视觉十四讲：第七讲_3D-2D：P3P
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视觉十四讲：第七讲_3D-2D：P3P
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1.P3P
P3P輸入數(shù)據(jù)為三對(duì)3D-2D的匹配點(diǎn)，一個(gè)單目相機(jī)，經(jīng)過(guò)初始化，得到初始的3D點(diǎn)，就可以依次得到后續(xù)的姿態(tài)和3D點(diǎn)。
ABC是上一時(shí)刻求的的3D點(diǎn)， abc是與上一次時(shí)刻的匹配點(diǎn)。利用相似原理，可求出abc在相機(jī)坐標(biāo)下的3D坐標(biāo)，最后就可以把問(wèn)題轉(zhuǎn)換為3D-3D坐標(biāo)的估計(jì)問(wèn)題。
問(wèn)題：只利用3個(gè)點(diǎn)，不能運(yùn)用多余的信息；受噪聲影響，存在無(wú)匹配，容易算法失敗
通常做法是用P3P估計(jì)出相機(jī)位姿，然后再構(gòu)建最小二乘優(yōu)化問(wèn)題對(duì)估計(jì)值進(jìn)行優(yōu)化調(diào)整（Bundle Adjustment）
2.使用Pnp來(lái)求解
int main(int argc, char **argv) {
if (argc != 5) {
cout << "usage: pose_estimation_3d2d img1 img2 depth1 depth2" << endl;
return 1;
}
//-- 讀取圖像
Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
Mat img_2 = imread(argv[2], CV_LOAD_IMAGE_COLOR);
assert(img_1.data && img_2.data && "Can not load images!");
vector<KeyPoint> keypoints_1, keypoints_2;
vector<DMatch> matches;
//獲取匹配點(diǎn)
find_feature_matches(img_1, img_2, keypoints_1, keypoints_2, matches);
cout << "一共找到了" << matches.size() << "組匹配點(diǎn)" << endl;
// 建立3D點(diǎn)
Mat d1 = imread(argv[3], CV_LOAD_IMAGE_UNCHANGED); // 第一張圖的深度圖為16位無(wú)符號(hào)數(shù)，單通道圖像
Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
vector<Point3f> pts_3d;
vector<Point2f> pts_2d;
for (DMatch m:matches) {
//取出第一張圖匹配點(diǎn)的深度數(shù)據(jù)
//Mat.ptr<>(行)[列]
ushort d = d1.ptr<unsigned short>(int(keypoints_1[m.queryIdx].pt.y))[int(keypoints_1[m.queryIdx].pt.x)];
if (d == 0) // bad depth
continue;
float dd = d / 5000.0;
//將圖1的匹配點(diǎn)的像素坐標(biāo)轉(zhuǎn)相機(jī)歸一化坐標(biāo)
Point2d p1 = pixel2cam(keypoints_1[m.queryIdx].pt, K);
//轉(zhuǎn)換為相機(jī)坐標(biāo)的3D點(diǎn)
pts_3d.push_back(Point3f(p1.x * dd, p1.y * dd, dd));
//獲取圖2的匹配點(diǎn)的像素坐標(biāo)
pts_2d.push_back(keypoints_2[m.trainIdx].pt);
}
cout << "3d-2d pairs: " << pts_3d.size() << endl;
/**************pnp**************/
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
Mat r, t;
solvePnP(pts_3d, pts_2d, K, Mat(), r, t, false); // 調(diào)用OpenCV 的 PnP 求解，可選擇EPNP，DLS等方法
Mat R;
cv::Rodrigues(r, R); // r為旋轉(zhuǎn)向量形式，用Rodrigues公式轉(zhuǎn)換為矩陣
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "solve pnp in opencv cost time: " << time_used.count() << " seconds." << endl;
cout << "R=" << endl << R << endl;
cout << "t=" << endl << t << endl;
}
3.使用高斯牛頓法來(lái)優(yōu)化求解
1.構(gòu)建最小二乘問(wèn)題：
(T^{*}=argminfrac{1}{2} displaystyle sum^{n}_{i=1}||u_{i}-frac{1}{s_{i}}KTP_{i}||^{2}_{2})
誤差是觀測(cè)像素點(diǎn)-投影像素點(diǎn)，稱(chēng)為重投影誤差
使用高斯牛頓法的重點(diǎn)在于求誤差項(xiàng)對(duì)于每個(gè)優(yōu)化變量的導(dǎo)數(shù)
線性化：(e(x+Delta x) approx e(x) + J^{T}Delta x)
高斯的增量方程為： ((displaystyle sum^{100}_{i=1} J_{i}(sigma^{2})^{-1} J_{i}^{T})Delta x_{k}=displaystyle sum^{100}_{i=1} -J_{i}(sigma^{2})^{-1} e_{i})
(HDelta x_{k}=b)
2.求雅可比矩陣：
1.使用非齊次坐標(biāo)，像素誤差e是2維，x為相機(jī)位姿是6維，(J^{T})是一個(gè)2*6的矩陣。
2.將P變換到相機(jī)坐標(biāo)下為(P^{'}=[X^{'},Y^{'},Z^{'}]^{T}),則：(su=KP^{'})
3.消去s得：(u=f_{x}frac{X^{'}}{Z^{'}}+c_{x}) (v=f_{y}frac{Y^{'}}{Z^{'}}+c_{y})
4.對(duì)T左乘擾動(dòng)量(delta xi),考慮e的變化關(guān)于擾動(dòng)量的導(dǎo)數(shù)。則(frac{partial e}{partial delta xi}= frac{partial e}{partial P^{'}} frac{partial P^{'}}{partial delta xi})
5.容易得出(frac{partial e}{partial P^{'}}) = (-left[ egin{matrix} frac{f_{x}}{Z^{'}} & 0 & -frac{f_{x}X^{'}}{Z^{'2}} \ 0 & frac{f_{y}}{Z^{'}} & -frac{f_{y}Y^{'}}{Z^{'2}} end{matrix} ight])
6.由李代數(shù)導(dǎo)數(shù)得：(frac{partial (TP)}{partial delta xi} = left[ egin{matrix} I & -P^{' Lambda} \ 0^{T} & 0^{T} end{matrix} ight])
7.在(P^{'})的定義中，取了前三維，所以(frac{partial P^{'}}{partial delta xi} = left[ egin{matrix} I & -P^{' Lambda} end{matrix} ight])
8.將兩個(gè)式子相乘就可以得到雅可比矩陣：
(frac{partial e}{partial delta xi} = - left[ egin{matrix} frac{f_{x}}{Z^{'}} & 0 & -frac{f_{x}X^{'}}{Z^{'2}} & -frac{f_{x}X^{'}Y^{'}}{Z^{'2}} & f_{x} + frac{f_{x}X^{'2}}{Z^{'2}} &- frac{f_{x}Y^{'}}{Z^{'}} \ 0 & frac{f_{y}}{Z^{'}} & -frac{f_{y}Y^{'}}{Z^{'2}} & -f_{y} - frac{f_{y}Y^{'2}}{Z^{'2}} & frac{f_{y}X^{'}Y^{'}}{Z^{'2}} & frac{f_{y}X^{'}}{Z^{'}} end{matrix} ight])
3.程序：
void bundleAdjustmentGaussNewton(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose) {
typedef Eigen::Matrix<double, 6, 1> Vector6d;
const int iterations = 10;
double cost = 0, lastCost = 0;
double fx = K.at<double>(0, 0);
double fy = K.at<double>(1, 1);
double cx = K.at<double>(0, 2);
double cy = K.at<double>(1, 2);
for (int iter = 0; iter < iterations; iter++) {
Eigen::Matrix<double, 6, 6> H = Eigen::Matrix<double, 6, 6>::Zero();
Vector6d b = Vector6d::Zero();
cost = 0;
// compute cost
for (int i = 0; i < points_3d.size(); i++) {
//世界坐標(biāo)轉(zhuǎn)為相機(jī)坐標(biāo)
Eigen::Vector3d pc = pose * points_3d[i];
double inv_z = 1.0 / pc[2];
double inv_z2 = inv_z * inv_z;
//相機(jī)坐標(biāo)轉(zhuǎn)為像素坐標(biāo)
Eigen::Vector2d proj(fx * pc[0] / pc[2] + cx, fy * pc[1] / pc[2] + cy);
Eigen::Vector2d e = points_2d[i] - proj; //誤差，觀測(cè)值-預(yù)測(cè)值，反之取負(fù)
cost += e.squaredNorm(); //誤差里的每項(xiàng)平方和
Eigen::Matrix<double, 2, 6> J;
//雅可比矩陣賦值
J << -fx * inv_z,
0,
fx * pc[0] * inv_z2,
fx * pc[0] * pc[1] * inv_z2,
-fx - fx * pc[0] * pc[0] * inv_z2,
fx * pc[1] * inv_z,
0,
-fy * inv_z,
fy * pc[1] * inv_z2,
fy + fy * pc[1] * pc[1] * inv_z2,
-fy * pc[0] * pc[1] * inv_z2,
-fy * pc[0] * inv_z;
H += J.transpose() * J;
b += -J.transpose() * e;
}
Vector6d dx;
dx = H.ldlt().solve(b);
if (isnan(dx[0])) {
cout << "result is nan!" << endl;
break;
}
if (iter > 0 && cost >= lastCost) {
// cost increase, update is not good
cout << "cost: " << cost << ", last cost: " << lastCost << endl;
break;
}
// update your estimation
//更新位姿
pose = Sophus::SE3d::exp(dx) * pose;
lastCost = cost;
cout << "iteration " << iter << " cost=" << std::setprecision(12) << cost << endl;
//范數(shù),誤差足夠小
if (dx.norm() < 1e-6) {
// converge
break;
}
}
cout << "pose by g-n:
" << pose.matrix() << endl;
}
4.使用g2o來(lái)進(jìn)行BA優(yōu)化
節(jié)點(diǎn)(待優(yōu)化的變量)： 第二個(gè)相機(jī)的位姿 (T in SE(3))
邊(誤差)： 每個(gè)3D在第二個(gè)相機(jī)中的投影
1.構(gòu)建節(jié)點(diǎn)和邊框架：
// 曲線模型的頂點(diǎn)，模板參數(shù)：優(yōu)化變量維度和數(shù)據(jù)類(lèi)型
class VertexPose : public g2o::BaseVertex<6, Sophus::SE3d> {
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
// 初始化
virtual void setToOriginImpl() override {
_estimate = Sophus::SE3d();
}
//更新估計(jì)值
virtual void oplusImpl(const double *update) override {
Eigen::Matrix<double, 6, 1> update_eigen;
update_eigen << update[0], update[1], update[2], update[3], update[4], update[5];
_estimate = Sophus::SE3d::exp(update_eigen) * _estimate;
}
virtual bool read(istream &in) override {}
virtual bool write(ostream &out) const override {}
};
// 誤差模型 模板參數(shù)：觀測(cè)值維度，類(lèi)型，連接頂點(diǎn)類(lèi)型
class EdgeProjection : public g2o::BaseUnaryEdge<2, Eigen::Vector2d, VertexPose> {
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
//輸入的變量：位姿，相機(jī)內(nèi)參
EdgeProjection(const Eigen::Vector3d &pos, const Eigen::Matrix3d &K) : _pos3d(pos), _K(K) {}
//計(jì)算誤差
virtual void computeError() override {
const VertexPose *v = static_cast<VertexPose *> (_vertices[0]);
//獲取估計(jì)值
Sophus::SE3d T = v->estimate();
//將3D世界坐標(biāo)轉(zhuǎn)為相機(jī)像素坐標(biāo)
Eigen::Vector3d pos_pixel = _K * (T * _pos3d);
//歸一化
pos_pixel /= pos_pixel[2];
//計(jì)算誤差
_error = _measurement - pos_pixel.head<2>();
}
//計(jì)算雅可比矩陣，公式上面已推導(dǎo)
virtual void linearizeOplus() override {
const VertexPose *v = static_cast<VertexPose *> (_vertices[0]);
Sophus::SE3d T = v->estimate();
//世界坐標(biāo)轉(zhuǎn)化為相機(jī)坐標(biāo)
Eigen::Vector3d pos_cam = T * _pos3d;
//獲取相機(jī)內(nèi)參
double fx = _K(0, 0);
double fy = _K(1, 1);
double cx = _K(0, 2);
double cy = _K(1, 2);
double X = pos_cam[0];
double Y = pos_cam[1];
double Z = pos_cam[2];
double Z2 = Z * Z;
//傳入雅可比矩陣參數(shù)
_jacobianOplusXi
<< -fx / Z, 0, fx * X / Z2, fx * X * Y / Z2, -fx - fx * X * X / Z2, fx * Y / Z,
0, -fy / Z, fy * Y / (Z * Z), fy + fy * Y * Y / Z2, -fy * X * Y / Z2, -fy * X / Z;
}
virtual bool read(istream &in) override {}
virtual bool write(ostream &out) const override {}
private:
Eigen::Vector3d _pos3d;
Eigen::Matrix3d _K;
};
2.組成圖優(yōu)化：
void bundleAdjustmentG2O(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose) {
// 構(gòu)建圖優(yōu)化，先設(shè)定g2o
typedef g2o::BlockSolver<g2o::BlockSolverTraits<6, 3>> BlockSolverType; // 位姿維度為6，誤差維度為3
typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 線性求解器類(lèi)型
// 梯度下降方法，可以從GN, LM, DogLeg 中選
auto solver = new g2o::OptimizationAlgorithmGaussNewton(
g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));
g2o::SparseOptimizer optimizer; // 圖模型
optimizer.setAlgorithm(solver); // 設(shè)置求解器
optimizer.setVerbose(true); // 打開(kāi)調(diào)試輸出
// 往圖中添加節(jié)點(diǎn)
VertexPose *vertex_pose = new VertexPose(); // camera vertex_pose
vertex_pose->setId(0);
vertex_pose->setEstimate(Sophus::SE3d());
optimizer.addVertex(vertex_pose);
// K 相機(jī)內(nèi)參
Eigen::Matrix3d K_eigen;
K_eigen <<
K.at<double>(0, 0), K.at<double>(0, 1), K.at<double>(0, 2),
K.at<double>(1, 0), K.at<double>(1, 1), K.at<double>(1, 2),
K.at<double>(2, 0), K.at<double>(2, 1), K.at<double>(2, 2);
// edges 邊
int index = 1;
for (size_t i = 0; i < points_2d.size(); ++i) {
auto p2d = points_2d[i];
auto p3d = points_3d[i];
EdgeProjection *edge = new EdgeProjection(p3d, K_eigen);
edge->setId(index);
edge->setVertex(0, vertex_pose); // 設(shè)置連接的頂點(diǎn)
edge->setMeasurement(p2d); //傳入觀測(cè)值
edge->setInformation(Eigen::Matrix2d::Identity()); // 信息矩陣
optimizer.addEdge(edge);
index++;
}
//執(zhí)行優(yōu)化
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
optimizer.setVerbose(true);
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;
//獲取結(jié)果
cout << "pose estimated by g2o =
" << vertex_pose->estimate().matrix() << endl;
pose = vertex_pose->estimate();
}
5.完整代碼
#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <Eigen/Core>
#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/sparse_optimizer.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/solver.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/solvers/dense/linear_solver_dense.h>
#include <sophus/se3.hpp>
#include <chrono>
using namespace std;
using namespace cv;
void find_feature_matches(
const Mat &img_1, const Mat &img_2,
std::vector<KeyPoint> &keypoints_1,
std::vector<KeyPoint> &keypoints_2,
std::vector<DMatch> &matches);
// 像素坐標(biāo)轉(zhuǎn)相機(jī)歸一化坐標(biāo)
Point2d pixel2cam(const Point2d &p, const Mat &K);
// BA by g2o
//STL容器中的元素是Eigen的數(shù)據(jù)結(jié)構(gòu)，例如這里定義一個(gè)vector容器，元素是Vector2d
typedef vector<Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d>> VecVector2d;
typedef vector<Eigen::Vector3d, Eigen::aligned_allocator<Eigen::Vector3d>> VecVector3d;
void bundleAdjustmentG2O(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose
);
// BA by gauss-newton
void bundleAdjustmentGaussNewton(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose
);
int main(int argc, char **argv) {
if (argc != 5) {
cout << "usage: pose_estimation_3d2d img1 img2 depth1 depth2" << endl;
return 1;
}
//-- 讀取圖像
Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
Mat img_2 = imread(argv[2], CV_LOAD_IMAGE_COLOR);
assert(img_1.data && img_2.data && "Can not load images!");
vector<KeyPoint> keypoints_1, keypoints_2;
vector<DMatch> matches;
//獲取匹配點(diǎn)
find_feature_matches(img_1, img_2, keypoints_1, keypoints_2, matches);
cout << "一共找到了" << matches.size() << "組匹配點(diǎn)" << endl;
// 建立3D點(diǎn)
Mat d1 = imread(argv[3], CV_LOAD_IMAGE_UNCHANGED); // 第一張圖的深度圖為16位無(wú)符號(hào)數(shù)，單通道圖像
Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
vector<Point3f> pts_3d;
vector<Point2f> pts_2d;
for (DMatch m:matches) {
//取出第一張圖匹配點(diǎn)的深度數(shù)據(jù)
ushort d = d1.ptr<unsigned short>(int(keypoints_1[m.queryIdx].pt.y))[int(keypoints_1[m.queryIdx].pt.x)];
if (d == 0) // bad depth
continue;
float dd = d / 5000.0;
//將圖1的匹配點(diǎn)的像素坐標(biāo)轉(zhuǎn)相機(jī)歸一化坐標(biāo)
Point2d p1 = pixel2cam(keypoints_1[m.queryIdx].pt, K);
//轉(zhuǎn)換為相機(jī)坐標(biāo)的3D點(diǎn)
pts_3d.push_back(Point3f(p1.x * dd, p1.y * dd, dd));
//獲取圖2的匹配點(diǎn)的像素坐標(biāo)
pts_2d.push_back(keypoints_2[m.trainIdx].pt);
}
cout << "3d-2d pairs: " << pts_3d.size() << endl;
/**************pnp**************/
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
Mat r, t;
solvePnP(pts_3d, pts_2d, K, Mat(), r, t, false); // 調(diào)用OpenCV 的 PnP 求解，可選擇EPNP，DLS等方法
Mat R;
cv::Rodrigues(r, R); // r為旋轉(zhuǎn)向量形式，用Rodrigues公式轉(zhuǎn)換為矩陣
chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "solve pnp in opencv cost time: " << time_used.count() << " seconds." << endl;
cout << "R=" << endl << R << endl;
cout << "t=" << endl << t << endl;
/********************************/
VecVector3d pts_3d_eigen;
VecVector2d pts_2d_eigen;
//
for (size_t i = 0; i < pts_3d.size(); ++i) {
//圖1的3D點(diǎn)
pts_3d_eigen.push_back(Eigen::Vector3d(pts_3d[i].x, pts_3d[i].y, pts_3d[i].z));
//圖2的2D點(diǎn)
pts_2d_eigen.push_back(Eigen::Vector2d(pts_2d[i].x, pts_2d[i].y));
}
//高斯牛頓法優(yōu)化
cout << "calling bundle adjustment by gauss newton" << endl;
Sophus::SE3d pose_gn;
t1 = chrono::steady_clock::now();
bundleAdjustmentGaussNewton(pts_3d_eigen, pts_2d_eigen, K, pose_gn);
t2 = chrono::steady_clock::now();
time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "solve pnp by gauss newton cost time: " << time_used.count() << " seconds." << endl;
//g2o優(yōu)化
cout << "calling bundle adjustment by g2o" << endl;
Sophus::SE3d pose_g2o;
t1 = chrono::steady_clock::now();
bundleAdjustmentG2O(pts_3d_eigen, pts_2d_eigen, K, pose_g2o);
t2 = chrono::steady_clock::now();
time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
cout << "solve pnp by g2o cost time: " << time_used.count() << " seconds." << endl;
return 0;
}
void find_feature_matches(const Mat &img_1, const Mat &img_2,
std::vector<KeyPoint> &keypoints_1,
std::vector<KeyPoint> &keypoints_2,
std::vector<DMatch> &matches) {
//-- 初始化
Mat descriptors_1, descriptors_2;
// used in OpenCV3
Ptr<FeatureDetector> detector = ORB::create();
Ptr<DescriptorExtractor> descriptor = ORB::create();
// use this if you are in OpenCV2
// Ptr<FeatureDetector> detector = FeatureDetector::create ( "ORB" );
// Ptr<DescriptorExtractor> descriptor = DescriptorExtractor::create ( "ORB" );
Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");
//-- 第一步:檢測(cè) Oriented FAST 角點(diǎn)位置
detector->detect(img_1, keypoints_1);
detector->detect(img_2, keypoints_2);
//-- 第二步:根據(jù)角點(diǎn)位置計(jì)算 BRIEF 描述子
descriptor->compute(img_1, keypoints_1, descriptors_1);
descriptor->compute(img_2, keypoints_2, descriptors_2);
//-- 第三步:對(duì)兩幅圖像中的BRIEF描述子進(jìn)行匹配，使用 Hamming 距離
vector<DMatch> match;
// BFMatcher matcher ( NORM_HAMMING );
matcher->match(descriptors_1, descriptors_2, match);
//-- 第四步:匹配點(diǎn)對(duì)篩選
double min_dist = 10000, max_dist = 0;
//找出所有匹配之間的最小距離和最大距離, 即是最相似的和最不相似的兩組點(diǎn)之間的距離
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
", max_dist);
printf("-- Min dist : %f
", min_dist);
//當(dāng)描述子之間的距離大于兩倍的最小距離時(shí),即認(rèn)為匹配有誤.但有時(shí)候最小距離會(huì)非常小,設(shè)置一個(gè)經(jīng)驗(yàn)值30作為下限.
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 bundleAdjustmentGaussNewton(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose) {
typedef Eigen::Matrix<double, 6, 1> Vector6d;
const int iterations = 10;
double cost = 0, lastCost = 0;
double fx = K.at<double>(0, 0);
double fy = K.at<double>(1, 1);
double cx = K.at<double>(0, 2);
double cy = K.at<double>(1, 2);
for (int iter = 0; iter < iterations; iter++) {
Eigen::Matrix<double, 6, 6> H = Eigen::Matrix<double, 6, 6>::Zero();
Vector6d b = Vector6d::Zero();
cost = 0;
// compute cost
for (int i = 0; i < points_3d.size(); i++) {
//世界坐標(biāo)轉(zhuǎn)為相機(jī)坐標(biāo)
Eigen::Vector3d pc = pose * points_3d[i];
double inv_z = 1.0 / pc[2];
double inv_z2 = inv_z * inv_z;
//相機(jī)坐標(biāo)轉(zhuǎn)為像素坐標(biāo)
Eigen::Vector2d proj(fx * pc[0] / pc[2] + cx, fy * pc[1] / pc[2] + cy);
Eigen::Vector2d e = points_2d[i] - proj; //誤差，觀測(cè)值-預(yù)測(cè)值，反之取負(fù)
cost += e.squaredNorm(); //誤差里的每項(xiàng)平方和
Eigen::Matrix<double, 2, 6> J;
//雅可比矩陣賦值
J << -fx * inv_z,
0,
fx * pc[0] * inv_z2,
fx * pc[0] * pc[1] * inv_z2,
-fx - fx * pc[0] * pc[0] * inv_z2,
fx * pc[1] * inv_z,
0,
-fy * inv_z,
fy * pc[1] * inv_z2,
fy + fy * pc[1] * pc[1] * inv_z2,
-fy * pc[0] * pc[1] * inv_z2,
-fy * pc[0] * inv_z;
H += J.transpose() * J;
b += -J.transpose() * e;
}
Vector6d dx;
dx = H.ldlt().solve(b);
if (isnan(dx[0])) {
cout << "result is nan!" << endl;
break;
}
if (iter > 0 && cost >= lastCost) {
// cost increase, update is not good
cout << "cost: " << cost << ", last cost: " << lastCost << endl;
break;
}
// update your estimation
//更新位姿
pose = Sophus::SE3d::exp(dx) * pose;
lastCost = cost;
cout << "iteration " << iter << " cost=" << std::setprecision(12) << cost << endl;
if (dx.norm() < 1e-6) {
// converge
break;
}
}
cout << "pose by g-n:
" << pose.matrix() << endl;
}
/// vertex and edges used in g2o ba
class VertexPose : public g2o::BaseVertex<6, Sophus::SE3d> {
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
virtual void setToOriginImpl() override {
_estimate = Sophus::SE3d();
}
/// left multiplication on SE3
virtual void oplusImpl(const double *update) override {
Eigen::Matrix<double, 6, 1> update_eigen;
update_eigen << update[0], update[1], update[2], update[3], update[4], update[5];
_estimate = Sophus::SE3d::exp(update_eigen) * _estimate;
}
virtual bool read(istream &in) override {}
virtual bool write(ostream &out) const override {}
};
class EdgeProjection : public g2o::BaseUnaryEdge<2, Eigen::Vector2d, VertexPose> {
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW;
EdgeProjection(const Eigen::Vector3d &pos, const Eigen::Matrix3d &K) : _pos3d(pos), _K(K) {}
virtual void computeError() override {
const VertexPose *v = static_cast<VertexPose *> (_vertices[0]);
Sophus::SE3d T = v->estimate();
Eigen::Vector3d pos_pixel = _K * (T * _pos3d);
pos_pixel /= pos_pixel[2];
_error = _measurement - pos_pixel.head<2>();
}
virtual void linearizeOplus() override {
const VertexPose *v = static_cast<VertexPose *> (_vertices[0]);
Sophus::SE3d T = v->estimate();
Eigen::Vector3d pos_cam = T * _pos3d;
double fx = _K(0, 0);
double fy = _K(1, 1);
double cx = _K(0, 2);
double cy = _K(1, 2);
double X = pos_cam[0];
double Y = pos_cam[1];
double Z = pos_cam[2];
double Z2 = Z * Z;
_jacobianOplusXi
<< -fx / Z, 0, fx * X / Z2, fx * X * Y / Z2, -fx - fx * X * X / Z2, fx * Y / Z,
0, -fy / Z, fy * Y / (Z * Z), fy + fy * Y * Y / Z2, -fy * X * Y / Z2, -fy * X / Z;
}
virtual bool read(istream &in) override {}
virtual bool write(ostream &out) const override {}
private:
Eigen::Vector3d _pos3d;
Eigen::Matrix3d _K;
};
void bundleAdjustmentG2O(
const VecVector3d &points_3d,
const VecVector2d &points_2d,
const Mat &K,
Sophus::SE3d &pose) {
// 構(gòu)建圖優(yōu)化，先設(shè)定g2o
typedef g2o::BlockSolver<g2o::BlockSolverTraits<6, 3>> BlockSolverType; // pose is 6, landmark is 3
typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 線性求解器類(lèi)型
// 梯度下降方法，可以從GN, LM, DogLeg 中選
auto solver = new g2o::OptimizationAlgorithmGaussNewton(
g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));
g2o::SparseOptimizer optimizer; // 圖模型
optimizer.setAlgorithm(solver); // 設(shè)置求解器
optimizer.setVerbose(true); // 打開(kāi)調(diào)試輸出
// vertex
VertexPose *vertex_pose = new VertexPose(); // camera vertex_pose
vertex_pose->setId(0);
vertex_pose->setEstimate(Sophus::SE3d());
optimizer.addVertex(vertex_pose);
// K
Eigen::Matrix3d K_eigen;
K_eigen <<
K.at<double>(0, 0), K.at<double>(0, 1), K.at<double>(0, 2),
K.at<double>(1, 0), K.at<double>(1, 1), K.at<double>(1, 2),
K.at<double>(2, 0), K.at<double>(2, 1), K.at<double>(2, 2);
// edges
int index = 1;
for (size_t i = 0; i < points_2d.size(); ++i) {
auto p2d = points_2d[i];
auto p3d = points_3d[i];
EdgeProjection *edge = new EdgeProjection(p3d, K_eigen);
edge->setId(index);
edge->setVertex(0, vertex_pose);
edge->setMeasurement(p2d);
edge->setInformation(Eigen::Matrix2d::Identity());
optimizer.addEdge(edge);
index++;
}
chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
optimizer.setVerbose(true);
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 << "pose estimated by g2o =
" << vertex_pose->estimate().matrix() << endl;
pose = vertex_pose->estimate();
}
CMakeLists.txt:
cmake_minimum_required(VERSION 2.8)
project(3d2d)
set(CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} -std=c++11")
list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)
include_directories(inc)
aux_source_directory(src DIR_SRCS)
SET(SOUR_FILE ${DIR_SRCS})
find_package(OpenCV 3 REQUIRED)
find_package(G2O REQUIRED)
find_package(Sophus REQUIRED)
include_directories(
${OpenCV_INCLUDE_DIRS}
${G2O_INCLUDE_DIRS}
${Sophus_INCLUDE_DIRS}
"/usr/include/eigen3/"
)
add_executable(3d2d ${SOUR_FILE})
target_link_libraries(3d2d ${OpenCV_LIBS})
target_link_libraries(3d2d g2o_core g2o_stuff)
cmake文件夾:FindG2O.cmake
# Find the header files
FIND_PATH(G2O_INCLUDE_DIR g2o/core/base_vertex.h
${G2O_ROOT}/include
$ENV{G2O_ROOT}/include
$ENV{G2O_ROOT}
/usr/local/include
/usr/include
/opt/local/include
/sw/local/include
/sw/include
NO_DEFAULT_PATH
)
# Macro to unify finding both the debug and release versions of the
# libraries; this is adapted from the OpenSceneGraph FIND_LIBRARY
# macro.
MACRO(FIND_G2O_LIBRARY MYLIBRARY MYLIBRARYNAME)
FIND_LIBRARY("${MYLIBRARY}_DEBUG"
NAMES "g2o_${MYLIBRARYNAME}_d"
PATHS
${G2O_ROOT}/lib/Debug
${G2O_ROOT}/lib
$ENV{G2O_ROOT}/lib/Debug
$ENV{G2O_ROOT}/lib
NO_DEFAULT_PATH
)
FIND_LIBRARY("${MYLIBRARY}_DEBUG"
NAMES "g2o_${MYLIBRARYNAME}_d"
PATHS
~/Library/Frameworks
/Library/Frameworks
/usr/local/lib
/usr/local/lib64
/usr/lib
/usr/lib64
/opt/local/lib
/sw/local/lib
/sw/lib
)
FIND_LIBRARY(${MYLIBRARY}
NAMES "g2o_${MYLIBRARYNAME}"
PATHS
${G2O_ROOT}/lib/Release
${G2O_ROOT}/lib
$ENV{G2O_ROOT}/lib/Release
$ENV{G2O_ROOT}/lib
NO_DEFAULT_PATH
)
FIND_LIBRARY(${MYLIBRARY}
NAMES "g2o_${MYLIBRARYNAME}"
PATHS
~/Library/Frameworks
/Library/Frameworks
/usr/local/lib
/usr/local/lib64
/usr/lib
/usr/lib64
/opt/local/lib
/sw/local/lib
/sw/lib
)
IF(NOT ${MYLIBRARY}_DEBUG)
IF(MYLIBRARY)
SET(${MYLIBRARY}_DEBUG ${MYLIBRARY})
ENDIF(MYLIBRARY)
ENDIF( NOT ${MYLIBRARY}_DEBUG)
ENDMACRO(FIND_G2O_LIBRARY LIBRARY LIBRARYNAME)
# Find the core elements
FIND_G2O_LIBRARY(G2O_STUFF_LIBRARY stuff)
FIND_G2O_LIBRARY(G2O_CORE_LIBRARY core)
# Find the CLI library
FIND_G2O_LIBRARY(G2O_CLI_LIBRARY cli)
# Find the pluggable solvers
FIND_G2O_LIBRARY(G2O_SOLVER_CHOLMOD solver_cholmod)
FIND_G2O_LIBRARY(G2O_SOLVER_CSPARSE solver_csparse)
FIND_G2O_LIBRARY(G2O_SOLVER_CSPARSE_EXTENSION csparse_extension)
FIND_G2O_LIBRARY(G2O_SOLVER_DENSE solver_dense)
FIND_G2O_LIBRARY(G2O_SOLVER_PCG solver_pcg)
FIND_G2O_LIBRARY(G2O_SOLVER_SLAM2D_LINEAR solver_slam2d_linear)
FIND_G2O_LIBRARY(G2O_SOLVER_STRUCTURE_ONLY solver_structure_only)
FIND_G2O_LIBRARY(G2O_SOLVER_EIGEN solver_eigen)
# Find the predefined types
FIND_G2O_LIBRARY(G2O_TYPES_DATA types_data)
FIND_G2O_LIBRARY(G2O_TYPES_ICP types_icp)
FIND_G2O_LIBRARY(G2O_TYPES_SBA types_sba)
FIND_G2O_LIBRARY(G2O_TYPES_SCLAM2D types_sclam2d)
FIND_G2O_LIBRARY(G2O_TYPES_SIM3 types_sim3)
FIND_G2O_LIBRARY(G2O_TYPES_SLAM2D types_slam2d)
FIND_G2O_LIBRARY(G2O_TYPES_SLAM3D types_slam3d)
# G2O solvers declared found if we found at least one solver
SET(G2O_SOLVERS_FOUND "NO")
IF(G2O_SOLVER_CHOLMOD OR G2O_SOLVER_CSPARSE OR G2O_SOLVER_DENSE OR G2O_SOLVER_PCG OR G2O_SOLVER_SLAM2D_LINEAR OR G2O_SOLVER_STRUCTURE_ONLY OR G2O_SOLVER_EIGEN)
SET(G2O_SOLVERS_FOUND "YES")
ENDIF(G2O_SOLVER_CHOLMOD OR G2O_SOLVER_CSPARSE OR G2O_SOLVER_DENSE OR G2O_SOLVER_PCG OR G2O_SOLVER_SLAM2D_LINEAR OR G2O_SOLVER_STRUCTURE_ONLY OR G2O_SOLVER_EIGEN)
# G2O itself declared found if we found the core libraries and at least one solver
SET(G2O_FOUND "NO")
IF(G2O_STUFF_LIBRARY AND G2O_CORE_LIBRARY AND G2O_INCLUDE_DIR AND G2O_SOLVERS_FOUND)
SET(G2O_FOUND "YES")
ENDIF(G2O_STUFF_LIBRARY AND G2O_CORE_LIBRARY AND G2O_INCLUDE_DIR AND G2O_SOLVERS_FOUND)
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