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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 boost;
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(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);
// calculate d and d_order for simple freetrack-like point correspondence
vector<Vec2f> points;
points.push_back(Vec2f(0,0));
points.push_back(Vec2f(M01[0], M01[1]));
points.push_back(Vec2f(M02[0], M02[1]));
// fit line to orthographically projected points
// ERROR: yields wrong results with colinear points?!
/*
Vec4f line;
fitLine(points, line, CV_DIST_L2, 0, 0.01, 0.01);
d[0] = line[0]; d[1] = line[1];
*/
// TODO: fix this
d = Vec2f(M01[0]-M02[0], M01[1]-M02[1]);
// sort model points
get_d_order(points, d_order);
}
void PointModel::get_d_order(const std::vector<cv::Vec2f>& points, int d_order[]) const
{
// get sort indices with respect to d scalar product
vector< pair<float,int> > d_vals;
for (int i = 0; i<points.size(); ++i)
d_vals.push_back(pair<float, int>(d.dot(points[i]), i));
struct
{
bool operator()(const pair<float, int>& a, const pair<float, int>& b) { return a.first < b.first; }
} comp;
sort(d_vals.begin(), d_vals.end(), comp);
for (int 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
}
bool PointTracker::track(const vector<Vec2f>& points, float f, float dt)
{
if (!point_model) return false;
if (!find_correspondences(points)) return false;
POSIT(f);
return true;
}
bool PointTracker::find_correspondences(const vector<Vec2f>& points)
{
if (points.size() != PointModel::N_POINTS) return false;
// sort points
int point_d_order[PointModel::N_POINTS];
point_model->get_d_order(points, point_d_order);
// set correspondences
for (int i=0; i<PointModel::N_POINTS; ++i)
{
p[point_model->d_order[i]] = points[point_d_order[i]];
}
return true;
}
void PointTracker::POSIT(float 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;
//TODO: do extrapolation or reinit here!
Vec3f k;
get_row(X_CM.R, 2, k);
float Z0 = X_CM.t[2];
Matx33f R_expected = Matx33f::eye();
//Matx33f R_expected = X_CM.R;
const int MAX_ITER = 100;
const float EPS_THRESHOLD = 1e-4;
int i=1;
for (; i<MAX_ITER; ++i)
{
epsilon_1 = k.dot(point_model->M01)/Z0;
epsilon_2 = k.dot(point_model->M02)/Z0;
// vector of scalar products <I0, M0i> and <J0, M0i>
Vec2f I0_M0i(p[1][0]*(1.0 + epsilon_1) - p[0][0],
p[2][0]*(1.0 + epsilon_2) - p[0][0]);
Vec2f J0_M0i(p[1][1]*(1.0 + epsilon_1) - p[0][1],
p[2][1]*(1.0 + epsilon_2) - p[0][1]);
// construct projection of I, J onto M0i plane: I0 and J0
I0_coeff = point_model->P * I0_M0i;
J0_coeff = point_model->P * J0_M0i;
I0 = I0_coeff[0]*point_model->M01 + I0_coeff[1]*point_model->M02;
J0 = J0_coeff[0]*point_model->M01 + J0_coeff[1]*point_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)*point_model->u;
I_2 = I0 - rho*cos(theta)*point_model->u;
J_1 = J0 + rho*sin(theta)*point_model->u;
J_2 = J0 - rho*sin(theta)*point_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 * f;
// 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;
}
X_CM.R = *R_current;
X_CM.t[0] = p[0][0] * Z0/f;
X_CM.t[1] = p[0][1] * Z0/f;
X_CM.t[2] = Z0;
//qDebug()<<"iter: "<<i;
//qDebug()<<"t: "<<X_CM.t[0]<<' '<<X_CM.t[1]<<' '<<X_CM.t[2];
//Vec3f r;
//Rodrigues(X_CM.R, r);
//qDebug()<<"r: "<<r[0]<<' '<<r[1]<<' '<<r[2]<<'\n';
}
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