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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);
+ // 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);
+}
+
+#ifdef OPENTRACK_API
+static bool d_vals_sort(const pair<float,int> a, const pair<float,int> b)
+{
+ return a.first < b.first;
+}
+#endif
+
+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 (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::reset()
+{
+ // enter init phase
+ X_CM = FrameTrafo();
+}
+
+void PointTracker::track(const vector<Vec2f>& projected_points, const PointModel& model)
+{
+ const PointOrder& order = find_correspondences(projected_points, model);
+ int iters = POSIT(model, order);
+ qDebug()<<"POSIT iterations:"<<iters;
+}
+
+PointTracker::PointOrder PointTracker::find_correspondences(const std::vector<cv::Vec2f>& projected_points, const PointModel& model)
+{
+ // ... otherwise we look at the distance to the projection of the expected model points
+ // project model points under current pose
+ Vec2f p_exp[3];
+ p_exp[0] = project(Vec3f(0,0,0));
+ p_exp[1] = project(model.get_M01());
+ p_exp[2] = project(model.get_M02());
+
+ // set correspondences by minimum distance to projected model point
+ bool point_taken[PointModel::N_POINTS];
+ for (int i=0; i<PointModel::N_POINTS; ++i)
+ point_taken[i] = false;
+
+ PointOrder p;
+ for (int i=0; i<PointModel::N_POINTS; ++i)
+ p.points[i] = Vec2f(0, 0);
+
+ for (int i=0; i<PointModel::N_POINTS; ++i)
+ {
+ float min_sdist = 1e4;
+ int min_idx = 0;
+ // find closest point to projected model point i
+ for (int j=0; j<PointModel::N_POINTS; ++j)
+ {
+ Vec2f d = p_exp[i]-projected_points[j];
+ float sdist = d.dot(d);
+ if (sdist < min_sdist)
+ {
+ min_idx = j;
+ min_sdist = sdist;
+ }
+ }
+ // if one point is closest to more than one model point, abort
+ if (point_taken[min_idx]) return p;
+ point_taken[min_idx] = true;
+ p.points[i] = projected_points[min_idx];
+ }
+ return p;
+}
+
+
+
+int PointTracker::POSIT(const PointModel& model, const PointOrder& order_)
+{
+ // 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;
+ R_expected = X_CM.R; // later we want to be close to the last (predicted) rotation
+
+ // initial pose = last (predicted) pose
+ Vec3f k;
+ get_row(R_expected, 2, k);
+ float Z0 = std::abs(X_CM.t[2]) < 1e-3 ? 1e3 : X_CM.t[2];
+
+ 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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