《视觉 SLAM 十四讲》第 7 讲 视觉里程计1 【如何根据图像 估计 相机运动】【特征点法】

Gaoshu1012023-10-09 16:54

github源码链接V2

文章目录

  • [第 7 讲 视觉里程计1](#第 7 讲 视觉里程计1)
    • [7.1 特征点法](#7.1 特征点法)
      • [7.1.1 特征点](#7.1.1 特征点)
      • [7.1.2 ORB 特征](#7.1.2 ORB 特征)
        • [FAST 关键点 ⟹ \Longrightarrow ⟹ Oriented FAST](#FAST 关键点 ⟹ \Longrightarrow ⟹ Oriented FAST)
        • [BRIEF 描述子](#BRIEF 描述子)
      • [7.1.3 特征匹配](#7.1.3 特征匹配)
    • [7.2 实践 【Code】](#7.2 实践 【Code】)
          • [本讲 CMakeLists.txt](#本讲 CMakeLists.txt)
      • [7.2.1 使用 OpenCV 进行 ORB 的特征匹配 【Code】](#7.2.1 使用 OpenCV 进行 ORB 的特征匹配 【Code】)
      • [7.2.2 手写 ORB 特征](#7.2.2 手写 ORB 特征)
    • [估计 相机运动【相机位姿 估计】 3种情形 【对极几何、ICP、PnP】](#估计 相机运动【相机位姿 估计】 3种情形 【对极几何、ICP、PnP】)
    • [7.3 2D-2D: 对极几何 单目相机(无距离信息)](#7.3 2D-2D: 对极几何 单目相机(无距离信息))
      • [7.3.2 本质矩阵 E \bm{E} E](#7.3.2 本质矩阵 E \bm{E} E)
      • [7.3.3 单应矩阵(Homography)【墙、地面】](#7.3.3 单应矩阵(Homography)【墙、地面】)
    • [7.4 实践：对极约束 求解相机运动 【Code】](#7.4 实践：对极约束 求解相机运动 【Code】)
    • [7.5 三角测量](#7.5 三角测量)
    • [7.6 实践： 已知相机位姿，通过三角测量求特征点的空间位置 【Code】](#7.6 实践： 已知相机位姿，通过三角测量求特征点的空间位置 【Code】)
      • [7.6.2 三角测量的矛盾 ： 增加平移 Yes or No](#7.6.2 三角测量的矛盾 ： 增加平移 Yes or No)
    • [7.7 3D-2D: PnP (Perspective-n-Point) 【最重要】](#7.7 3D-2D: PnP (Perspective-n-Point) 【最重要】)
      • [7.7.1 直接线性变换(DLT)](#7.7.1 直接线性变换(DLT))
      • [7.7.2 P3P 【3对点 估计位姿】](#7.7.2 P3P 【3对点 估计位姿】)
      • [7.7.3 最小化 重投影误差 求解PnP](#7.7.3 最小化 重投影误差 求解PnP)
    • [7.8 实践： 求解 PnP 【Code】](#7.8 实践： 求解 PnP 【Code】)
    • [7.9 3D-3D: ICP(Iterative Closest Point, ICP，迭代最近点) 已知两个图的深度](#7.9 3D-3D: ICP(Iterative Closest Point, ICP，迭代最近点) 已知两个图的深度)
      • [7.9.1 SVD 方法](#7.9.1 SVD 方法)
      • [7.9.2 非线性优化方法](#7.9.2 非线性优化方法)
    • [7.10 使用 SVD 及 非线性优化 来求解 ICP 【Code】](#7.10 使用 SVD 及 非线性优化 来求解 ICP 【Code】)
    • 其它
        • [查看opencv 版本命令](#查看opencv 版本命令)

第 7 讲 视觉里程计1

图像特征点

在单幅 图像中 提取特征点 及 多幅图像 中 匹配特征点 的方法

对极几何 恢复图像之间 的 摄像机 的三维运动

PNP ICP

后续内容： 4 个模块 (视觉里程计、后端优化、回环检测、地图构建)

什么是特征点、如何提取和匹配特征点 、如何根据配对的特征点估计相机运动。

7.1 特征点法

前端【视觉里程计】 ： 根据相邻图像的信息 估计 相机运动，给后端提供初值基础。

基于特征点法 的前端： 对光照、动态物体不敏感。

视觉里程计 的两大类 算法： 特征点法 和 直接法。

  • 如何提取、匹配图像特征点，然后估计两帧之间的相机运动和场景结构。【两帧间视觉里程计】
  • 也称为 两视图几何 （Two-view geometry）

7.1.1 特征点

视觉里程计的核心： 如何根据图像 估计相机运动

有代表性的点

经典 SLAM 模型：路标
视觉SLAM：图像特征    ⟺    \iff ⟺ 路标

灰度值： 受光照、形变、物体材质影响严重，不稳定。

角点 、边缘、区块

角点： 在不同图像之间 的 辨识度 更强。

2000年以前提出的特征：

更加稳定 的局部图像特征：

可重复：相同的特征 可在不同图像中找到

可区别： 不同特征 表达不同
高效率： 同一图像，特征点的数量 远小于 像素数量。
本地性： 特征 仅与 一小片 图像区域相关。 【局部性？】

SIFT(尺度不变特征变换， Scale-Invariant Feature Transform)

计算量大

在一张图像中计算SIFT特征点    ⟺    \iff ⟺ 提取SIFT关键点， 并计算SIFT描述子。

关键点： 特征点的位置、朝向、大小等

描述子： 描述 该关键点 周围像素的信息。

两个特征点的描述子在向量空间上的距离相近    ⟺    \iff ⟺ 同样的特征点

ORB(Oriented FAST and Rotated BRIEF): 特征子具有旋转、尺度不变性，速度提升。
质量和性能之间的折中 成本、速度、匹配效果

7.1.2 ORB 特征

ORB贡献 ：

FAST角点提取 计算了 特征点的方向， 为后续 BRIEF描述子 增加了旋转不变性。

FAST 关键点 ⟹ \Longrightarrow ⟹ Oriented FAST

FAST 一种角点 检测 局部像素 灰度变化 明显的地方。 速度快

只比较 像素亮度 大小

预测试 ： 排除绝大多数不是角点 的像素。 加速 角点 检测

因为 一般要求 16个点里 N = 12 且连续， 因此 根据 这个间隔 4 要是超过两个点，就无法满足条件了。

避免 角点集中：在一定区域内 仅保留对应极大值的角点。非极大值抑制(Non-maximal suppression)

  • Code 非极大值抑制 算法

优点：速度快【仅比较像素间亮度的差异】
不足：

1、重复性不强， 分布不均匀。

2、不具有 方向信息。 ⟹ \Longrightarrow ⟹ 灰度质心法(Intensity Centroid)

3、固定取半径为 3 的圆， 存在尺度问题 远看是角点，近看不是 ⟹ \Longrightarrow ⟹ 构建图像金字塔

FAST ⟹ \Longrightarrow ⟹ ORB 中的 Oriented FAST 【尺度+旋转】

质心： 以 图像块 灰度值 作为权重的中心

BRIEF 描述子

原始的BRIEF 描述子 不具有旋转不变性，在图像发生旋转时容易丢失。

7.1.3 特征匹配

特征匹配 数据关联 当前看到的路标与之前看到的路标之间的对应关系。

  • 匹配 描述子

场景中 经常存在 大量重复纹理，特征描述相似 ⟶ \longrightarrow ⟶ 误匹配

两个二进制串之间的汉明距离------ 不同位数 的个数。

快速近似最近邻 (FLANN)

适用场景：匹配点数量极多

7.2 实践 【Code】

本讲 CMakeLists.txt

CMakeLists.txt

bash 复制代码 
cmake_minimum_required(VERSION 2.8)
project(vo1)

set(CMAKE_CXX_STANDARD 17)
set(CMAKE_BUILD_TYPE "Release")
add_definitions("-DENABLE_SSE")
set(CMAKE_CXX_FLAGS "-std=c++14 -O2 ${SSE_FLAGS} -msse4")
list(APPEND CMAKE_MODULE_PATH ${PROJECT_SOURCE_DIR}/cmake)

find_package(OpenCV 4.2.0 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(orb_cv orb_cv.cpp)
target_link_libraries(orb_cv ${OpenCV_LIBS})

#[[  # 块注释，用于选择 只运行 某个.cpp   #[[]]
add_executable(orb_self orb_self.cpp)
target_link_libraries(orb_self ${OpenCV_LIBS})


# add_executable( pose_estimation_2d2d pose_estimation_2d2d.cpp extra.cpp ) # use this if in OpenCV2 
add_executable(pose_estimation_2d2d pose_estimation_2d2d.cpp)
target_link_libraries(pose_estimation_2d2d ${OpenCV_LIBS})


# # add_executable( triangulation triangulation.cpp extra.cpp) # use this if in opencv2
add_executable(triangulation triangulation.cpp)
target_link_libraries(triangulation ${OpenCV_LIBS})


add_executable(pose_estimation_3d2d pose_estimation_3d2d.cpp)
target_link_libraries(pose_estimation_3d2d
        g2o_core g2o_stuff
        ${OpenCV_LIBS}
        ${Sophus_LIBRARIES})


add_executable(pose_estimation_3d3d pose_estimation_3d3d.cpp)
target_link_libraries(pose_estimation_3d3d
        g2o_core g2o_stuff
        ${OpenCV_LIBS}
        ${Sophus_LIBRARIES})

]]

7.2.1 使用 OpenCV 进行 ORB 的特征匹配 【Code】

报错：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/orb_cv.cpp:16:31: error: 'CV_LOAD_IMAGE_COLOR' was not declared in this scope
   16 |   Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
bash 复制代码 
mkdir build && cd build
cmake ..
make 
./orb_cv ../1.png ../2.png

orb_cv.cpp

cpp 复制代码 
#include <iostream>
#include <opencv4/opencv2/core/core.hpp>
#include <opencv4/opencv2/features2d/features2d.hpp>
#include <opencv4/opencv2/highgui/highgui.hpp>
#include <chrono>

using namespace std;
using namespace cv;

int main(int argc, char **argv) {
  if (argc != 3) {
    cout << "usage: feature_extraction img1 img2" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], cv::IMREAD_COLOR);  //OpenCV4 需要 改这里
  Mat img_2 = imread(argv[2], cv::IMREAD_COLOR);
  assert(img_1.data != nullptr && img_2.data != nullptr);

  //-- 初始化
  std::vector<KeyPoint> keypoints_1, keypoints_2;
  Mat descriptors_1, descriptors_2;
  Ptr<FeatureDetector> detector = ORB::create();
  Ptr<DescriptorExtractor> descriptor = ORB::create();
  Ptr<DescriptorMatcher> matcher = DescriptorMatcher::create("BruteForce-Hamming");

  //-- 第一步:检测 Oriented FAST 角点位置
  chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
  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);
  chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
  chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "extract ORB cost = " << time_used.count() << " seconds. " << endl;

  Mat outimg1;
  drawKeypoints(img_1, keypoints_1, outimg1, Scalar::all(-1), DrawMatchesFlags::DEFAULT);
  imshow("ORB features", outimg1);

  //-- 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> matches;
  t1 = chrono::steady_clock::now();
  matcher->match(descriptors_1, descriptors_2, matches);
  t2 = chrono::steady_clock::now();
  time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "match ORB cost = " << time_used.count() << " seconds. " << endl;

  //-- 第四步:匹配点对筛选
  // 计算最小距离和最大距离
  auto min_max = minmax_element(matches.begin(), matches.end(),
                                [](const DMatch &m1, const DMatch &m2) { return m1.distance < m2.distance; });
  double min_dist = min_max.first->distance;
  double max_dist = min_max.second->distance;

  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.
  std::vector<DMatch> good_matches;
  for (int i = 0; i < descriptors_1.rows; i++) {
    if (matches[i].distance <= max(2 * min_dist, 30.0)) {
      good_matches.push_back(matches[i]);
    }
  }

  //-- 第五步:绘制匹配结果
  Mat img_match;
  Mat img_goodmatch;
  drawMatches(img_1, keypoints_1, img_2, keypoints_2, matches, img_match);
  drawMatches(img_1, keypoints_1, img_2, keypoints_2, good_matches, img_goodmatch);
  imshow("all matches", img_match);
  imshow("good matches", img_goodmatch);
  waitKey(0);

  return 0;
}


去除误匹配： 汉明距离小于最小距离的 2 倍

7.2.2 手写 ORB 特征

改图片 路径

bash 复制代码 
cd build
cmake ..
make 
./orb_self

orb_self.cpp

cpp 复制代码 
//
// Created by xiang on 18-11-25.
//

#include <opencv4/opencv2/opencv.hpp>
#include <string>
#include <nmmintrin.h>
#include <chrono>

using namespace std;

// global variables
string first_file = "../1.png"; // 要 改路径   如果 cd build 的话
string second_file = "../2.png";

// 32 bit unsigned int, will have 8, 8x32=256
typedef vector<uint32_t> DescType; // Descriptor type

/**
 * compute descriptor of orb keypoints
 * @param img input image
 * @param keypoints detected fast keypoints
 * @param descriptors descriptors
 *
 * NOTE: if a keypoint goes outside the image boundary (8 pixels), descriptors will not be computed and will be left as
 * empty
 */
void ComputeORB(const cv::Mat &img, vector<cv::KeyPoint> &keypoints, vector<DescType> &descriptors);

/**
 * brute-force match two sets of descriptors
 * @param desc1 the first descriptor
 * @param desc2 the second descriptor
 * @param matches matches of two images
 */
void BfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches);

int main(int argc, char **argv) {

  // load image
  cv::Mat first_image = cv::imread(first_file, 0);
  cv::Mat second_image = cv::imread(second_file, 0);
  assert(first_image.data != nullptr && second_image.data != nullptr);

  // detect FAST keypoints1 using threshold=40
  chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
  vector<cv::KeyPoint> keypoints1;
  cv::FAST(first_image, keypoints1, 40);
  vector<DescType> descriptor1;
  ComputeORB(first_image, keypoints1, descriptor1);

  // same for the second
  vector<cv::KeyPoint> keypoints2;
  vector<DescType> descriptor2;
  cv::FAST(second_image, keypoints2, 40);
  ComputeORB(second_image, keypoints2, descriptor2);
  chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
  chrono::duration<double> time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "extract ORB cost = " << time_used.count() << " seconds. " << endl;

  // find matches
  vector<cv::DMatch> matches;
  t1 = chrono::steady_clock::now();
  BfMatch(descriptor1, descriptor2, matches);
  t2 = chrono::steady_clock::now();
  time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
  cout << "match ORB cost = " << time_used.count() << " seconds. " << endl;
  cout << "matches: " << matches.size() << endl;

  // plot the matches
  cv::Mat image_show;
  cv::drawMatches(first_image, keypoints1, second_image, keypoints2, matches, image_show);
  cv::imshow("matches", image_show);
  cv::imwrite("matches.png", image_show);
  cv::waitKey(0);

  cout << "done." << endl;
  return 0;
}

// -------------------------------------------------------------------------------------------------- //
// ORB pattern
int ORB_pattern[256 * 4] = {
  8, -3, 9, 5/*mean (0), correlation (0)*/,
  4, 2, 7, -12/*mean (1.12461e-05), correlation (0.0437584)*/,
  -11, 9, -8, 2/*mean (3.37382e-05), correlation (0.0617409)*/,
  7, -12, 12, -13/*mean (5.62303e-05), correlation (0.0636977)*/,
  2, -13, 2, 12/*mean (0.000134953), correlation (0.085099)*/,
  1, -7, 1, 6/*mean (0.000528565), correlation (0.0857175)*/,
  -2, -10, -2, -4/*mean (0.0188821), correlation (0.0985774)*/,
  -13, -13, -11, -8/*mean (0.0363135), correlation (0.0899616)*/,
  -13, -3, -12, -9/*mean (0.121806), correlation (0.099849)*/,
  10, 4, 11, 9/*mean (0.122065), correlation (0.093285)*/,
  -13, -8, -8, -9/*mean (0.162787), correlation (0.0942748)*/,
  -11, 7, -9, 12/*mean (0.21561), correlation (0.0974438)*/,
  7, 7, 12, 6/*mean (0.160583), correlation (0.130064)*/,
  -4, -5, -3, 0/*mean (0.228171), correlation (0.132998)*/,
  -13, 2, -12, -3/*mean (0.00997526), correlation (0.145926)*/,
  -9, 0, -7, 5/*mean (0.198234), correlation (0.143636)*/,
  12, -6, 12, -1/*mean (0.0676226), correlation (0.16689)*/,
  -3, 6, -2, 12/*mean (0.166847), correlation (0.171682)*/,
  -6, -13, -4, -8/*mean (0.101215), correlation (0.179716)*/,
  11, -13, 12, -8/*mean (0.200641), correlation (0.192279)*/,
  4, 7, 5, 1/*mean (0.205106), correlation (0.186848)*/,
  5, -3, 10, -3/*mean (0.234908), correlation (0.192319)*/,
  3, -7, 6, 12/*mean (0.0709964), correlation (0.210872)*/,
  -8, -7, -6, -2/*mean (0.0939834), correlation (0.212589)*/,
  -2, 11, -1, -10/*mean (0.127778), correlation (0.20866)*/,
  -13, 12, -8, 10/*mean (0.14783), correlation (0.206356)*/,
  -7, 3, -5, -3/*mean (0.182141), correlation (0.198942)*/,
  -4, 2, -3, 7/*mean (0.188237), correlation (0.21384)*/,
  -10, -12, -6, 11/*mean (0.14865), correlation (0.23571)*/,
  5, -12, 6, -7/*mean (0.222312), correlation (0.23324)*/,
  5, -6, 7, -1/*mean (0.229082), correlation (0.23389)*/,
  1, 0, 4, -5/*mean (0.241577), correlation (0.215286)*/,
  9, 11, 11, -13/*mean (0.00338507), correlation (0.251373)*/,
  4, 7, 4, 12/*mean (0.131005), correlation (0.257622)*/,
  2, -1, 4, 4/*mean (0.152755), correlation (0.255205)*/,
  -4, -12, -2, 7/*mean (0.182771), correlation (0.244867)*/,
  -8, -5, -7, -10/*mean (0.186898), correlation (0.23901)*/,
  4, 11, 9, 12/*mean (0.226226), correlation (0.258255)*/,
  0, -8, 1, -13/*mean (0.0897886), correlation (0.274827)*/,
  -13, -2, -8, 2/*mean (0.148774), correlation (0.28065)*/,
  -3, -2, -2, 3/*mean (0.153048), correlation (0.283063)*/,
  -6, 9, -4, -9/*mean (0.169523), correlation (0.278248)*/,
  8, 12, 10, 7/*mean (0.225337), correlation (0.282851)*/,
  0, 9, 1, 3/*mean (0.226687), correlation (0.278734)*/,
  7, -5, 11, -10/*mean (0.00693882), correlation (0.305161)*/,
  -13, -6, -11, 0/*mean (0.0227283), correlation (0.300181)*/,
  10, 7, 12, 1/*mean (0.125517), correlation (0.31089)*/,
  -6, -3, -6, 12/*mean (0.131748), correlation (0.312779)*/,
  10, -9, 12, -4/*mean (0.144827), correlation (0.292797)*/,
  -13, 8, -8, -12/*mean (0.149202), correlation (0.308918)*/,
  -13, 0, -8, -4/*mean (0.160909), correlation (0.310013)*/,
  3, 3, 7, 8/*mean (0.177755), correlation (0.309394)*/,
  5, 7, 10, -7/*mean (0.212337), correlation (0.310315)*/,
  -1, 7, 1, -12/*mean (0.214429), correlation (0.311933)*/,
  3, -10, 5, 6/*mean (0.235807), correlation (0.313104)*/,
  2, -4, 3, -10/*mean (0.00494827), correlation (0.344948)*/,
  -13, 0, -13, 5/*mean (0.0549145), correlation (0.344675)*/,
  -13, -7, -12, 12/*mean (0.103385), correlation (0.342715)*/,
  -13, 3, -11, 8/*mean (0.134222), correlation (0.322922)*/,
  -7, 12, -4, 7/*mean (0.153284), correlation (0.337061)*/,
  6, -10, 12, 8/*mean (0.154881), correlation (0.329257)*/,
  -9, -1, -7, -6/*mean (0.200967), correlation (0.33312)*/,
  -2, -5, 0, 12/*mean (0.201518), correlation (0.340635)*/,
  -12, 5, -7, 5/*mean (0.207805), correlation (0.335631)*/,
  3, -10, 8, -13/*mean (0.224438), correlation (0.34504)*/,
  -7, -7, -4, 5/*mean (0.239361), correlation (0.338053)*/,
  -3, -2, -1, -7/*mean (0.240744), correlation (0.344322)*/,
  2, 9, 5, -11/*mean (0.242949), correlation (0.34145)*/,
  -11, -13, -5, -13/*mean (0.244028), correlation (0.336861)*/,
  -1, 6, 0, -1/*mean (0.247571), correlation (0.343684)*/,
  5, -3, 5, 2/*mean (0.000697256), correlation (0.357265)*/,
  -4, -13, -4, 12/*mean (0.00213675), correlation (0.373827)*/,
  -9, -6, -9, 6/*mean (0.0126856), correlation (0.373938)*/,
  -12, -10, -8, -4/*mean (0.0152497), correlation (0.364237)*/,
  10, 2, 12, -3/*mean (0.0299933), correlation (0.345292)*/,
  7, 12, 12, 12/*mean (0.0307242), correlation (0.366299)*/,
  -7, -13, -6, 5/*mean (0.0534975), correlation (0.368357)*/,
  -4, 9, -3, 4/*mean (0.099865), correlation (0.372276)*/,
  7, -1, 12, 2/*mean (0.117083), correlation (0.364529)*/,
  -7, 6, -5, 1/*mean (0.126125), correlation (0.369606)*/,
  -13, 11, -12, 5/*mean (0.130364), correlation (0.358502)*/,
  -3, 7, -2, -6/*mean (0.131691), correlation (0.375531)*/,
  7, -8, 12, -7/*mean (0.160166), correlation (0.379508)*/,
  -13, -7, -11, -12/*mean (0.167848), correlation (0.353343)*/,
  1, -3, 12, 12/*mean (0.183378), correlation (0.371916)*/,
  2, -6, 3, 0/*mean (0.228711), correlation (0.371761)*/,
  -4, 3, -2, -13/*mean (0.247211), correlation (0.364063)*/,
  -1, -13, 1, 9/*mean (0.249325), correlation (0.378139)*/,
  7, 1, 8, -6/*mean (0.000652272), correlation (0.411682)*/,
  1, -1, 3, 12/*mean (0.00248538), correlation (0.392988)*/,
  9, 1, 12, 6/*mean (0.0206815), correlation (0.386106)*/,
  -1, -9, -1, 3/*mean (0.0364485), correlation (0.410752)*/,
  -13, -13, -10, 5/*mean (0.0376068), correlation (0.398374)*/,
  7, 7, 10, 12/*mean (0.0424202), correlation (0.405663)*/,
  12, -5, 12, 9/*mean (0.0942645), correlation (0.410422)*/,
  6, 3, 7, 11/*mean (0.1074), correlation (0.413224)*/,
  5, -13, 6, 10/*mean (0.109256), correlation (0.408646)*/,
  2, -12, 2, 3/*mean (0.131691), correlation (0.416076)*/,
  3, 8, 4, -6/*mean (0.165081), correlation (0.417569)*/,
  2, 6, 12, -13/*mean (0.171874), correlation (0.408471)*/,
  9, -12, 10, 3/*mean (0.175146), correlation (0.41296)*/,
  -8, 4, -7, 9/*mean (0.183682), correlation (0.402956)*/,
  -11, 12, -4, -6/*mean (0.184672), correlation (0.416125)*/,
  1, 12, 2, -8/*mean (0.191487), correlation (0.386696)*/,
  6, -9, 7, -4/*mean (0.192668), correlation (0.394771)*/,
  2, 3, 3, -2/*mean (0.200157), correlation (0.408303)*/,
  6, 3, 11, 0/*mean (0.204588), correlation (0.411762)*/,
  3, -3, 8, -8/*mean (0.205904), correlation (0.416294)*/,
  7, 8, 9, 3/*mean (0.213237), correlation (0.409306)*/,
  -11, -5, -6, -4/*mean (0.243444), correlation (0.395069)*/,
  -10, 11, -5, 10/*mean (0.247672), correlation (0.413392)*/,
  -5, -8, -3, 12/*mean (0.24774), correlation (0.411416)*/,
  -10, 5, -9, 0/*mean (0.00213675), correlation (0.454003)*/,
  8, -1, 12, -6/*mean (0.0293635), correlation (0.455368)*/,
  4, -6, 6, -11/*mean (0.0404971), correlation (0.457393)*/,
  -10, 12, -8, 7/*mean (0.0481107), correlation (0.448364)*/,
  4, -2, 6, 7/*mean (0.050641), correlation (0.455019)*/,
  -2, 0, -2, 12/*mean (0.0525978), correlation (0.44338)*/,
  -5, -8, -5, 2/*mean (0.0629667), correlation (0.457096)*/,
  7, -6, 10, 12/*mean (0.0653846), correlation (0.445623)*/,
  -9, -13, -8, -8/*mean (0.0858749), correlation (0.449789)*/,
  -5, -13, -5, -2/*mean (0.122402), correlation (0.450201)*/,
  8, -8, 9, -13/*mean (0.125416), correlation (0.453224)*/,
  -9, -11, -9, 0/*mean (0.130128), correlation (0.458724)*/,
  1, -8, 1, -2/*mean (0.132467), correlation (0.440133)*/,
  7, -4, 9, 1/*mean (0.132692), correlation (0.454)*/,
  -2, 1, -1, -4/*mean (0.135695), correlation (0.455739)*/,
  11, -6, 12, -11/*mean (0.142904), correlation (0.446114)*/,
  -12, -9, -6, 4/*mean (0.146165), correlation (0.451473)*/,
  3, 7, 7, 12/*mean (0.147627), correlation (0.456643)*/,
  5, 5, 10, 8/*mean (0.152901), correlation (0.455036)*/,
  0, -4, 2, 8/*mean (0.167083), correlation (0.459315)*/,
  -9, 12, -5, -13/*mean (0.173234), correlation (0.454706)*/,
  0, 7, 2, 12/*mean (0.18312), correlation (0.433855)*/,
  -1, 2, 1, 7/*mean (0.185504), correlation (0.443838)*/,
  5, 11, 7, -9/*mean (0.185706), correlation (0.451123)*/,
  3, 5, 6, -8/*mean (0.188968), correlation (0.455808)*/,
  -13, -4, -8, 9/*mean (0.191667), correlation (0.459128)*/,
  -5, 9, -3, -3/*mean (0.193196), correlation (0.458364)*/,
  -4, -7, -3, -12/*mean (0.196536), correlation (0.455782)*/,
  6, 5, 8, 0/*mean (0.1972), correlation (0.450481)*/,
  -7, 6, -6, 12/*mean (0.199438), correlation (0.458156)*/,
  -13, 6, -5, -2/*mean (0.211224), correlation (0.449548)*/,
  1, -10, 3, 10/*mean (0.211718), correlation (0.440606)*/,
  4, 1, 8, -4/*mean (0.213034), correlation (0.443177)*/,
  -2, -2, 2, -13/*mean (0.234334), correlation (0.455304)*/,
  2, -12, 12, 12/*mean (0.235684), correlation (0.443436)*/,
  -2, -13, 0, -6/*mean (0.237674), correlation (0.452525)*/,
  4, 1, 9, 3/*mean (0.23962), correlation (0.444824)*/,
  -6, -10, -3, -5/*mean (0.248459), correlation (0.439621)*/,
  -3, -13, -1, 1/*mean (0.249505), correlation (0.456666)*/,
  7, 5, 12, -11/*mean (0.00119208), correlation (0.495466)*/,
  4, -2, 5, -7/*mean (0.00372245), correlation (0.484214)*/,
  -13, 9, -9, -5/*mean (0.00741116), correlation (0.499854)*/,
  7, 1, 8, 6/*mean (0.0208952), correlation (0.499773)*/,
  7, -8, 7, 6/*mean (0.0220085), correlation (0.501609)*/,
  -7, -4, -7, 1/*mean (0.0233806), correlation (0.496568)*/,
  -8, 11, -7, -8/*mean (0.0236505), correlation (0.489719)*/,
  -13, 6, -12, -8/*mean (0.0268781), correlation (0.503487)*/,
  2, 4, 3, 9/*mean (0.0323324), correlation (0.501938)*/,
  10, -5, 12, 3/*mean (0.0399235), correlation (0.494029)*/,
  -6, -5, -6, 7/*mean (0.0420153), correlation (0.486579)*/,
  8, -3, 9, -8/*mean (0.0548021), correlation (0.484237)*/,
  2, -12, 2, 8/*mean (0.0616622), correlation (0.496642)*/,
  -11, -2, -10, 3/*mean (0.0627755), correlation (0.498563)*/,
  -12, -13, -7, -9/*mean (0.0829622), correlation (0.495491)*/,
  -11, 0, -10, -5/*mean (0.0843342), correlation (0.487146)*/,
  5, -3, 11, 8/*mean (0.0929937), correlation (0.502315)*/,
  -2, -13, -1, 12/*mean (0.113327), correlation (0.48941)*/,
  -1, -8, 0, 9/*mean (0.132119), correlation (0.467268)*/,
  -13, -11, -12, -5/*mean (0.136269), correlation (0.498771)*/,
  -10, -2, -10, 11/*mean (0.142173), correlation (0.498714)*/,
  -3, 9, -2, -13/*mean (0.144141), correlation (0.491973)*/,
  2, -3, 3, 2/*mean (0.14892), correlation (0.500782)*/,
  -9, -13, -4, 0/*mean (0.150371), correlation (0.498211)*/,
  -4, 6, -3, -10/*mean (0.152159), correlation (0.495547)*/,
  -4, 12, -2, -7/*mean (0.156152), correlation (0.496925)*/,
  -6, -11, -4, 9/*mean (0.15749), correlation (0.499222)*/,
  6, -3, 6, 11/*mean (0.159211), correlation (0.503821)*/,
  -13, 11, -5, 5/*mean (0.162427), correlation (0.501907)*/,
  11, 11, 12, 6/*mean (0.16652), correlation (0.497632)*/,
  7, -5, 12, -2/*mean (0.169141), correlation (0.484474)*/,
  -1, 12, 0, 7/*mean (0.169456), correlation (0.495339)*/,
  -4, -8, -3, -2/*mean (0.171457), correlation (0.487251)*/,
  -7, 1, -6, 7/*mean (0.175), correlation (0.500024)*/,
  -13, -12, -8, -13/*mean (0.175866), correlation (0.497523)*/,
  -7, -2, -6, -8/*mean (0.178273), correlation (0.501854)*/,
  -8, 5, -6, -9/*mean (0.181107), correlation (0.494888)*/,
  -5, -1, -4, 5/*mean (0.190227), correlation (0.482557)*/,
  -13, 7, -8, 10/*mean (0.196739), correlation (0.496503)*/,
  1, 5, 5, -13/*mean (0.19973), correlation (0.499759)*/,
  1, 0, 10, -13/*mean (0.204465), correlation (0.49873)*/,
  9, 12, 10, -1/*mean (0.209334), correlation (0.49063)*/,
  5, -8, 10, -9/*mean (0.211134), correlation (0.503011)*/,
  -1, 11, 1, -13/*mean (0.212), correlation (0.499414)*/,
  -9, -3, -6, 2/*mean (0.212168), correlation (0.480739)*/,
  -1, -10, 1, 12/*mean (0.212731), correlation (0.502523)*/,
  -13, 1, -8, -10/*mean (0.21327), correlation (0.489786)*/,
  8, -11, 10, -6/*mean (0.214159), correlation (0.488246)*/,
  2, -13, 3, -6/*mean (0.216993), correlation (0.50287)*/,
  7, -13, 12, -9/*mean (0.223639), correlation (0.470502)*/,
  -10, -10, -5, -7/*mean (0.224089), correlation (0.500852)*/,
  -10, -8, -8, -13/*mean (0.228666), correlation (0.502629)*/,
  4, -6, 8, 5/*mean (0.22906), correlation (0.498305)*/,
  3, 12, 8, -13/*mean (0.233378), correlation (0.503825)*/,
  -4, 2, -3, -3/*mean (0.234323), correlation (0.476692)*/,
  5, -13, 10, -12/*mean (0.236392), correlation (0.475462)*/,
  4, -13, 5, -1/*mean (0.236842), correlation (0.504132)*/,
  -9, 9, -4, 3/*mean (0.236977), correlation (0.497739)*/,
  0, 3, 3, -9/*mean (0.24314), correlation (0.499398)*/,
  -12, 1, -6, 1/*mean (0.243297), correlation (0.489447)*/,
  3, 2, 4, -8/*mean (0.00155196), correlation (0.553496)*/,
  -10, -10, -10, 9/*mean (0.00239541), correlation (0.54297)*/,
  8, -13, 12, 12/*mean (0.0034413), correlation (0.544361)*/,
  -8, -12, -6, -5/*mean (0.003565), correlation (0.551225)*/,
  2, 2, 3, 7/*mean (0.00835583), correlation (0.55285)*/,
  10, 6, 11, -8/*mean (0.00885065), correlation (0.540913)*/,
  6, 8, 8, -12/*mean (0.0101552), correlation (0.551085)*/,
  -7, 10, -6, 5/*mean (0.0102227), correlation (0.533635)*/,
  -3, -9, -3, 9/*mean (0.0110211), correlation (0.543121)*/,
  -1, -13, -1, 5/*mean (0.0113473), correlation (0.550173)*/,
  -3, -7, -3, 4/*mean (0.0140913), correlation (0.554774)*/,
  -8, -2, -8, 3/*mean (0.017049), correlation (0.55461)*/,
  4, 2, 12, 12/*mean (0.01778), correlation (0.546921)*/,
  2, -5, 3, 11/*mean (0.0224022), correlation (0.549667)*/,
  6, -9, 11, -13/*mean (0.029161), correlation (0.546295)*/,
  3, -1, 7, 12/*mean (0.0303081), correlation (0.548599)*/,
  11, -1, 12, 4/*mean (0.0355151), correlation (0.523943)*/,
  -3, 0, -3, 6/*mean (0.0417904), correlation (0.543395)*/,
  4, -11, 4, 12/*mean (0.0487292), correlation (0.542818)*/,
  2, -4, 2, 1/*mean (0.0575124), correlation (0.554888)*/,
  -10, -6, -8, 1/*mean (0.0594242), correlation (0.544026)*/,
  -13, 7, -11, 1/*mean (0.0597391), correlation (0.550524)*/,
  -13, 12, -11, -13/*mean (0.0608974), correlation (0.55383)*/,
  6, 0, 11, -13/*mean (0.065126), correlation (0.552006)*/,
  0, -1, 1, 4/*mean (0.074224), correlation (0.546372)*/,
  -13, 3, -9, -2/*mean (0.0808592), correlation (0.554875)*/,
  -9, 8, -6, -3/*mean (0.0883378), correlation (0.551178)*/,
  -13, -6, -8, -2/*mean (0.0901035), correlation (0.548446)*/,
  5, -9, 8, 10/*mean (0.0949843), correlation (0.554694)*/,
  2, 7, 3, -9/*mean (0.0994152), correlation (0.550979)*/,
  -1, -6, -1, -1/*mean (0.10045), correlation (0.552714)*/,
  9, 5, 11, -2/*mean (0.100686), correlation (0.552594)*/,
  11, -3, 12, -8/*mean (0.101091), correlation (0.532394)*/,
  3, 0, 3, 5/*mean (0.101147), correlation (0.525576)*/,
  -1, 4, 0, 10/*mean (0.105263), correlation (0.531498)*/,
  3, -6, 4, 5/*mean (0.110785), correlation (0.540491)*/,
  -13, 0, -10, 5/*mean (0.112798), correlation (0.536582)*/,
  5, 8, 12, 11/*mean (0.114181), correlation (0.555793)*/,
  8, 9, 9, -6/*mean (0.117431), correlation (0.553763)*/,
  7, -4, 8, -12/*mean (0.118522), correlation (0.553452)*/,
  -10, 4, -10, 9/*mean (0.12094), correlation (0.554785)*/,
  7, 3, 12, 4/*mean (0.122582), correlation (0.555825)*/,
  9, -7, 10, -2/*mean (0.124978), correlation (0.549846)*/,
  7, 0, 12, -2/*mean (0.127002), correlation (0.537452)*/,
  -1, -6, 0, -11/*mean (0.127148), correlation (0.547401)*/
};

// compute the descriptor
void ComputeORB(const cv::Mat &img, vector<cv::KeyPoint> &keypoints, vector<DescType> &descriptors) {
  const int half_patch_size = 8;
  const int half_boundary = 16;
  int bad_points = 0;
  for (auto &kp: keypoints) {
    if (kp.pt.x < half_boundary || kp.pt.y < half_boundary ||
        kp.pt.x >= img.cols - half_boundary || kp.pt.y >= img.rows - half_boundary) {
      // outside
      bad_points++;
      descriptors.push_back({});
      continue;
    }

    float m01 = 0, m10 = 0;
    for (int dx = -half_patch_size; dx < half_patch_size; ++dx) {
      for (int dy = -half_patch_size; dy < half_patch_size; ++dy) {
        uchar pixel = img.at<uchar>(kp.pt.y + dy, kp.pt.x + dx);
        m10 += dx * pixel;
        m01 += dy * pixel;
      }
    }

    // angle should be arc tan(m01/m10);
    float m_sqrt = sqrt(m01 * m01 + m10 * m10) + 1e-18; // avoid divide by zero
    float sin_theta = m01 / m_sqrt;
    float cos_theta = m10 / m_sqrt;

    // compute the angle of this point
    DescType desc(8, 0);
    for (int i = 0; i < 8; i++) {
      uint32_t d = 0;
      for (int k = 0; k < 32; k++) {
        int idx_pq = i * 32 + k;
        cv::Point2f p(ORB_pattern[idx_pq * 4], ORB_pattern[idx_pq * 4 + 1]);
        cv::Point2f q(ORB_pattern[idx_pq * 4 + 2], ORB_pattern[idx_pq * 4 + 3]);

        // rotate with theta
        cv::Point2f pp = cv::Point2f(cos_theta * p.x - sin_theta * p.y, sin_theta * p.x + cos_theta * p.y)
                         + kp.pt;
        cv::Point2f qq = cv::Point2f(cos_theta * q.x - sin_theta * q.y, sin_theta * q.x + cos_theta * q.y)
                         + kp.pt;
        if (img.at<uchar>(pp.y, pp.x) < img.at<uchar>(qq.y, qq.x)) {
          d |= 1 << k;
        }
      }
      desc[i] = d;
    }
    descriptors.push_back(desc);
  }

  cout << "bad/total: " << bad_points << "/" << keypoints.size() << endl;
}

// brute-force matching
void BfMatch(const vector<DescType> &desc1, const vector<DescType> &desc2, vector<cv::DMatch> &matches) {
  const int d_max = 40;

  for (size_t i1 = 0; i1 < desc1.size(); ++i1) {
    if (desc1[i1].empty()) continue;
    cv::DMatch m{i1, 0, 256};
    for (size_t i2 = 0; i2 < desc2.size(); ++i2) {
      if (desc2[i2].empty()) continue;
      int distance = 0;
      for (int k = 0; k < 8; k++) {
        distance += _mm_popcnt_u32(desc1[i1][k] ^ desc2[i2][k]);
      }
      if (distance < d_max && distance < m.distance) {
        m.distance = distance;
        m.trainIdx = i2;
      }
    }
    if (m.distance < d_max) {
      matches.push_back(m);
    }
  }
}

估计 相机运动【相机位姿 估计】 3种情形 【对极几何、ICP、PnP】

1、相机为单目 ： 根据两组2D点 估计运动 对极几何

2、相机可获得距离信息(双目、RGB-D等)：两组3D点 估计运动 ICP

3、一组 3D + 一组 2D ： PnP

7.3 2D-2D: 对极几何 单目相机(无距离信息)

通过 二维图像点的对应关系， 恢复两帧之间摄像机的运动。

极平面(Epipolar plane)： O 1 , O 2 , P 三点形成的平面 O_1, O_2, P三点形成的平面 O1,O2,P三点形成的平面

  • 注意 点 P P P 是 O 1 p 1 O_1p_1 O1p1 延长线 和 O 2 p 2 O_2p_2 O2p2 延长线 的交点

极点(Epipoles)： e 1 , e 2 e_1, e_2 e1,e2 【 O 1 O 2 O_1O_2 O1O2 连线 与 像平面 I 1 , I 2 I_1,I_2 I1,I2的交点】
极线(Epipolar line)： p 1 e 1 ( l 1 ) 、 p 2 e 2 ( l 2 ) p_1e_1(l_1)、p_2e_2(l_2) p1e1(l1)、p2e2(l2)
基线： O 1 O 2 O_1O_2 O1O2

像平面： I 1 ， I 2 I_1，I_2 I1，I2

假设 I 1 I_1 I1 中特征点 p 1 p_1 p1 匹配到 I 2 I_2 I2 中特征点 p 2 p_2 p2




本质矩阵(Essential Matrix) E = t ∧ R \bm{E} =\bm{t}^{\land}\bm{R} E=t∧R
基础矩阵(Fundamental Matrix) F = K − T E K − 1 \bm{F}=\bm{K}^{-T}\bm{E}\bm{K}^{-1} F=K−TEK−1

  • E \bm{E} E 和 F \bm{F} F 只差了相机内参 K \bm{K} K 部分

对于归一化坐标 x 1 , x 2 \bm{x}_1, \bm{x}_2 x1,x2 ： x 2 T E x 1 = 0 \bm{x}_2^T\bm{E}\bm{x}_1=0 x2TEx1=0 【本质矩阵】

对于匹配的像素坐标 p 1 , p 2 \bm{p}_1, \bm{p}_2 p1,p2 ： p 2 T F p 1 = 0 \bm{p}_2^T\bm{F}\bm{p}_1=0 p2TFp1=0 【基础矩阵】

对极约束作用:

给出了两个匹配点的空间位置关系，将相机位姿估计问题变为以下两步：

1、根据配对点的像素位置 求出 E \bm{E} E 或 F \bm{F} F

2、根据 E \bm{E} E 或 F \bm{F} F 求出 R , t \bm{R,t} R,t

以 E \bm{E} E 为例，如何求解这两个问题

7.3.2 本质矩阵 E \bm{E} E

求解 E \bm{E} E：



根据已经估得的本质矩阵 E \bm{E} E， 恢复相机的运动 R , t \bm{R,t} R,t



7.3.3 单应矩阵(Homography)【墙、地面】

单应矩阵(Homography) H \bm{H} H：描述两个平面之间的映射关系。

  • 运动估计 适用场景：场景中的特征点都落在同一平面上(墙、地面等)

  • 无人机携带的俯视相机 或 扫地机携带的顶视相机


求解单应矩阵 H \bm{H} H:



直接线性变换法(Direct Linear Transform, DLT)

7.4 实践：对极约束 求解相机运动 【Code】


OpenCV官网相关API

报错：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_2d2d.cpp:36:31: error: 'CV_LOAD_IMAGE_COLOR' was not declared in this scope
   36 |   Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
      |                               ^~~~~~~~~~~~~~~~~~~
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_2d2d.cpp: In function 'void pose_estimation_2d2d(std::vector<cv::KeyPoint>, std::vector<cv::KeyPoint>, std::vector<cv::DMatch>, cv::Mat&, cv::Mat&)':
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_2d2d.cpp:143:61: error: 'CV_FM_8POINT' was not declared in this scope
  143 |   fundamental_matrix = findFundamentalMat(points1, points2, CV_FM_8POINT);
      |                                                             ^~~~~~~~~~~~

解决方案链接

之前 遇到了问题，改了CmakeLists.txt 很多地方，遇到了别的问题【Segmentation fault (core dumped)】，卡了挺久。重新复制原版CmakeLists.txt ，只改了OpenCV版本，CMAKE标准改成14。


bash 复制代码 
cd build
cmake ..
make
./pose_estimation_2d2d ../1.png ../2.png

pose_estimation_2d2d.cpp

cpp 复制代码 
#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/calib3d/calib3d.hpp>
// #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<KeyPoint> &keypoints_1,
  std::vector<KeyPoint> &keypoints_2,
  std::vector<DMatch> &matches);

void pose_estimation_2d2d(
  std::vector<KeyPoint> keypoints_1,
  std::vector<KeyPoint> 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" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], IMREAD_COLOR);  // OpenCV4 要改这里
  Mat img_2 = imread(argv[2], IMREAD_COLOR);
  assert(img_1.data && img_2.data && "Can not load images!");

  vector<KeyPoint> keypoints_1, keypoints_2;
  vector<DMatch> 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);

  //-- 验证E=t^R*scale
  Mat t_x =
    (Mat_<double>(3, 3) << 0, -t.at<double>(2, 0), t.at<double>(1, 0),
      t.at<double>(2, 0), 0, -t.at<double>(0, 0),
      -t.at<double>(1, 0), t.at<double>(0, 0), 0);

  cout << "t^R=" << endl << t_x * R << endl;

  //-- 验证对极约束
  Mat K = (Mat_<double>(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_<double>(3, 1) << pt1.x, pt1.y, 1);
    Point2d pt2 = pixel2cam(keypoints_2[m.trainIdx].pt, K);
    Mat y2 = (Mat_<double>(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<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: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_2d2d(std::vector<KeyPoint> keypoints_1,
                          std::vector<KeyPoint> keypoints_2,
                          std::vector<DMatch> matches,
                          Mat &R, Mat &t) {
  // 相机内参,TUM Freiburg2
  Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);

  //-- 把匹配点转换为vector<Point2f>的形式
  vector<Point2f> points1; 
  vector<Point2f> 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, FM_8POINT);  // OpenCV4 修改
  cout << "fundamental_matrix is " << endl << fundamental_matrix << endl;

  //-- 计算本质矩阵
  Point2d principal_point(325.1, 249.7);  //相机光心, TUM dataset标定值
  double focal_length = 521;      //相机焦距, TUM dataset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
  //-- 但是本例中场景不是平面，单应矩阵意义不大
  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.
  // 此函数仅在Opencv3中提供
  recoverPose(essential_matrix, points1, points2, R, t, focal_length, principal_point);
  cout << "R is " << endl << R << endl;
  cout << "t is " << endl << t << endl;

}
讨论！！！



7.5 三角测量

在单目 SLAM 中，仅通过 单张图像 无法获得像素的深度信息，需要通过三角测量(Triangulation)（或三角化） 估计地图点的深度

三角测量： 通过不同位置对同一路标点进行观察，从观察到的位置判断路标点的距离。

  • 通过不同季节观察到的星星的角度，估计它与我们的距离。


7.6 实践： 已知相机位姿，通过三角测量求特征点的空间位置 【Code】

bash 复制代码 
cd build
cmake ..
make 
./triangulation ../1.png ../2.png



triangulation.cpp

cpp 复制代码 
#include <iostream>
#include <opencv4/opencv2/opencv.hpp>
// #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<KeyPoint> &keypoints_1,
  std::vector<KeyPoint> &keypoints_2,
  std::vector<DMatch> &matches);

void pose_estimation_2d2d(
  const std::vector<KeyPoint> &keypoints_1,
  const std::vector<KeyPoint> &keypoints_2,
  const std::vector<DMatch> &matches,
  Mat &R, Mat &t);

void triangulation(
  const vector<KeyPoint> &keypoint_1,
  const vector<KeyPoint> &keypoint_2,
  const std::vector<DMatch> &matches,
  const Mat &R, const Mat &t,
  vector<Point3d> &points
);

/// 作图用
inline cv::Scalar get_color(float depth) {
  float up_th = 50, low_th = 10, th_range = up_th - low_th;
  if (depth > up_th) depth = up_th;
  if (depth < low_th) depth = low_th;
  return cv::Scalar(255 * depth / th_range, 0, 255 * (1 - depth / th_range));
}

// 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" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], cv::IMREAD_COLOR); // OpenCV4 要修改 IMREAD_COLOR
  Mat img_2 = imread(argv[2], cv::IMREAD_COLOR);

  vector<KeyPoint> keypoints_1, keypoints_2;
  vector<DMatch> 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);

  //-- 三角化
  vector<Point3d> 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_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
  Mat img1_plot = img_1.clone();
  Mat img2_plot = img_2.clone();
  for (int i = 0; i < matches.size(); i++) {
    // 第一个图
    float depth1 = points[i].z;
    cout << "depth: " << depth1 << endl;
    Point2d pt1_cam = pixel2cam(keypoints_1[matches[i].queryIdx].pt, K);
    cv::circle(img1_plot, keypoints_1[matches[i].queryIdx].pt, 2, get_color(depth1), 2);

    // 第二个图
    Mat pt2_trans = R * (Mat_<double>(3, 1) << points[i].x, points[i].y, points[i].z) + t;
    float depth2 = pt2_trans.at<double>(2, 0);
    cv::circle(img2_plot, keypoints_2[matches[i].trainIdx].pt, 2, get_color(depth2), 2);
  }
  cv::imshow("img 1", img1_plot);
  cv::imshow("img 2", img2_plot);
  cv::waitKey();

  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: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]);
    }
  }
}

void pose_estimation_2d2d(
  const std::vector<KeyPoint> &keypoints_1,
  const std::vector<KeyPoint> &keypoints_2,
  const std::vector<DMatch> &matches,
  Mat &R, Mat &t) {
  // 相机内参,TUM Freiburg2
  Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);

  //-- 把匹配点转换为vector<Point2f>的形式
  vector<Point2f> points1;
  vector<Point2f> 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);
  }

  //-- 计算本质矩阵
  Point2d principal_point(325.1, 249.7);        //相机主点, TUM dataset标定值
  int focal_length = 521;            //相机焦距, TUM dataset标定值
  Mat essential_matrix;
  essential_matrix = findEssentialMat(points1, points2, focal_length, principal_point);

  //-- 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);
}

void triangulation(
  const vector<KeyPoint> &keypoint_1,
  const vector<KeyPoint> &keypoint_2,
  const std::vector<DMatch> &matches,
  const Mat &R, const Mat &t,
  vector<Point3d> &points) {
  Mat T1 = (Mat_<float>(3, 4) <<
    1, 0, 0, 0,
    0, 1, 0, 0,
    0, 0, 1, 0);
  Mat T2 = (Mat_<float>(3, 4) <<
    R.at<double>(0, 0), R.at<double>(0, 1), R.at<double>(0, 2), t.at<double>(0, 0),
    R.at<double>(1, 0), R.at<double>(1, 1), R.at<double>(1, 2), t.at<double>(1, 0),
    R.at<double>(2, 0), R.at<double>(2, 1), R.at<double>(2, 2), t.at<double>(2, 0)
  );

  Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
  vector<Point2f> 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 < pts_4d.cols; i++) {
    Mat x = pts_4d.col(i);
    x /= x.at<float>(3, 0); // 归一化
    Point3d p(
      x.at<float>(0, 0),
      x.at<float>(1, 0),
      x.at<float>(2, 0)
    );
    points.push_back(p);
  }
}

Point2f pixel2cam(const Point2d &p, const Mat &K) {
  return Point2f
    (
      (p.x - K.at<double>(0, 2)) / K.at<double>(0, 0),
      (p.y - K.at<double>(1, 2)) / K.at<double>(1, 1)
    );
}

7.6.2 三角测量的矛盾 ： 增加平移 Yes or No

1、平移很小时， 像素上的不确定性 将导致 较大的深度不确定性。

  • 特征点 运动一个 像素 Δ x \Delta x Δx ⟶ \longrightarrow ⟶ 视线角 变换一个角度 Δ θ \Delta \theta Δθ ⟶ \longrightarrow ⟶ 将测量到 深度值变化 Δ d \Delta d Δd
  • 当 t \bm{t} t 较大时， Δ d \Delta d Δd 将明显变小。说明平移较大时，在同样的相机分辨率下，三角化测量将会更精确。

提高三角化精度的 2 种方法：

1、提高特征点的提取精度，也就是提高图像分辨率 ⟶ \longrightarrow ⟶ 图像变大，增加计算成本

2、增大平移量 ⟶ \longrightarrow ⟶ 图像外观发生明显变化，使得特征提取与匹配变得困难

三角化的矛盾 【视差(parallax)】: 增大平移，可能导致匹配失效；而平移太小，则三角化精度不够。


2D-2D 的 对极几何法 的 不足

1、需要8个或8个以上的点对

2、存在初始化、纯旋转和尺度的问题

7.7 3D-2D: PnP (Perspective-n-Point) 【最重要】

当知道 n 个 3D 空间点及其投影位置时，如何估计相机的位姿。

如果两张图像中的一张特征点的 3D 位置已知，最少需要 3 个点对(以及至少一个额外点验证结果) 即可估计相机运动。

特征点的3D位置获取方法： 三角化 或 RGB-D相机的深度图
双目/RGB-D 单目 视觉里程计 PnP估计相机运动 需先初始化

3D-2D 方法的优点：

不需要使用对极约束，又可以在很少的匹配点获得较好的运动估计。

7.7.1 直接线性变换(DLT)

适用场景：

1、已知一组3D点的位置，以及它们在某个相机中的投影位置，求该相机的位姿。

2、给定地图和图像，求解相机状态。

3、把 3D 点看成在另一个相机坐标系中的点， 用来求解两个相机的相对运动。



7.7.2 P3P 【3对点 估计位姿】


P3P 不足：

1、只用了 3个点的信息，浪费了其它信息

2、如果3D 点 或 2D 点 受噪声影响，或存在 误匹配 ，则算法失效。

------> EPnP、UPnP

  • 利用更多的信息，用迭代的方式对相机位姿进行优化，尽可能消除噪声的影响。

SLAM中的通常做法： 先使用 P3P/EPnP 等方法估计相机位姿，再构建最小二乘优化问题对估计值进行调整。

7.7.3 最小化 重投影误差 求解PnP

线性方法： 先求相机位姿，再求空间点位置

非线性优化： 把相机和三维点放在一起优化 【Bundle Adjustment】



3D 点的投影位置 与 观测位置 作差 【重投影误差】



优化特征点的空间位置：

7.8 实践： 求解 PnP 【Code】

7.8.1 使用 PnP 求解位姿

要修改的报错：

报错1：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d2d.cpp:37:11: error: 'Sophus::SE3d' has not been declared
   37 |   Sophus::SE3d &pose
      |           ^~~~
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d2d.cpp:45:11: error: 'Sophus::SE3d' has not been declared
   45 |   Sophus::SE3d &pose

代码里所有的 SE3d 去掉d

报错2：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d2d.cpp:54:31: error: 'CV_LOAD_IMAGE_COLOR' was not declared in this scope
   54 |   Mat img_1 = imread(argv[1], CV_LOAD_IMAGE_COLOR);
      |                               ^~~~~~~~~~~~~~~~~~~
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d2d.cpp:64:28: error: 'CV_LOAD_IMAGE_UNCHANGED' was not declared in this scope
   64 |   Mat d1 = imread(argv[3], CV_LOAD_IMAGE_UNCHANGED);       // 深度图为16位无符号数，单通道图像
bash 复制代码 
opencv3                 opencv4
CV_LOAD_IMAGE_UNCHANGED IMREAD_UNCHANGED
CV_LOAD_IMAGE_GRAYSCALE IMREAD_GRAYSCALE
CV_LOAD_IMAGE_COLOR     IMREAD_COLOR
CV_LOAD_IMAGE_ANYDEPTH  IMREAD_ANYDEPTH

报错3：

bash 复制代码 
/usr/local/include/g2o/stuff/tuple_tools.h:41:46: error: 'tuple_size_v' is not a member of 'std'; did you mean 'tuple_size'?
   41 |       f, t, i, std::make_index_sequence<std::tuple_size_v<std::decay_t<T>>>());

解决办法：

在 CMakeLists.txt 中添加 set(CMAKE_CXX_STANDARD 17)

报错4：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d2d.cpp:318:10: error: 'make_unique' is not a member of 'g2o'; did you mean 'std::make_unique'?
  318 |     g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));

类似第6讲，直接替换 代码块

cpp 复制代码 
  // 构建图优化，先设定g2o   typedef  别名替换
  /*typedef g2o::BlockSolver<g2o::BlockSolverTraits<3, 1>> BlockSolverType;  // 每个误差项优化变量维度为3，误差值维度为1
  typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 线性求解器类型
  */
  std::unique_ptr<g2o::BlockSolverX::LinearSolverType> linearSolver 
       (new g2o::LinearSolverDense<g2o::BlockSolverX::PoseMatrixType>());

  // 梯度下降方法，可以从GN, LM, DogLeg 中选
  /*auto solver = new g2o::OptimizationAlgorithmGaussNewton(
    g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));*/
  std::unique_ptr<g2o::BlockSolverX> solver_ptr (new g2o::BlockSolverX(std::move(linearSolver)));
  g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(std::move(solver_ptr));
  g2o::SparseOptimizer optimizer;     // 图模型
  optimizer.setAlgorithm(solver);   // 设置求解器
  optimizer.setVerbose(true);       // 打开调试输出

报错5：

bash 复制代码 
/usr/bin/ld: CMakeFiles/pose_estimation_3d2d.dir/pose_estimation_3d2d.cpp.o: in function `bundleAdjustmentGaussNewton(std::vector<Eigen::Matrix<double, 3, 1, 0, 3, 1>, Eigen::aligned_allocator<Eigen::Matrix<double, 3, 1, 0, 3, 1> > > const&, std::vector<Eigen::Matrix<double, 2, 1, 0, 2, 1>, Eigen::aligned_allocator<Eigen::Matrix<double, 2, 1, 0, 2, 1> > > const&, cv::Mat const&, Sophus::SE3&)':
pose_estimation_3d2d.cpp:(.text+0x2a4f): undefined reference to `Sophus::SE3::operator*(Eigen::Matrix<double, 3, 1, 0, 3, 1> const&) const'
/usr/bin/ld: pose_estimation_3d2d.cpp:(.text+0x3254): undefined reference to `Sophus::SE3::exp(Eigen::Matrix<double, 6, 1, 0, 6, 1> const&)'

是CMakeLists.txt 里没链接到 Sophus，加上即可

bash 复制代码 
add_executable(pose_estimation_3d2d pose_estimation_3d2d.cpp)
target_link_libraries(pose_estimation_3d2d
        g2o_core g2o_stuff
        ${OpenCV_LIBS}
        ${Sophus_LIBRARIES})
bash 复制代码 
cd build 
cmake ..
make 
./pose_estimation_3d2d ../1.png ../2.png ../1_depth.png ../2_depth.png


pose_estimation_3d2d.cpp

cpp 复制代码 
#include <iostream>
#include <opencv4/opencv2/core/core.hpp>
#include <opencv4/opencv2/features2d/features2d.hpp>
#include <opencv4/opencv2/highgui/highgui.hpp>
#include <opencv4/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.h>
#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);

// 像素坐标转相机归一化坐标
Point2d pixel2cam(const Point2d &p, const Mat &K);

// BA by g2o
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::SE3 &pose
);

// BA by gauss-newton
void bundleAdjustmentGaussNewton(
  const VecVector3d &points_3d,
  const VecVector2d &points_2d,
  const Mat &K,
  Sophus::SE3 &pose
);

int main(int argc, char **argv) {
  if (argc != 5) {
    cout << "usage: pose_estimation_3d2d img1 img2 depth1 depth2" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], IMREAD_COLOR);
  Mat img_2 = imread(argv[2], IMREAD_COLOR);
  assert(img_1.data && img_2.data && "Can not load images!");

  vector<KeyPoint> keypoints_1, keypoints_2;
  vector<DMatch> 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;

  // 建立3D点
  Mat d1 = imread(argv[3], IMREAD_UNCHANGED);       // 深度图为16位无符号数，单通道图像
  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) {
    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;
    Point2d p1 = pixel2cam(keypoints_1[m.queryIdx].pt, K);
    pts_3d.push_back(Point3f(p1.x * dd, p1.y * dd, dd));
    pts_2d.push_back(keypoints_2[m.trainIdx].pt);
  }

  cout << "3d-2d pairs: " << pts_3d.size() << endl;

  chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
  Mat r, t;
  solvePnP(pts_3d, pts_2d, K, Mat(), r, t, false); // 调用OpenCV 的 PnP 求解，可选择EPNP，DLS等方法
  Mat R;
  cv::Rodrigues(r, R); // r为旋转向量形式，用Rodrigues公式转换为矩阵
  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) {
    pts_3d_eigen.push_back(Eigen::Vector3d(pts_3d[i].x, pts_3d[i].y, pts_3d[i].z));
    pts_2d_eigen.push_back(Eigen::Vector2d(pts_2d[i].x, pts_2d[i].y));
  }

  cout << "calling bundle adjustment by gauss newton" << endl;
  Sophus::SE3 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;

  cout << "calling bundle adjustment by g2o" << endl;
  Sophus::SE3 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: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 bundleAdjustmentGaussNewton(
  const VecVector3d &points_3d,
  const VecVector2d &points_2d,
  const Mat &K,
  Sophus::SE3 &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++) {
      Eigen::Vector3d pc = pose * points_3d[i];
      double inv_z = 1.0 / pc[2];
      double inv_z2 = inv_z * inv_z;
      Eigen::Vector2d proj(fx * pc[0] / pc[2] + cx, fy * pc[1] / pc[2] + cy);

      Eigen::Vector2d e = points_2d[i] - proj;

      cost += e.squaredNorm();
      Eigen::Matrix<double, 2, 6> J;
      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
    pose = Sophus::SE3::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: \n" << pose.matrix() << endl;
}

/// vertex and edges used in g2o ba
class VertexPose : public g2o::BaseVertex<6, Sophus::SE3> {
public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

  virtual void setToOriginImpl() override {
    _estimate = Sophus::SE3();
  }

  /// 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::SE3::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::SE3 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::SE3 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::SE3 &pose) {

  // 构建图优化，先设定g2o   typedef  别名替换
  /*typedef g2o::BlockSolver<g2o::BlockSolverTraits<3, 1>> BlockSolverType;  // 每个误差项优化变量维度为3，误差值维度为1
  typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 线性求解器类型
  */
  std::unique_ptr<g2o::BlockSolverX::LinearSolverType> linearSolver 
       (new g2o::LinearSolverDense<g2o::BlockSolverX::PoseMatrixType>());

  // 梯度下降方法，可以从GN, LM, DogLeg 中选
  /*auto solver = new g2o::OptimizationAlgorithmGaussNewton(
    g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));*/
  std::unique_ptr<g2o::BlockSolverX> solver_ptr (new g2o::BlockSolverX(std::move(linearSolver)));
  g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(std::move(solver_ptr));
  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 *vertex_pose = new VertexPose(); // camera vertex_pose
  vertex_pose->setId(0);
  vertex_pose->setEstimate(Sophus::SE3());
  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 =\n" << vertex_pose->estimate().matrix() << endl;
  pose = vertex_pose->estimate();
}

7.8.3 使用 g2o 进行 BA 优化

7.9 3D-3D: ICP(Iterative Closest Point, ICP，迭代最近点) 已知两个图的深度


迭代最近点： 认为距离最近的两个点为同一个。

7.9.1 SVD 方法




7.9.2 非线性优化方法





7.10 使用 SVD 及 非线性优化 来求解 ICP 【Code】

7.10.1 SVD方法

通过特征匹配 获取两组 3D 点，最后用 ICP 计算 位姿变换

7.10.2 非线性优化方法

根据 7.8 节改一遍

新的报错：

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d3d.cpp:81:50: error: 'Sophus::SO3d' has not been declared
   81 |     _jacobianOplusXi.block<3, 3>(0, 3) = Sophus::SO3d::hat(xyz_trans);

去掉d，改成 SO3

bash 复制代码 
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d3d.cpp: In function 'void bundleAdjustment(const std::vector<cv::Point3_<float> >&, const std::vector<cv::Point3_<float> >&, cv::Mat&, cv::Mat&)':
/home/xixi/Downloads/slambook2-master/ch7/pose_estimation_3d3d.cpp:298:41: error: 'const EstimateType' {aka 'const class Sophus::SE3'} has no member named 'rotationMatrix'; did you mean 'rotation_matrix'?
  298 |   Eigen::Matrix3d R_ = pose->estimate().rotationMatrix();
      |                                         ^~~~~~~~~~~~~~
      |                                         rotation_matrix

按照提示改成

bash 复制代码 
  Eigen::Matrix3d R_ = pose->estimate().rotation_matrix();
bash 复制代码 
cd build 
cmake ..
make 
./pose_estimation_3d3d ../1.png ../2.png ../1_depth.png ../2_depth.png


pose_estimation_3d3d.cpp

cpp 复制代码 
#include <iostream>
#include <opencv4/opencv2/core/core.hpp>
#include <opencv4/opencv2/features2d/features2d.hpp>
#include <opencv4/opencv2/highgui/highgui.hpp>
#include <opencv4/opencv2/calib3d/calib3d.hpp>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <Eigen/Geometry>
#include <Eigen/SVD>
#include <g2o/core/base_vertex.h>
#include <g2o/core/base_unary_edge.h>
#include <g2o/core/block_solver.h>
#include <g2o/core/optimization_algorithm_gauss_newton.h>
#include <g2o/core/optimization_algorithm_levenberg.h>
#include <g2o/solvers/dense/linear_solver_dense.h>
#include <chrono>
#include <sophus/se3.h>

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);

// 像素坐标转相机归一化坐标
Point2d pixel2cam(const Point2d &p, const Mat &K);

void pose_estimation_3d3d(
  const vector<Point3f> &pts1,
  const vector<Point3f> &pts2,
  Mat &R, Mat &t
);

void bundleAdjustment(
  const vector<Point3f> &points_3d,
  const vector<Point3f> &points_2d,
  Mat &R, Mat &t
);

/// vertex and edges used in g2o ba
class VertexPose : public g2o::BaseVertex<6, Sophus::SE3> {
public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

  virtual void setToOriginImpl() override {
    _estimate = Sophus::SE3();
  }

  /// 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::SE3::exp(update_eigen) * _estimate;
  }

  virtual bool read(istream &in) override {}

  virtual bool write(ostream &out) const override {}
};

/// g2o edge
class EdgeProjectXYZRGBDPoseOnly : public g2o::BaseUnaryEdge<3, Eigen::Vector3d, VertexPose> {
public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW;

  EdgeProjectXYZRGBDPoseOnly(const Eigen::Vector3d &point) : _point(point) {}

  virtual void computeError() override {
    const VertexPose *pose = static_cast<const VertexPose *> ( _vertices[0] );
    _error = _measurement - pose->estimate() * _point;
  }

  virtual void linearizeOplus() override {
    VertexPose *pose = static_cast<VertexPose *>(_vertices[0]);
    Sophus::SE3 T = pose->estimate();
    Eigen::Vector3d xyz_trans = T * _point;
    _jacobianOplusXi.block<3, 3>(0, 0) = -Eigen::Matrix3d::Identity();
    _jacobianOplusXi.block<3, 3>(0, 3) = Sophus::SO3::hat(xyz_trans);
  }

  bool read(istream &in) {}

  bool write(ostream &out) const {}

protected:
  Eigen::Vector3d _point;
};

int main(int argc, char **argv) {
  if (argc != 5) {
    cout << "usage: pose_estimation_3d3d img1 img2 depth1 depth2" << endl;
    return 1;
  }
  //-- 读取图像
  Mat img_1 = imread(argv[1], IMREAD_COLOR);
  Mat img_2 = imread(argv[2], IMREAD_COLOR);

  vector<KeyPoint> keypoints_1, keypoints_2;
  vector<DMatch> 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;

  // 建立3D点
  Mat depth1 = imread(argv[3], IMREAD_UNCHANGED);       // 深度图为16位无符号数，单通道图像
  Mat depth2 = imread(argv[4], IMREAD_UNCHANGED);       // 深度图为16位无符号数，单通道图像
  Mat K = (Mat_<double>(3, 3) << 520.9, 0, 325.1, 0, 521.0, 249.7, 0, 0, 1);
  vector<Point3f> pts1, pts2;

  for (DMatch m:matches) {
    ushort d1 = depth1.ptr<unsigned short>(int(keypoints_1[m.queryIdx].pt.y))[int(keypoints_1[m.queryIdx].pt.x)];
    ushort d2 = depth2.ptr<unsigned short>(int(keypoints_2[m.trainIdx].pt.y))[int(keypoints_2[m.trainIdx].pt.x)];
    if (d1 == 0 || d2 == 0)   // bad depth
      continue;
    Point2d p1 = pixel2cam(keypoints_1[m.queryIdx].pt, K);
    Point2d p2 = pixel2cam(keypoints_2[m.trainIdx].pt, K);
    float dd1 = float(d1) / 5000.0;
    float dd2 = float(d2) / 5000.0;
    pts1.push_back(Point3f(p1.x * dd1, p1.y * dd1, dd1));
    pts2.push_back(Point3f(p2.x * dd2, p2.y * dd2, dd2));
  }

  cout << "3d-3d pairs: " << pts1.size() << endl;
  Mat R, t;
  pose_estimation_3d3d(pts1, pts2, R, t);
  cout << "ICP via SVD results: " << endl;
  cout << "R = " << R << endl;
  cout << "t = " << t << endl;
  cout << "R_inv = " << R.t() << endl;
  cout << "t_inv = " << -R.t() * t << endl;

  cout << "calling bundle adjustment" << endl;

  bundleAdjustment(pts1, pts2, R, t);

  // verify p1 = R * p2 + t
  for (int i = 0; i < 5; i++) {
    cout << "p1 = " << pts1[i] << endl;
    cout << "p2 = " << pts2[i] << endl;
    cout << "(R*p2+t) = " <<
         R * (Mat_<double>(3, 1) << pts2[i].x, pts2[i].y, pts2[i].z) + t
         << endl;
    cout << endl;
  }
}

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: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  别名替换
  /*typedef g2o::BlockSolver<g2o::BlockSolverTraits<3, 1>> BlockSolverType;  // 每个误差项优化变量维度为3，误差值维度为1
  typedef g2o::LinearSolverDense<BlockSolverType::PoseMatrixType> LinearSolverType; // 线性求解器类型
  */
  std::unique_ptr<g2o::BlockSolverX::LinearSolverType> linearSolver 
       (new g2o::LinearSolverDense<g2o::BlockSolverX::PoseMatrixType>());

  // 梯度下降方法，可以从GN, LM, DogLeg 中选
  /*auto solver = new g2o::OptimizationAlgorithmGaussNewton(
    g2o::make_unique<BlockSolverType>(g2o::make_unique<LinearSolverType>()));*/
  std::unique_ptr<g2o::BlockSolverX> solver_ptr (new g2o::BlockSolverX(std::move(linearSolver)));
  g2o::OptimizationAlgorithmGaussNewton* solver = new g2o::OptimizationAlgorithmGaussNewton(std::move(solver_ptr));
  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::SE3());
  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().rotation_matrix();
  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));
}

使用了越来越多的信息：

对极几何 PnP ICP
没有深度 一个图的深度 两个图的深度

7.11 小结

其它

查看opencv 版本命令
bash 复制代码 
sudo apt update
sudo apt install libopencv-dev python3-opencv
bash 复制代码 
python3 -c "import cv2; print(cv2.__version__)"

sophus安装
Ubuntu20.04安装Ceres和g2o

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