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/* Copyright (c) 2012 Patrick Ruoff
*
* Permission to use, copy, modify, and/or distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*/
#include "point_tracker.h"
#include <vector>
#include <algorithm>
#include <cmath>
#include <QDebug>
using namespace cv;
using namespace std;
const float PI = 3.14159265358979323846f;
// ----------------------------------------------------------------------------
static void get_row(const Matx33f& m, int i, Vec3f& v)
{
v[0] = m(i,0);
v[1] = m(i,1);
v[2] = m(i,2);
}
static void set_row(Matx33f& m, int i, const Vec3f& v)
{
m(i,0) = v[0];
m(i,1) = v[1];
m(i,2) = v[2];
}
PointModel::PointModel() :
M01 { 0, 0, 0 },
M02 { 0, 0, 0 }
{
}
PointModel::PointModel(Vec3f M01, Vec3f M02)
: M01(M01), M02(M02)
{
// calculate u
u = M01.cross(M02);
u /= norm(u);
// calculate projection matrix on M01,M02 plane
float s11 = M01.dot(M01);
float s12 = M01.dot(M02);
float s22 = M02.dot(M02);
P = 1.0/(s11*s22-s12*s12) * Matx22f(s22, -s12, -s12, s11);
}
#ifdef OPENTRACK_API
static bool d_vals_sort(const pair<float,int> a, const pair<float,int> b)
{
return a.first < b.first;
}
#endif
template<typename vec>
void PointModel::get_d_order(const std::vector<vec>& points, int d_order[], vec d) const
{
// fit line to orthographically projected points
vector< pair<float,int> > d_vals;
// get sort indices with respect to d scalar product
for (unsigned i = 0; i<points.size(); ++i)
d_vals.push_back(pair<float, int>(d.dot(points[i]), i));
std::sort(d_vals.begin(),
d_vals.end(),
#ifdef OPENTRACK_API
d_vals_sort
#else
comp
#endif
);
for (unsigned i = 0; i<points.size(); ++i)
d_order[i] = d_vals[i].second;
}
PointTracker::PointTracker()
{
X_CM.t[2] = 1000; // default position: 1 m away from cam;
}
void PointTracker::track(const vector<Vec2f>& points, const PointModel& model, float f)
{
const PointOrder& order = find_correspondences(points, model);
POSIT(model, order, f);
}
PointTracker::PointOrder PointTracker::find_correspondences(const std::vector<cv::Vec2f>& points, const PointModel& model)
{
// We do a simple freetrack-like sorting in the init phase...
// sort points
int point_d_order[PointModel::N_POINTS];
int model_d_order[PointModel::N_POINTS];
model.get_d_order(points, point_d_order,
cv::Vec2f(points[0][0]-points[1][0], points[0][1]-points[1][1]));
// calculate d and d_order for simple freetrack-like point correspondence
model.get_d_order(std::vector<cv::Vec3f>{ Vec3f{0,0,0}, model.M01, model.M02 },
model_d_order,
cv::Vec3f(model.M01[0]-model.M02[0],
model.M01[1]-model.M02[1],
model.M01[2]-model.M02[2]));
// set correspondences
PointOrder p;
for (int i=0; i<PointModel::N_POINTS; ++i)
p.points[model_d_order[i]] = points[point_d_order[i]];
return p;
}
int PointTracker::POSIT(const PointModel& model, const PointOrder& order_, float focal_length)
{
// POSIT algorithm for coplanar points as presented in
// [Denis Oberkampf, Daniel F. DeMenthon, Larry S. Davis: "Iterative Pose Estimation Using Coplanar Feature Points"]
// we use the same notation as in the paper here
// The expected rotation used for resolving the ambiguity in POSIT:
// In every iteration step the rotation closer to R_expected is taken
Matx33f R_expected = Matx33f::eye();
// initial pose = last (predicted) pose
Vec3f k;
get_row(R_expected, 2, k);
float Z0 = 1000.f;
float old_epsilon_1 = 0;
float old_epsilon_2 = 0;
float epsilon_1 = 1;
float epsilon_2 = 1;
Vec3f I0, J0;
Vec2f I0_coeff, J0_coeff;
Vec3f I_1, J_1, I_2, J_2;
Matx33f R_1, R_2;
Matx33f* R_current;
const int MAX_ITER = 100;
const float EPS_THRESHOLD = 1e-4;
const cv::Vec2f* order = order_.points;
int i=1;
for (; i<MAX_ITER; ++i)
{
epsilon_1 = k.dot(model.M01)/Z0;
epsilon_2 = k.dot(model.M02)/Z0;
// vector of scalar products <I0, M0i> and <J0, M0i>
Vec2f I0_M0i(order[1][0]*(1.0 + epsilon_1) - order[0][0],
order[2][0]*(1.0 + epsilon_2) - order[0][0]);
Vec2f J0_M0i(order[1][1]*(1.0 + epsilon_1) - order[0][1],
order[2][1]*(1.0 + epsilon_2) - order[0][1]);
// construct projection of I, J onto M0i plane: I0 and J0
I0_coeff = model.P * I0_M0i;
J0_coeff = model.P * J0_M0i;
I0 = I0_coeff[0]*model.M01 + I0_coeff[1]*model.M02;
J0 = J0_coeff[0]*model.M01 + J0_coeff[1]*model.M02;
// calculate u component of I, J
float II0 = I0.dot(I0);
float IJ0 = I0.dot(J0);
float JJ0 = J0.dot(J0);
float rho, theta;
if (JJ0 == II0) {
rho = sqrt(abs(2*IJ0));
theta = -PI/4;
if (IJ0<0) theta *= -1;
}
else {
rho = sqrt(sqrt( (JJ0-II0)*(JJ0-II0) + 4*IJ0*IJ0 ));
theta = atan( -2*IJ0 / (JJ0-II0) );
if (JJ0 - II0 < 0) theta += PI;
theta /= 2;
}
// construct the two solutions
I_1 = I0 + rho*cos(theta)*model.u;
I_2 = I0 - rho*cos(theta)*model.u;
J_1 = J0 + rho*sin(theta)*model.u;
J_2 = J0 - rho*sin(theta)*model.u;
float norm_const = 1.0/norm(I_1); // all have the same norm
// create rotation matrices
I_1 *= norm_const; J_1 *= norm_const;
I_2 *= norm_const; J_2 *= norm_const;
set_row(R_1, 0, I_1);
set_row(R_1, 1, J_1);
set_row(R_1, 2, I_1.cross(J_1));
set_row(R_2, 0, I_2);
set_row(R_2, 1, J_2);
set_row(R_2, 2, I_2.cross(J_2));
// the single translation solution
Z0 = norm_const * focal_length;
// pick the rotation solution closer to the expected one
// in simple metric d(A,B) = || I - A * B^T ||
float R_1_deviation = norm(Matx33f::eye() - R_expected * R_1.t());
float R_2_deviation = norm(Matx33f::eye() - R_expected * R_2.t());
if (R_1_deviation < R_2_deviation)
R_current = &R_1;
else
R_current = &R_2;
get_row(*R_current, 2, k);
// check for convergence condition
if (abs(epsilon_1 - old_epsilon_1) + abs(epsilon_2 - old_epsilon_2) < EPS_THRESHOLD)
break;
old_epsilon_1 = epsilon_1;
old_epsilon_2 = epsilon_2;
}
// apply results
X_CM.R = *R_current;
X_CM.t[0] = order[0][0] * Z0/focal_length;
X_CM.t[1] = order[0][1] * Z0/focal_length;
X_CM.t[2] = Z0;
return i;
//Rodrigues(X_CM.R, r);
//qDebug()<<"iter: "<<i;
//qDebug()<<"t: "<<X_CM.t[0]<<' '<<X_CM.t[1]<<' '<<X_CM.t[2];
//Vec3f r;
//
//qDebug()<<"r: "<<r[0]<<' '<<r[1]<<' '<<r[2]<<'\n';
}
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