视觉里程计2（SLAM十四讲ch7）-对极几何，三角测量
对极几何 2D2D
对极几何（Epipolar Geometry）是Structure from Motion问题中，在两个相机位置产生的两幅图像的之间存在的一种特殊几何关系，是sfm问题中2D-2D求解两帧间相机姿态的基本模型。
相机位姿估计问题——》
1.根据配对点的像素位置求出本质矩阵E或者基础矩阵F
2.根据E或者F求出R,t
E,F只相差了相机内参，而相机内参在SLAM中通常已知。
对极约束
摘自 高翔《视觉SLAM十四讲》第七章
本质矩阵
单应矩阵
实践
同样使用高翔《视觉SLAM十四讲》ch7中的例程
pose_estimation_2d2d.cpp
#include
#include
#include
#include
#include
// #include "extra.h" // use this if in OpenCV2
using namespace std;
using namespace cv;
/****************************************************
* 本程序演示了如何使用2D-2D的特征匹配估计相机运动
* **************************************************/
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 ( int argc, char** argv )
{
if ( argc != 3 )
{
cout<<"usage: pose_estimation_2d2d img1 img2"< keypoints_1, keypoints_2;
vector matches;
find_feature_matches ( img_1, img_2, keypoints_1, keypoints_2, matches );
cout<<"一共找到了"< ( 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="< ( 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;
}
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=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 ( 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,TUM Freiburg2
Mat K = ( Mat_ ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 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 "< ./build/pose_estimation_2d2d 1.png 2.png
三角测量
实践
利用对极几何求解的相机位姿。通过三角化求出特征点的空间位置。调用OpenCV提供的triangulation函数进行三角化
triangulation.cpp
#include
#include
#include
#include
#include
// #include "extra.h" // used in opencv2
using namespace std;
using namespace cv;
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 (
const std::vector& keypoints_1,
const std::vector& keypoints_2,
const std::vector< DMatch >& matches,
Mat& R, Mat& t );
void triangulation (
const vector& keypoint_1,
const vector& keypoint_2,
const std::vector< DMatch >& matches,
const Mat& R, const Mat& t,
vector& points
);
// 像素坐标转相机归一化坐标
Point2f pixel2cam( const Point2d& p, const Mat& K );
int main ( int argc, char** argv )
{
if ( argc != 3 )
{
cout<<"usage: triangulation img1 img2"< keypoints_1, keypoints_2;
vector matches;
find_feature_matches ( img_1, img_2, keypoints_1, keypoints_2, matches );
cout<<"一共找到了"< points;
triangulation( keypoints_1, keypoints_2, matches, R, t, points );
//-- 验证三角化点与特征点的重投影关系
Mat K = ( Mat_ ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1 );
for ( int i=0; i& 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=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] );
}
}
}
void pose_estimation_2d2d (
const std::vector& keypoints_1,
const std::vector& keypoints_2,
const std::vector< DMatch >& matches,
Mat& R, Mat& t )
{
// 相机内参,TUM Freiburg2
Mat K = ( Mat_ ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 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 "<& keypoint_1,
const vector< KeyPoint >& keypoint_2,
const std::vector< DMatch >& matches,
const Mat& R, const Mat& t,
vector< Point3d >& points )
{
Mat T1 = (Mat_ (3,4) <<
1,0,0,0,
0,1,0,0,
0,0,1,0);
Mat T2 = (Mat_ (3,4) <<
R.at(0,0), R.at(0,1), R.at(0,2), t.at(0,0),
R.at(1,0), R.at(1,1), R.at(1,2), t.at(1,0),
R.at(2,0), R.at(2,1), R.at(2,2), t.at(2,0)
);
Mat K = ( Mat_ ( 3,3 ) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1 );
vector pts_1, pts_2;
for ( DMatch m:matches )
{
// 将像素坐标转换至相机坐标
pts_1.push_back ( pixel2cam( keypoint_1[m.queryIdx].pt, K) );
pts_2.push_back ( pixel2cam( keypoint_2[m.trainIdx].pt, K) );
}
Mat pts_4d;
cv::triangulatePoints( T1, T2, pts_1, pts_2, pts_4d );
// 转换成非齐次坐标
for ( int i=0; i(3,0); // 归一化
Point3d p (
x.at(0,0),
x.at(1,0),
x.at(2,0)
);
points.push_back( p );
}
}
Point2f pixel2cam ( const Point2d& p, const Mat& K )
{
return Point2f
(
( p.x - K.at(0,2) ) / K.at(0,0),
( p.y - K.at(1,2) ) / K.at(1,1)
);
}
./build/triangulation 1.png 2.png
