Parent: [DefTracking::Track](deftracking__track.md) As far as I understand it: * Uses g2o library for the optimisation (graph-based SLAM) * cost function terms are converted to edges and nodes * each cost function term seems to correspond to an edge in the graph * in g2o paper/tutorial: [an edge is fully characterised by its error function and its information matrix](http://www.evernote.com/shard/s484/nl/217355218/ed9e53f1-76f2-48bd-a0c1-3b59ebf0326c) int DefPoseOptimization(Frame \*pFrame, Map \*mMap, double RegLap, double RegInex, double RegTemp, uint NeighboursLayers) // define optimiser, set solver optimizer = new ... optimizer.setSolver(...) // create node for current frame (value = camera pose Tcw) vSE3->setEstimate(Converter::toSE3Quat(pFrame\->mTcw)); vSE3->setId(0); optimizer.addVertex(vSE3); // add mesh points to graph (as nodes) setMeshNodes(optimizer, mMap); // set MapPoint (feature) vertices const int N = pFrame\->N; // how many features in the current frame vpEdgesMono.reserve(N); vnIndexEdgeMono.reserve(N); // iterate over each feature map point in the current frame (camera observation) ![unknown_filename.3.png](./_resources/DefOptimizer__DefPoseOptimization.resources/unknown_filename.3.png) { MapPoint \*pMP = pFrame\->mvpMapPoints\[i\]; // observation: 2x1 matrix (2D image point), x and y coords cv::KeyPoint &kpUn = pFrame\->mvKeysUn\[i\]; Eigen::Matrix obs << kpUn.pt.x, kpUn.pt.y; // define edge (defined by error function and info. matrix) \*e = new g2o::EdgeNodesCamera(); // get the 3 nodes of the facet, in which the mappoint/feature is embedded std::set NodesMp = static\_cast(pMP)->getFacet()->getNodes(); e->resize(NodesMp.size() + 1); // set 0-th vertex of edge e->setVertex(0, dynamic\_cast( optimizer.vertex(0))); // iterate over NodesMp (each node is 'it') { e->setVertex(ui, dynamic\_cast( optimizer.vertex((\*it)->getIndex()))); ViewedNodes.insert(\*it); } // now e has 4 vertices // set 2D observation associated with the edge e->setMeasurement(obs); // set information vector of the edge, Huber e->setInformation(Eigen::Matrix2d::Identity() \* invSigma2 / N); e->setRobustKernel(rk); // compute error (between observation/meas and projected point?) e->fx = pFrame\->fx; ... // camera parameters (from calibration matrix) e->computeError(); optimizer.addEdge(e); } // temporal smoothness ![unknown_filename.1.png](./_resources/DefOptimizer__DefPoseOptimization.resources/unknown_filename.1.png) // iterate over all viewednodes (roughly num. features x 3 facet nodes?) { OptLap \= ViewedNodes; \*e = new g2o::EdgesReference(); e->setVertex(0, dynamic\_cast( optimizer.vertex((\*it)->getIndex()))); e->setMeasurement(v) // v from initial pose of viewednodes e->setInformation(...) optimizer.addEdge(e); e->computeError(); // add neighbouring nodes to OptLap } // Laplacian regulariser ![unknown_filename.png](./_resources/DefOptimizer__DefPoseOptimization.resources/unknown_filename.png) { // iterate over OptLap ... e->setMeasurement(InitialMeanCurvature); e->setInformation(RegLap \* Eigen::Vector1D::Identity() / OptLap.size()); optimizer.addEdge(e); } // Inextensibility ![unknown_filename.2.png](./_resources/DefOptimizer__DefPoseOptimization.resources/unknown_filename.2.png) { // iterate over medges (derived from OptLap) s << (\*ite)->getDist(); e->setMeasurement(s); e->setInformation(RegInex \* Eigen::Vector1D::Identity() / medges.size()); e->computeError(); optimizer.addEdge(e); } optimizer.optimize(50); // Reprojection error? ![unknown_filename.3.png](./_resources/DefOptimizer__DefPoseOptimization.resources/unknown_filename.3.png) { // Iterate over vpEdgesMono \*e = vpEdgesMono\[i\]; ... e->computeError(); auto a = e->errorData(); double er = sqrt(pow(a\[0\], 2) + pow(a\[1\], 2)); sumError += er; cout << "Reprojection error: " << sumError / n << endl; } // new vertex that seems to return the pose from optimiser vSE3\_recov = static\_cast(optimizer.vertex(0)); SE3quat\_recov = vSE3\_recov->estimate(); pose = Converter::toCvMat(SE3quat\_recov);

Notation	Description
$P(A)$	prior held belief
$B$	evidence that is observed
$P(A\lvert B)$	posterior (updated belief)

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Conditional probability

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