init - begin_init;
begin_time = omp_get_wtime();
int total_iter = 0;
double test_total_time = 0.0;
bool stop1 = false;
par.max_icp = 6;
while(!stop1)
{
par.max_icp = std::min(par.max_icp+1, 10);
/// ICP
for(int icp=0; icp<par.max_icp; ++icp) {
total_iter++;
int n_linsearch = 0;
energy = get_energy(par.f, W, nu1);
if(par.use_AA)
{
if(energy < prev_energy)
{
prev_energy = energy;
}
else
{
// line search
double alpha = 0.0;
Vector6 new_t = LG_T;
Eigen::VectorXd lowest_W = W;
Eigen::Matrix3Xd lowest_Qp = Qp;
Eigen::Matrix3Xd lowest_Qn = Qn;
Eigen::Affine3d lowest_T = T;
n_linsearch++;
alpha = 1;
new_t = LG_T + alpha * Dir;
T.matrix() = VecToLog(new_t).exp();
/// Find closest point
#pragma omp parallel for
for(int i=0; i<X.cols(); i++) {
X.col(i) = T * ori_X.col(i);
int id = kdtree.closest(X.col(i).data());
Qp.col(i) = Y.col(id);
Qn.col(i) = norm_y.col(id);
W[i] = std::abs(Qn.col(i).transpose() * (X.col(i) - Qp.col(i)));
}
double test_energy = get_energy(par.f, W, nu1);
if(test_energy < energy)
{
accelerator_.reset(new_t.data());
energy = test_energy;
}
else
{
Qp = lowest_Qp;
Qn = lowest_Qn;
W = lowest_W;
T = lowest_T;
}
prev_energy = energy;
}
}
else
{
prev_energy = energy;
}
end_time = omp_get_wtime();
run_time = end_time - begin_time;
energys.push_back(prev_energy);
times.push_back(run_time);
if(par.has_groundtruth)
{
gt_mse = (X - X_gt).squaredNorm()/X.cols();
}
gt_mses.push_back(gt_mse);
/// Compute weights
robust_weight(par.f, W, nu1);
/// Rotation and translation update
point_to_plane_gaussnewton(ori_X, Qp, Qn, W, T.matrix(), Dir);
LG_T = LogToVec(LogMatrix(T.matrix()));
LG_T += Dir;
T.matrix() = VecToLog(LG_T).exp();
// Anderson acc
if(par.use_AA)
{
Vector6 AA_t;
AA_t = accelerator_.compute(LG_T.data());
T.matrix() = VecToLog(AA_t).exp();
}
if(par.print_energy)
std::cout << "icp iter = " << total_iter << ", gt_mse = " << gt_mse
<< ", nu1 = " << nu1 << ", acept_aa= " << n_linsearch
<< ", energy = " << prev_energy << std::endl;
/// Find closest point
#pragma omp parallel for
for(int i=0; i<X.cols(); i++) {
X.col(i) = T * ori_X.col(i);
int id = kdtree.closest(X.col(i).data());
Qp.col(i) = Y.col(id);
Qn.col(i) = norm_y.col(id);
W[i] = std::abs(Qn.col(i).transpose() * (X.col(i) - Qp.col(i)));
}
/// Stopping criteria
double stop2 = (T.matrix() - To1).norm();
To1 = T.matrix();
if(stop2 < par.stop) break;
}
if(par.f == ICP::WELSCH)
{
stop1 = fabs(nu1 - nu2)<SAME_THRESHOLD? true: false;
nu1 = nu1*par.nu_alpha > nu2 ? nu1*par.nu_alpha : nu2;
if(par.use_AA)
{
accelerator_.reset(LogToVec(LogMatrix(T.matrix())).data());
prev_energy = std::numeric_limits<double>::max();
}
}
else
stop1 = true;
}
par.res_trans = T.matrix();
///calc convergence energy
W = (Qn.array()*(X - Qp).array()).colwise().sum().abs().transpose();
energy = get_energy(par.f, W, nu1);
gt_mse = (X - X_gt).squaredNorm() / X.cols();
T.translation().noalias() += -T.rotation()*source_mean + target_mean;
X.colwise() += target_mean;
norm_x = T.rotation()*norm_x;
///save convergence result
par.convergence_energy = energy;
par.convergence_gt_mse = gt_mse;
par.res_trans = T.matrix();
///output
if (par.print_output)
{
std::ofstream out_res(par.out_path);
if (!out_res.is_open())
{
std::cout << "Can't open out file " << par.out_path << std::endl;
}
///output time and energy
out_res.precision(16);
for (int i = 0; i<total_iter; i++)
{
out_res << times[i] << " "<< energys[i] << " " << gt_mses[i] << std::endl;
}
out_res.close();
std::cout << " write res to " << par.out_path << std::endl;
}
}
};
#endif
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