概述
- 特征点的投影模型为 \(p=\frac{1}{Z} KP\)，\(P\)为世界坐标系下某点的坐标（\(Z\)为z方向的坐标），\(p\)为对应图像特征点。\(K\)为内参，在标定好的相机下，\(K\)已知
- 根据对极几何约束，假设\(p_{2}\)为相机位姿运动\(R\)，\(t\)后与前一帧的特征点\(p_{1}\)匹配的特征点，则有
\[s_1p_1 = KP\]
\[s_2p_2 = K(RP+t)\] - 参考视觉slam14讲的推导，这里可以得到对极约束
\[{p}_2^T{K^{ - T}}{t^ \wedge }RK{H^{ - 1}}{p_1} = 0\]
可以通过8点法求解本质矩阵进而得到\(R\)，\(t\) - 每两帧之间的位姿递推误差积累很快，因此直接递推的位姿是不太稳定的。
- \(t\)的缩放尺寸不确定，因此不能获得绝对位置
测试代码
主要基于视觉slam14讲的代码，稍微改动的测试，尽管能够求解姿态但是并不十分准确，后续考虑使用双目相机实现定位功能
#include
#include
#include
#include
#include "opencv2/features2d/features2d.hpp"
#include
#include
#include
#include
//#include "stdafx.h"
using namespace cv;
using namespace std;
void find_feature_matches(
const Mat& img_1, const Mat& img_2,
std::vector& keypoints_1,
std::vector& keypoints_2,
std::vector< DMatch >& matches);
void pose_estimation_2d2d(
std::vector keypoints_1,
std::vector keypoints_2,
std::vector< DMatch > matches,
Mat& R, Mat& t);
// 像素坐标转相机归一化坐标
Point2d pixel2cam(const Point2d& p, const Mat& K);
int main()
{
VideoCapture cap1;
//VideoCapture cap2;
cap1.open(1);//白色摄像头
//cap2.open(2);//黑色摄像头
//if (!cap1.isOpened()||!cap2.isOpened())
if (!cap1.isOpened())
{
return -1;
}
//将摄像头从640*480改成320*240，速度从200ms提升至50ms
//cap1.set(CV_CAP_PROP_FRAME_WIDTH, 320);
//cap1.set(CV_CAP_PROP_FRAME_HEIGHT, 240);
//cap2.set(CV_CAP_PROP_FRAME_WIDTH, 320);
//cap2.set(CV_CAP_PROP_FRAME_HEIGHT, 240);
//namedWindow("Video", 1);
//namedWindow("Video", 2);
//namedWindow("pts", 3);
//Mat frame;
Mat img_1;
Mat img_2;
while (1)
{
cap1 >> img_1;
Sleep(10);
cap1 >> img_2;
if (!img_1.data || !img_2.data)
{
cout << "error reading images " << endl;
return -1;
}
vector keypoints_1, keypoints_2;
vector matches;
find_feature_matches(img_1, img_2, keypoints_1, keypoints_2, matches);
//cout << "一共找到了" << matches.size() << "组匹配点" << endl;
//-- 估计两张图像间运动
Mat R, t;
pose_estimation_2d2d(keypoints_1, keypoints_2, matches, R, t);
//cout << "R:" << endl << R << endl;
//cout << "t:" << endl << t << endl;
////-- 验证E=t^R*scale
//Mat t_x = (Mat_(3, 3) <<
// 0, -t.at(2, 0), t.at(1, 0),
// t.at(2, 0), 0, -t.at(0, 0),
// -t.at(1.0), t.at(0, 0), 0);
//cout << "t^R=" << endl << t_x*R << endl;
////-- 验证对极约束
//Mat K = (Mat_(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
//for (DMatch m : matches)
//{
// Point2d pt1 = pixel2cam(keypoints_1[m.queryIdx].pt, K);
// Mat y1 = (Mat_(3, 1) << pt1.x, pt1.y, 1);
// Point2d pt2 = pixel2cam(keypoints_2[m.trainIdx].pt, K);
// Mat y2 = (Mat_(3, 1) << pt2.x, pt2.y, 1);
// Mat d = y2.t() * t_x * R * y1;
// cout << "epipolar constraint = " << d << endl;
//}
waitKey(1);
}
cap1.release();
//cap2.release();
return 0;
}
void find_feature_matches(const Mat& img_1, const Mat& img_2,
std::vector& keypoints_1,
std::vector& keypoints_2,
std::vector< DMatch >& matches)
{
//-- 初始化
Mat descriptors_1, descriptors_2;
// used in OpenCV3
Ptr detector = ORB::create();
Ptr descriptor = ORB::create();
// use this if you are in OpenCV2
// Ptr detector = FeatureDetector::create ( "ORB" );
// Ptr descriptor = DescriptorExtractor::create ( "ORB" );
Ptr 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 match;
//BFMatcher matcher ( NORM_HAMMING );
matcher->match(descriptors_1, descriptors_2, match);
//-- 第四步:匹配点对筛选
double min_dist = match[0].distance, max_dist = match[0].distance;
//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(0, 2)) / K.at(0, 0),
(p.y - K.at(1, 2)) / K.at(1, 1)
);
}
void pose_estimation_2d2d(std::vector keypoints_1,
std::vector keypoints_2,
std::vector< DMatch > matches,
Mat& R, Mat& t)
{
// 相机内参,需要标定得到
/*1225.22831056496 36.6177252813478 342.784169613124
0 1178.20016318321 187.290755011276
0 0 1*/
/*1296.76842892674 46.6256354215592 409.717933143672
0 1210.08953016730 69.8389243159229
0 0 1*/
//Mat K = (Mat_(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
Mat K = (Mat_(3, 3) << 1296.76842892674, 46.6256354215592, 409.717933143672, 0, 1210.08953016730, 69.8389243159229, 0, 0, 1);
//-- 把匹配点转换为vector的形式
vector points1;
vector points2;
for (int i = 0; i < (int)matches.size(); i++)
{
points1.push_back(keypoints_1[matches[i].queryIdx].pt);
points2.push_back(keypoints_2[matches[i].trainIdx].pt);
}
//-- 计算基础矩阵
Mat fundamental_matrix;
fundamental_matrix = findFundamentalMat(points1, points2, CV_FM_8POINT);
//cout << "fundamental_matrix is " << endl << fundamental_matrix << endl;
//-- 计算本质矩阵
Point2d principal_point(409.717933143672, 69.8389243159229); //相机光心, 标定值
double focal_length = 1296.76842892674; //相机焦距, 标定值
Mat essential_matrix;
essential_matrix = findEssentialMat(points1, points2, focal_length, principal_point);
//cout << "essential_matrix is " << endl << essential_matrix << endl;
//-- 计算单应矩阵
Mat homography_matrix;
homography_matrix = findHomography(points1, points2, RANSAC, 3);
//cout << "homography_matrix is " << endl << homography_matrix << endl;
//-- 从本质矩阵中恢复旋转和平移信息.
recoverPose(essential_matrix, points1, points2, R, t, focal_length, principal_point);
//cout << "R is " << endl << R << endl;
//cout << "t is " << endl << t << endl;
cout << R << endl;
}