视觉SLAM十四讲 第七讲 视觉里程计1 3D-3D位姿求解 代码解析
总体思路
- 对两幅图像img_1，img_2提取特征点
- 特征点匹配
- 通过相机内参求取特征点对应的相机坐标X,Y，获取特征点的深度信息Z。
- 通过SVD分解，求除相机的位姿R，t。
- 计算质心p1 += pts1[i];p1 = Point3f(Vec3f(p1) / N);
- 去质心q1[i] = pts1[i] - p1;q2[i] = pts2[i] - p2;
- 构建W矩阵q1*q2^T
- 对W矩阵进行SVD分解，得到U，V矩阵
- 由UV矩阵，获得旋转矩阵 R = U V T R=UV^T R=UVT
- 由 t ∗ = p − R p ′ t^{*}=p-Rp' t∗=p−Rp′得到平移矩阵。
- 由R，t和两组匹配到的特征点的相机坐标，进行BA优化。
- 顶点（优化变量）
- 相机位姿_estimate = Sophus::SE3d();
- 相机位姿的增量_estimate = Sophus::SE3d::exp(update_eigen) * _estimate;
- 边（误差项）
- 由相机位姿，将第一个相机的特征点相机坐标，投影到第二个相机的相机坐标下，与提取特征点 经相机内参生成的位姿作差_error = _measurement - pose->estimate() * _point;
- 单个误差关于位姿的导数
- 3D坐标对相机位姿的误差
∂ P ′ ∂ δ ξ = ∂ ( T P ) ∂ δ ξ = ( T P ) ⊙ = [ I − P ′ ∧ 0 T 0 T ] \frac{\partial P'}{\partial \delta \xi}=\frac{\partial(TP)}{\partial \delta \xi}=(TP)^\odot=\left[ \begin{matrix}I&-P'^{\wedge}\\0^T&0^T\end{matrix}\right] ∂δξ∂P′=∂δξ∂(TP)=(TP)⊙=[I0T−P′∧0T] - 因此，使用李代数扰动模型
∂ e ∂ δ ξ = − ( e x p ( ξ ∧ ) p i ′ ) ⊙ = [ − I P ′ ∧ 0 T 0 T ] \frac{\partial e}{\partial \delta \xi}=-(exp(\xi ^{\wedge})p_i')^\odot=\left[ \begin{matrix}-I&P'^{\wedge}\\0^T&0^T\end{matrix}\right] ∂δξ∂e=−(exp(ξ∧)pi′)⊙=[−I0TP′∧0T]
- 3D坐标对相机位姿的误差
- g2o库求解过程
optimizer.addVertex(pose);
对每个特征点增加optimizer.addEdge(edge);
optimizer.initializeOptimization();
optimizer.optimize(10);
- 顶点（优化变量）
代码参考
#include detector = FeatureDetector::create ( "ORB" );
// Ptr descriptor = DescriptorExtractor::create ( "ORB" );
Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");
//-- 第一步:检测 Oriented FAST 角点位置
detector->detect(img_1, keypoints_1);
detector->detect(img_2, keypoints_2);
//-- 第二步:根据角点位置计算 BRIEF 描述子
descriptor->compute(img_1, keypoints_1, descriptors_1);
descriptor->compute(img_2, keypoints_2, descriptors_2);
//-- 第三步:对两幅图像中的BRIEF描述子进行匹配，使用 Hamming 距离
vector<DMatch> match;
// BFMatcher matcher ( NORM_HAMMING );
matcher->match(descriptors_1, descriptors_2, match);
//-- 第四步:匹配点对筛选
double min_dist = 10000, max_dist = 0;
//找出所有匹配之间的最小距离和最大距离, 即是最相似的和最不相似的两组点之间的距离
for (int i = 0; i < descriptors_1.rows; i++) {
double dist = match[i].distance;
if (dist < min_dist) min_dist = dist;
if (dist > max_dist) max_dist = dist;
}
printf("-- Max dist : %f \n", max_dist);
printf("-- Min dist : %f \n", min_dist);
//当描述子之间的距离大于两倍的最小距离时,即认为匹配有误.但有时候最小距离会非常小,设置一个经验值30作为下限.
for (int i = 0; i < descriptors_1.rows; i++) {
if (match[i].distance <= max(2 * min_dist, 30.0)) {
matches.push_back(match[i]);
}
}
}
Point2d pixel2cam(const Point2d &p, const Mat &K) {
return Point2d(
(p.x - K.at<double>(0, 2)) / K.at<double>(0, 0),
(p.y - K.at<double>(1, 2)) / K.at<double>(1, 1)
);
}
void pose_estimation_3d3d(const vector<Point3f> &pts1,
const vector<Point3f> &pts2,
Mat &R, Mat &t) {
Point3f p1, p2; // center of mass
int N = pts1.size();
for (int i = 0; i < N; i++) {
p1 += pts1[i];
p2 += pts2[i];
}
p1 = Point3f(Vec3f(p1) / N);
p2 = Point3f(Vec3f(p2) / N);
vector<Point3f> q1(N), q2(N); // remove the center
for (int i = 0; i < N; i++) {
q1[i] = pts1[i] - p1;
q2[i] = pts2[i] - p2;
}
// compute q1*q2^T
Eigen::Matrix3d W = Eigen::Matrix3d::Zero();
for (int i = 0; i < N; i++) {
W += Eigen::Vector3d(q1[i].x, q1[i].y, q1[i].z) * Eigen::Vector3d(q2[i].x, q2[i].y, q2[i].z).transpose();
}
cout << "W=" << W << endl;
// SVD on W
Eigen::JacobiSVD<Eigen::Matrix3d> svd(W, Eigen::ComputeFullU | Eigen::ComputeFullV);
Eigen::Matrix3d U = svd.matrixU();
Eigen::Matrix3d V = svd.matrixV();
cout << "U=" << U << endl;
cout << "V=" << V << endl;
Eigen::Matrix3d R_ = U * (V.transpose());
if (R_.determinant() < 0) {
R_ = -R_;
}
Eigen::Vector3d t_ = Eigen::Vector3d(p1.x, p1.y, p1.z) - R_ * Eigen::Vector3d(p2.x, p2.y, p2.z);
// convert to cv::Mat
R = (Mat_<double>(3, 3) <<
R_(0, 0), R_(0, 1), R_(0, 2),
R_(1, 0), R_(1, 1), R_(1, 2),
R_(2, 0), R_(2, 1), R_(2, 2)
);
t = (Mat_<double>(3, 1) << t_(0, 0), t_(1, 0), t_(2, 0));
}
void bundleAdjustment(
const vector<Point3f> &pts1,
const vector<Point3f> &pts2,
Mat &R, Mat &t) {
// 构建图优化，先设定g2o
typedef g2o::BlockSolverX BlockSolverType;
typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 线性求解器类型
// 梯度下降方法，可以从GN, LM, DogLeg 中选
auto solver = new g2o::OptimizationAlgorithmLevenberg(
g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));
g2o::SparseOptimizer optimizer; // 图模型
optimizer.setAlgorithm(solver); // 设置求解器
optimizer.setVerbose(true); // 打开调试输出
// vertex
VertexPose *pose = new VertexPose(); // camera pose
pose->setId(0);
pose->setEstimate(Sophus::SE3d());
optimizer.addVertex(pose);
// edges
for (size_t i = 0; i < pts1.size(); i++) {
EdgeProjectXYZRGBDPoseOnly *edge = new EdgeProjectXYZRGBDPoseOnly(
Eigen::Vector3d(pts2[i].x, pts2[i].y, pts2[i].z));
edge->setVertex(0, pose);
edge->setMeasurement(Eigen::Vector3d(
pts1[i].x, pts1[i].y, pts1[i].z));
edge->setInformation(Eigen::Matrix3d::Identity());
optimizer.addEdge(edge);
}
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
optimizer.initializeOptimization();
optimizer.optimize(10);
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "optimization costs time: " << time_used.count() << " seconds." << endl;
cout << endl << "after optimization:" << endl;
cout << "T=\n" << pose->estimate().matrix() << endl;
// convert to cv::Mat
Eigen::Matrix3d R_ = pose->estimate().rotationMatrix();
Eigen::Vector3d t_ = pose->estimate().translation();
R = (Mat_<double>(3, 3) <<
R_(0, 0), R_(0, 1), R_(0, 2),
R_(1, 0), R_(1, 1), R_(1, 2),
R_(2, 0), R_(2, 1), R_(2, 2)
);
t = (Mat_<double>(3, 1) << t_(0, 0), t_(1, 0), t_(2, 0));
}
参考资料
高翔《视觉SLAM十四讲：从理论到实践》及代码
2. 笔记，视觉SLAM十四讲 第七讲 视觉里程计1 Bundle Adjustment公式推导：