int main(int argc, char** argv)
{
int numPoints;
int maxIterations;
bool verbose;
std::vector<int> gaugeList;
g2o::CommandArgs arg;
arg.param("numPoints", numPoints, 100, "number of points sampled from the circle");
arg.param("i", maxIterations, 10, "perform n iterations");
arg.param("v", verbose, false, "verbose output of the optimization process");
arg.parseArgs(argc, argv);
// generate random data
Eigen::Vector2d center(4, 2);
double radius = 2.;
Eigen::Vector2d* points = new Eigen::Vector2d[numPoints];
for (int i = 0; i < numPoints; ++i) {
double r = g2o::Sampler::uniformRand(radius-0.1, radius+0.1);
double angle = g2o::Sampler::uniformRand(0., 2. * M_PI);
points[i].x() = center.x() + r * cos(angle);
points[i].y() = center.y() + r * sin(angle);
}
// some handy typedefs
typedef g2o::BlockSolver< g2o::BlockSolverTraits<Eigen::Dynamic, Eigen::Dynamic> > MyBlockSolver;
typedef g2o::LinearSolverCSparse<MyBlockSolver::PoseMatrixType> MyLinearSolver;
// setup the solver
g2o::SparseOptimizer optimizer;
optimizer.setVerbose(false);
MyLinearSolver* linearSolver = new MyLinearSolver();
MyBlockSolver* solver_ptr = new MyBlockSolver(linearSolver);
g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
//g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(solver_ptr);
optimizer.setAlgorithm(solver);
// build the optimization problem given the points
// 1. add the circle vertex
VertexCircle* circle = new VertexCircle();
circle->setId(0);
circle->setEstimate(Eigen::Vector3d(3,3,3)); // some initial value for the circle
optimizer.addVertex(circle);
// 2. add the points we measured
for (int i = 0; i < numPoints; ++i) {
EdgePointOnCircle* e = new EdgePointOnCircle;
e->setInformation(Eigen::Matrix<double, 1, 1>::Identity());
e->setVertex(0, circle);
e->setMeasurement(points[i]);
optimizer.addEdge(e);
}
// perform the optimization
optimizer.initializeOptimization();
optimizer.setVerbose(verbose);
optimizer.optimize(maxIterations);
if (verbose)
cout << endl;
// print out the result
cout << "Iterative least squares solution" << endl;
cout << "center of the circle " << circle->estimate().head<2>().transpose() << endl;
cout << "radius of the cirlce " << circle->estimate()(2) << endl;
cout << "error " << errorOfSolution(numPoints, points, circle->estimate()) << endl;
cout << endl;
// solve by linear least squares
// Let (a, b) be the center of the circle and r the radius of the circle.
// For a point (x, y) on the circle we have:
// (x - a)^2 + (y - b)^2 = r^2
// This leads to
// (-2x -2y 1)^T * (a b c) = -x^2 - y^2 (1)
// where c = a^2 + b^2 - r^2.
// Since we have a bunch of points, we accumulate Eqn (1) in a matrix and
// compute the normal equation to obtain a solution for (a b c).
// Afterwards the radius r is recovered.
Eigen::MatrixXd A(numPoints, 3);
Eigen::VectorXd b(numPoints);
for (int i = 0; i < numPoints; ++i) {
A(i, 0) = -2*points[i].x();
A(i, 1) = -2*points[i].y();
A(i, 2) = 1;
b(i) = -pow(points[i].x(), 2) - pow(points[i].y(), 2);
}
Eigen::Vector3d solution = (A.transpose()*A).ldlt().solve(A.transpose() * b);
// calculate the radius of the circle given the solution so far
solution(2) = sqrt(pow(solution(0), 2) + pow(solution(1), 2) - solution(2));
cout << "Linear least squares solution" << endl;
cout << "center of the circle " << solution.head<2>().transpose() << endl;
cout << "radius of the cirlce " << solution(2) << endl;
cout << "error " << errorOfSolution(numPoints, points, solution) << endl;
// clean up
delete[] points;
return 0;
}
int main(int argc, char** argv)
{
int numPoints;
int maxIterations;
bool verbose;
std::vector<int> gaugeList;
g2o::CommandArgs arg;
arg.param("numPoints", numPoints, 100, "number of points sampled from the circle");
arg.param("i", maxIterations, 10, "perform n iterations");
arg.param("v", verbose, false, "verbose output of the optimization process");
arg.parseArgs(argc, argv);
// generate random data
Eigen::Vector2d center(4, 2);
double radius = 2.;
Eigen::Vector2d* points = new Eigen::Vector2d[numPoints];
for (int i = 0; i < numPoints; ++i) {
double r = g2o::sampleUniform(radius-0.1, radius+0.1);
double angle = g2o::sampleUniform(0., 2. * M_PI);
points[i].x() = center.x() + r * cos(angle);
points[i].y() = center.y() + r * sin(angle);
}
// some handy typedefs
typedef g2o::BlockSolver< g2o::BlockSolverTraits<Eigen::Dynamic, Eigen::Dynamic> > MyBlockSolver;
typedef g2o::LinearSolverCSparse<MyBlockSolver::PoseMatrixType> MyLinearSolver;
// setup the solver
g2o::SparseOptimizer optimizer;
optimizer.setVerbose(false);
MyLinearSolver* linearSolver = new MyLinearSolver();
MyBlockSolver* solver_ptr = new MyBlockSolver(linearSolver);
g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
//g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(solver_ptr);
optimizer.setAlgorithm(solver);
// build the optimization problem given the points
// 1. add the circle vertex
VertexCircle* circle = new VertexCircle();
circle->setId(0);
circle->setEstimate(Eigen::Vector3d(3,3,3)); // some initial value for the circle
optimizer.addVertex(circle);
// 2. add the points we measured
for (int i = 0; i < numPoints; ++i) {
EdgePointOnCircle* e = new EdgePointOnCircle;
e->setInformation(Eigen::Matrix<double, 1, 1>::Identity());
e->setVertex(0, circle);
e->setMeasurement(points[i]);
optimizer.addEdge(e);
}
// perform the optimization
optimizer.initializeOptimization();
optimizer.setVerbose(verbose);
optimizer.optimize(maxIterations);
// print out the result
cout << "Estimated center of the circle " << circle->estimate().head<2>().transpose() << endl;
cout << "Estimated radius of the cirlce " << circle->estimate()(2) << endl;
// clean up
delete[] points;
return 0;
}
