光束平差法
采用光束平差法对射影空间下的多个相机运动矩阵及非编码元三维结构进行优化。光束平差法一般在各种重建算法的最后一步使用。这种优化方法的最大特点是可以处理数据丢失情况并提供真正的最大似然估计。
代价函数
argminPi,Mi∑i=1k∑j=1nvijd(Q(Pj,Mi),mij)2
-
k
为三维空间点个数；
-
n 为成像平面个数；
-
mij表示第
i
个三维点在第
j
$ 个成像平面对应的特征点坐标；
-
vij 表示点
i
在成像平面 j 上是否有投影，如果有
vij=1
，否则
vij=0
;
-
Pi
表示每个成像平面对应的外参数向量；
-
Mi
表示每个三维点的坐标向量；
-
Q(aj,bi)
是重投影函数，将三维点
Mi
映射到成像平面；
-
d(x,y)
为距离度量函数，一般为欧式距离函数。
代价函数求解-Levenberg_Marquardt方法
代码实现
void Optimizer::BundleAdjustment(const vector<KeyFrame *> &vpKFs, const vector<MapPoint *> &vpMP,
int nIterations, bool* pbStopFlag, const unsigned long nLoopKF, const bool bRobust)
{
vector<bool> vbNotIncludedMP;
vbNotIncludedMP.resize(vpMP.size());
g2o::SparseOptimizer optimizer;
g2o::BlockSolver_6_3::LinearSolverType * linearSolver;
linearSolver = new g2o::LinearSolverEigen<g2o::BlockSolver_6_3::PoseMatrixType>();
g2o::BlockSolver_6_3 * solver_ptr = new g2o::BlockSolver_6_3(linearSolver);
g2o::OptimizationAlgorithmLevenberg* solver = new g2o::OptimizationAlgorithmLevenberg(solver_ptr);
optimizer.setAlgorithm(solver);
if(pbStopFlag)
optimizer.setForceStopFlag(pbStopFlag);
long unsigned int maxKFid = 0;
// Set KeyFrame vertices
for(size_t i=0; i<vpKFs.size(); i++)
{
KeyFrame* pKF = vpKFs[i];
if(pKF->isBad())
continue;
g2o::VertexSE3Expmap * vSE3 = new g2o::VertexSE3Expmap();
vSE3->setEstimate(Converter::toSE3Quat(pKF->GetPose()));
vSE3->setId(pKF->mnId);
vSE3->setFixed(pKF->mnId==0);
optimizer.addVertex(vSE3);
if(pKF->mnId>maxKFid)
maxKFid=pKF->mnId;
}
const float thHuber2D = sqrt(5.99);
const float thHuber3D = sqrt(7.815);
// Set MapPoint vertices
for(size_t i=0; i<vpMP.size(); i++)
{
MapPoint* pMP = vpMP[i];
if(pMP->isBad())
continue;
g2o::VertexSBAPointXYZ* vPoint = new g2o::VertexSBAPointXYZ();
vPoint->setEstimate(Converter::toVector3d(pMP->GetWorldPos()));
const int id = pMP->mnId+maxKFid+1;
vPoint->setId(id);
vPoint->setMarginalized(true);
optimizer.addVertex(vPoint);
const map<KeyFrame*,size_t> observations = pMP->GetObservations();
int nEdges = 0;
//SET EDGES
for(map<KeyFrame*,size_t>::const_iterator mit=observations.begin(); mit!=observations.end(); mit++)
{
KeyFrame* pKF = mit->first;
if(pKF->isBad() || pKF->mnId>maxKFid)
continue;
nEdges++;
const cv::KeyPoint &kpUn = pKF->mvKeysUn[mit->second];
if(pKF->mvuRight[mit->second]<0)
{
Eigen::Matrix<double,2,1> obs;
obs << kpUn.pt.x, kpUn.pt.y;
g2o::EdgeSE3ProjectXYZ* e = new g2o::EdgeSE3ProjectXYZ();
e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKF->mnId)));
e->setMeasurement(obs);
const float &invSigma2 = pKF->mvInvLevelSigma2[kpUn.octave];
e->setInformation(Eigen::Matrix2d::Identity()*invSigma2);
if(bRobust)
{
g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
e->setRobustKernel(rk);
rk->setDelta(thHuber2D);
}
e->fx = pKF->fx;
e->fy = pKF->fy;
e->cx = pKF->cx;
e->cy = pKF->cy;
optimizer.addEdge(e);
}
else
{
Eigen::Matrix<double,3,1> obs;
const float kp_ur = pKF->mvuRight[mit->second];
obs << kpUn.pt.x, kpUn.pt.y, kp_ur;
g2o::EdgeStereoSE3ProjectXYZ* e = new g2o::EdgeStereoSE3ProjectXYZ();
e->setVertex(0, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(id)));
e->setVertex(1, dynamic_cast<g2o::OptimizableGraph::Vertex*>(optimizer.vertex(pKF->mnId)));
e->setMeasurement(obs);
const float &invSigma2 = pKF->mvInvLevelSigma2[kpUn.octave];
Eigen::Matrix3d Info = Eigen::Matrix3d::Identity()*invSigma2;
e->setInformation(Info);
if(bRobust)
{
g2o::RobustKernelHuber* rk = new g2o::RobustKernelHuber;
e->setRobustKernel(rk);
rk->setDelta(thHuber3D);
}
e->fx = pKF->fx;
e->fy = pKF->fy;
e->cx = pKF->cx;
e->cy = pKF->cy;
e->bf = pKF->mbf;
optimizer.addEdge(e);
}
}
if(nEdges==0)
{
optimizer.removeVertex(vPoint);
vbNotIncludedMP[i]=true;
}
else
{
vbNotIncludedMP[i]=false;
}
}
// Optimize!
optimizer.initializeOptimization();
optimizer.optimize(nIterations);
// Recover optimized data
//Keyframes
for(size_t i=0; i<vpKFs.size(); i++)
{
KeyFrame* pKF = vpKFs[i];
if(pKF->isBad())
continue;
g2o::VertexSE3Expmap* vSE3 = static_cast<g2o::VertexSE3Expmap*>(optimizer.vertex(pKF->mnId));
g2o::SE3Quat SE3quat = vSE3->estimate();
if(nLoopKF==0)
{
pKF->SetPose(Converter::toCvMat(SE3quat));
}
else
{
pKF->mTcwGBA.create(4,4,CV_32F);
Converter::toCvMat(SE3quat).copyTo(pKF->mTcwGBA);
pKF->mnBAGlobalForKF = nLoopKF;
}
}
//Points
for(size_t i=0; i<vpMP.size(); i++)
{
if(vbNotIncludedMP[i])
continue;
MapPoint* pMP = vpMP[i];
if(pMP->isBad())
continue;
g2o::VertexSBAPointXYZ* vPoint = static_cast<g2o::VertexSBAPointXYZ*>(optimizer.vertex(pMP->mnId+maxKFid+1));
if(nLoopKF==0)
{
pMP->SetWorldPos(Converter::toCvMat(vPoint->estimate()));
pMP->UpdateNormalAndDepth();
}
else
{
pMP->mPosGBA.create(3,1,CV_32F);
Converter::toCvMat(vPoint->estimate()).copyTo(pMP->mPosGBA);
pMP->mnBAGlobalForKF = nLoopKF;
}
}
}
流程图:
