SLAM第八讲实践：【前端2】基于Slambook2的LK光流，G-N实现单层光流以及多层光流以及直接法做VO的超详细实践

22.10.11 18.04
如果你之前看了我前面的所有实践过程，正确配置了相关库版本文件，那么可以继续看下去

这里直接拿高博的slambook1中的ch8

一.LK光流

1 在data中解压文件

其中文件的对应关系:

ground 是相机的pose信息
rgb文件夹是有关时间的信息
rgb.txt是时间与文件名
associate.py是深度图和彩色图（RGB）的对应关系的脚本文件

2 下面进入LKFLOW文件夹内

直接来一套组合拳

mkdir build
cd build
cmake ..
make

3 实现：./useLK +data的文件目录地址

二.高斯牛顿法实现单层光流和多层光流

1 optical_flow.cpp

//
// Created by czy on 2022/4/10.
//

#include 
#include 
#include 
#include 
#include 

using namespace std;
using namespace cv;

string file_1 = "../src/LK1.png";  // first image
string file_2 = "../src/LK2.png";  // second image

/// Optical flow tracker and interface
class OpticalFlowTracker {
public:
    OpticalFlowTracker(
            const Mat &img1_,
            const Mat &img2_,
            const vector<KeyPoint> &kp1_,
            vector<KeyPoint> &kp2_,
            vector<bool> &success_,
            bool inverse_ = true,
            bool has_initial_ = false) :
            img1(img1_), img2(img2_), kp1(kp1_), kp2(kp2_), success(success_), inverse(inverse_),
            has_initial(has_initial_) {}

    void calculateOpticalFlow(const Range &range);

private:
    const Mat &img1;
    const Mat &img2;
    const vector<KeyPoint> &kp1;
    vector<KeyPoint> &kp2;
    vector<bool> &success;
    bool inverse = true;
    bool has_initial = false;
};

/**
 * single level optical flow
 * @param [in] img1 the first image
 * @param [in] img2 the second image
 * @param [in] kp1 keypoints in img1
 * @param [in|out] kp2 keypoints in img2, if empty, use initial guess in kp1
 * @param [out] success true if a keypoint is tracked successfully
 * @param [in] inverse use inverse formulation?
 */
void OpticalFlowSingleLevel(
        const Mat &img1,
        const Mat &img2,
        const vector<KeyPoint> &kp1,
        vector<KeyPoint> &kp2,
        vector<bool> &success,
        bool inverse = false,
        bool has_initial_guess = false
);

/**
 * multi level optical flow, scale of pyramid is set to 2 by default
 * the image pyramid will be create inside the function
 * @param [in] img1 the first pyramid
 * @param [in] img2 the second pyramid
 * @param [in] kp1 keypoints in img1
 * @param [out] kp2 keypoints in img2
 * @param [out] success true if a keypoint is tracked successfully
 * @param [in] inverse set true to enable inverse formulation
 */
void OpticalFlowMultiLevel(
        const Mat &img1,
        const Mat &img2,
        const vector<KeyPoint> &kp1,
        vector<KeyPoint> &kp2,
        vector<bool> &success,
        bool inverse = false
);

/**
 * get a gray scale value from reference image (bi-linear interpolated)
 * 从参考图像中获取灰度值(双线性插值)
 * @param img
 * @param x
 * @param y
 * @return the interpolated value of this pixel
 */
inline float GetPixelValue(const cv::Mat &img, float x, float y) {
    // boundary check
    if (x < 0) x = 0;
    if (y < 0) y = 0;
    if (x >= img.cols) x = img.cols - 1;
    if (y >= img.rows) y = img.rows - 1;
    uchar *data = &img.data[int(y) * img.step + int(x)];
    float xx = x - floor(x);
    float yy = y - floor(y);
    return float(
            (1 - xx) * (1 - yy) * data[0] +
            xx * (1 - yy) * data[1] +
            (1 - xx) * yy * data[img.step] +
            xx * yy * data[img.step + 1]
    );
}

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

    // images, note they are CV_8UC1, not CV_8UC3
    Mat img1 = imread(file_1, 0);//如果设置，总是将图像转换为单通道灰度图像。
    Mat img2 = imread(file_2, 0);

    // key points, using GFTT here.
    vector<KeyPoint> kp1;
    /*
     * 之前角点检测的算法中,一个是cornerHarris计算角点，但
     * 是这种角点检测算法容易出现聚簇现象以及角点信息有丢失和位置偏移现象，
     * 所以后面又提出一种名为goodFeatureToTrack的角点检测算法，
     * opencv的feature2D接口集成了这种算法,名称为 GFTTDetector。
     * */
    Ptr<GFTTDetector> detector = GFTTDetector::create(500, 0.01, 20); // maximum 500 keypoints
    detector->detect(img1, kp1);

    // now lets track these key points in the second image
    //现在让我们在第二张图中跟踪这些关键点
    // first use single level LK in the validation picture
    //首先在验证图中使用单级LK
    vector<KeyPoint> kp2_single;
    vector<bool> success_single;
    OpticalFlowSingleLevel(img1, img2, kp1, kp2_single, success_single);

    // then test multi-level LK然后测试多级LK，多层光流
    vector<KeyPoint> kp2_multi;
    vector<bool> success_multi;
    chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
    OpticalFlowMultiLevel(img1, img2, kp1, kp2_multi, success_multi, true);
    chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
    auto time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
    cout << "optical flow by gauss-newton: " << time_used.count() << endl;

    // use opencv's flow for validation
    vector<Point2f> pt1, pt2;
    for (auto &kp: kp1) pt1.push_back(kp.pt);
    vector<uchar> status;
    vector<float> error;
    t1 = chrono::steady_clock::now();
    cv::calcOpticalFlowPyrLK(img1, img2, pt1, pt2, status, error);
    t2 = chrono::steady_clock::now();
    time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
    cout << "optical flow by opencv: " << time_used.count() << endl;

    // plot the differences of those functions
    Mat img2_single;
    cv::cvtColor(img2, img2_single, CV_GRAY2BGR);
    for (int i = 0; i < kp2_single.size(); i++) {
        if (success_single[i]) {
            cv::circle(img2_single, kp2_single[i].pt, 2, cv::Scalar(0, 250, 0), 2);
            cv::line(img2_single, kp1[i].pt, kp2_single[i].pt, cv::Scalar(0, 250, 0));
        }
    }

    Mat img2_multi;
    cv::cvtColor(img2, img2_multi, CV_GRAY2BGR);
    for (int i = 0; i < kp2_multi.size(); i++) {
        if (success_multi[i]) {
            cv::circle(img2_multi, kp2_multi[i].pt, 2, cv::Scalar(0, 250, 0), 2);
            cv::line(img2_multi, kp1[i].pt, kp2_multi[i].pt, cv::Scalar(0, 250, 0));
        }
    }

    Mat img2_CV;
    cv::cvtColor(img2, img2_CV, CV_GRAY2BGR);
    for (int i = 0; i < pt2.size(); i++) {
        if (status[i]) {
            cv::circle(img2_CV, pt2[i], 2, cv::Scalar(0, 250, 0), 2);
            cv::line(img2_CV, pt1[i], pt2[i], cv::Scalar(0, 250, 0));
        }
    }

    cv::imshow("tracked single level", img2_single);
    cv::imshow("tracked multi level", img2_multi);
    cv::imshow("tracked by opencv", img2_CV);
    cv::waitKey(0);

    return 0;
}

void OpticalFlowSingleLevel(
        const Mat &img1,
        const Mat &img2,
        const vector<KeyPoint> &kp1,
        vector<KeyPoint> &kp2,
        vector<bool> &success,
        bool inverse, bool has_initial)
{
    kp2.resize(kp1.size());
    success.resize(kp1.size());
    OpticalFlowTracker tracker(img1, img2, kp1, kp2, success, inverse, has_initial);
    //Range表示一个范围，即并行计算哪些需要追踪的点,kp1中存放的就是随机选的追踪点
    //bind是一个绑定函数，它相当于调用OpticalFlowTracker.calculateOpticalFlow()，
    //std::placeholders::_1是占位符，表示传入的参数是OpticalFlowTracker.calculateOpticalFlow()的第一个参数，
    // 此处Range(0, kp1.size())为传入的参数。

    parallel_for_(Range(0, kp1.size()),
                  std::bind(&OpticalFlowTracker::calculateOpticalFlow, &tracker, placeholders::_1));
}

void OpticalFlowTracker::calculateOpticalFlow(const Range &range) {
    // parameters
    int half_patch_size = 4;
    int iterations = 10;
    for (size_t i = range.start; i < range.end; i++) {
        auto kp = kp1[i];
        double dx = 0, dy = 0; // dx,dy need to be estimated
        if (has_initial) {
            dx = kp2[i].pt.x - kp.pt.x;
            dy = kp2[i].pt.y - kp.pt.y;
        }

        double cost = 0, lastCost = 0;
        bool succ = true; // indicate if this point succeeded指示这一点是否成功

        // Gauss-Newton iterations
        Eigen::Matrix2d H = Eigen::Matrix2d::Zero();    // hessian
        Eigen::Vector2d b = Eigen::Vector2d::Zero();    // bias
        Eigen::Vector2d J;  // jacobian
        for (int iter = 0; iter < iterations; iter++)
        {
            /*
             * 这里是采用反向（Inverse）光流法。
             * 在反向的光流法中，可以使用第一个图像的像素梯度代替第二个像素的梯度
             * 在反向光流法中，第一个图像的向素梯度是不变的，所以可以保留第一次迭代的结果，在后续的迭代中使用
             * 当雅可比不变时，H矩阵不变，每次迭代只需计算残差，可以节省一部分计算量
             */
            if (inverse == false) {//
                H = Eigen::Matrix2d::Zero();
                b = Eigen::Vector2d::Zero();
            } else {
                // only reset b
                b = Eigen::Vector2d::Zero();
            }

            cost = 0;

            // compute cost and jacobian
            for (int x = -half_patch_size; x < half_patch_size; x++)
                for (int y = -half_patch_size; y < half_patch_size; y++)
                {
                    double error = GetPixelValue(img1, kp.pt.x + x, kp.pt.y + y) -
                                   GetPixelValue(img2, kp.pt.x + x + dx, kp.pt.y + y + dy);;  // Jacobian
                    if (inverse == false) {
                        J = -1.0 * Eigen::Vector2d(//求解像素的导数
                                0.5 * (GetPixelValue(img2, kp.pt.x + dx + x + 1, kp.pt.y + dy + y) -
                                       GetPixelValue(img2, kp.pt.x + dx + x - 1, kp.pt.y + dy + y)),
                                0.5 * (GetPixelValue(img2, kp.pt.x + dx + x, kp.pt.y + dy + y + 1) -
                                       GetPixelValue(img2, kp.pt.x + dx + x, kp.pt.y + dy + y - 1))
                        );
                    } else if (iter == 0) {
                        // in inverse mode, J keeps same for all iterations
                        // NOTE this J does not change when dx, dy is updated, so we can store it and only compute error
                        J = -1.0 * Eigen::Vector2d(
                                0.5 * (GetPixelValue(img1, kp.pt.x + x + 1, kp.pt.y + y) -
                                       GetPixelValue(img1, kp.pt.x + x - 1, kp.pt.y + y)),
                                0.5 * (GetPixelValue(img1, kp.pt.x + x, kp.pt.y + y + 1) -
                                       GetPixelValue(img1, kp.pt.x + x, kp.pt.y + y - 1))
                        );
                    }
                    // compute H, b and set cost;
                    b += -error * J;
                    cost += error * error;
                    if (inverse == false || iter == 0) {
                        // also update H
                        H += J * J.transpose();
                    }
                }

            // compute update
            Eigen::Vector2d update = H.ldlt().solve(b);

            if (std::isnan(update[0])) {
                // sometimes occurred when we have a black or white patch and H is irreversible
                cout << "update is nan" << endl;
                succ = false;
                break;
            }

            if (iter > 0 && cost > lastCost) {
                break;
            }

            // update dx, dy
            dx += update[0];
            dy += update[1];
            lastCost = cost;
            succ = true;

            if (update.norm() < 1e-2) {
                // converge
                break;
            }
        }

        success[i] = succ;

        // set kp2
        kp2[i].pt = kp.pt + Point2f(dx, dy);
    }
}

void OpticalFlowMultiLevel(
        const Mat &img1,
        const Mat &img2,
        const vector<KeyPoint> &kp1,
        vector<KeyPoint> &kp2,
        vector<bool> &success,
        bool inverse) {

    // parameters
    int pyramids = 4;
    double pyramid_scale = 0.5;
    double scales[] = {1.0, 0.5, 0.25, 0.125};

    // create pyramids 创建金字塔图像
    chrono::steady_clock::time_point t1 = chrono::steady_clock::now();
    vector<Mat> pyr1, pyr2; // image pyramids
    for (int i = 0; i < pyramids; i++)
    {
        if (i == 0) {
            pyr1.push_back(img1);
            pyr2.push_back(img2);
        } else {
            Mat img1_pyr, img2_pyr;
            cv::resize(pyr1[i - 1], img1_pyr,
                       cv::Size(pyr1[i - 1].cols * pyramid_scale, pyr1[i - 1].rows * pyramid_scale));
            cv::resize(pyr2[i - 1], img2_pyr,
                       cv::Size(pyr2[i - 1].cols * pyramid_scale, pyr2[i - 1].rows * pyramid_scale));
            pyr1.push_back(img1_pyr);
            pyr2.push_back(img2_pyr);
        }
    }
    chrono::steady_clock::time_point t2 = chrono::steady_clock::now();
    auto time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
    cout << "build pyramid time: " << time_used.count() << endl;

    // coarse-to-fine LK tracking in pyramids从粗到细LK金字塔跟踪
    vector<KeyPoint> kp1_pyr, kp2_pyr;
    for (auto &kp:kp1)
    {
        auto kp_top = kp;
        kp_top.pt *= scales[pyramids - 1];
        kp1_pyr.push_back(kp_top);
        kp2_pyr.push_back(kp_top);
    }

    for (int level = pyramids - 1; level >= 0; level--) {
        // from coarse to fine
        success.clear();
        t1 = chrono::steady_clock::now();
        //调用单层的计算函数
        OpticalFlowSingleLevel(pyr1[level], pyr2[level], kp1_pyr, kp2_pyr, success, inverse, true);
        t2 = chrono::steady_clock::now();
        auto time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
        cout << "track pyr " << level << " cost time: " << time_used.count() << endl;

        if (level > 0) {
            for (auto &kp: kp1_pyr)
                kp.pt /= pyramid_scale;
            for (auto &kp: kp2_pyr)
                kp.pt /= pyramid_scale;
        }
    }

    for (auto &kp: kp2_pyr)
        kp2.push_back(kp);
}

2 CMakeLists.txt

cmake_minimum_required(VERSION 2.8)
project(optical_flow)

set(CMAKE_BUILD_TYPE "Release")
#add_definitions("-DENABLE_SSE")
#set(CMAKE_CXX_FLAGS "-std=c++11 ${SSE_FLAGS} -g -O3 -march=native")
set(CMAKE_CXX_STANDARD 14)
find_package(OpenCV 3 REQUIRED)

include_directories(
        ${OpenCV_INCLUDE_DIRS}
        "/usr/include/eigen3/"
)

add_executable(optical_flow src/optical_flow.cpp)
target_link_libraries(optical_flow ${OpenCV_LIBS})

3 输出结果

三.使用直接法

1 direct_method.cpp

#include 
#include 
#include 
#include 
#include 

using namespace std;

typedef vector<Eigen::Vector2d, Eigen::aligned_allocator<Eigen::Vector2d>> VecVector2d;

// Camera intrinsics
double fx = 718.856, fy = 718.856, cx = 607.1928, cy = 185.2157;
// baseline
double baseline = 0.573;//基线
// paths
string left_file = "../src/left.png";
string disparity_file = "../src/disparity.png";
boost::format fmt_others("../src/%06d.png");    // other files

// useful typedefs
typedef Eigen::Matrix<double, 6, 6> Matrix6d;
typedef Eigen::Matrix<double, 2, 6> Matrix26d;
typedef Eigen::Matrix<double, 6, 1> Vector6d;

/**
 * pose estimation using direct method
 * @param img1
 * @param img2
 * @param px_ref
 * @param depth_ref
 * @param T21
 */
void DirectPoseEstimationMultiLayer(
        const cv::Mat &img1,
        const cv::Mat &img2,
        const VecVector2d &px_ref,
        const vector<double> depth_ref,
        Sophus::SE3d &T21
);

/**
 * pose estimation using direct method
 * @param img1
 * @param img2
 * @param px_ref
 * @param depth_ref
 * @param T21
 */
void DirectPoseEstimationSingleLayer(
        const cv::Mat &img1,
        const cv::Mat &img2,
        const VecVector2d &px_ref,
        const vector<double> depth_ref,
        Sophus::SE3d &T21
);

// bilinear interpolation
inline float GetPixelValue(const cv::Mat &img, float x, float y) {
    // boundary check
    if (x < 0) x = 0;
    if (y < 0) y = 0;
    if (x >= img.cols) x = img.cols - 1;
    if (y >= img.rows) y = img.rows - 1;
    uchar *data = &img.data[int(y) * img.step + int(x)];
    float xx = x - floor(x);
    float yy = y - floor(y);
    return float(
            (1 - xx) * (1 - yy) * data[0] +
            xx * (1 - yy) * data[1] +
            (1 - xx) * yy * data[img.step] +
            xx * yy * data[img.step + 1]
    );
}

/// class for accumulator jacobians in parallel并行累加器雅可比矩阵的类
class JacobianAccumulator: public cv::ParallelLoopBody {
private:
    const cv::Mat &img1;
    const cv::Mat &img2;
    const VecVector2d &px_ref;
    const vector<double> depth_ref;
    Sophus::SE3d &T21;
    mutable VecVector2d projection; // projected points

    mutable std::mutex hessian_mutex;
    mutable Matrix6d H = Matrix6d::Zero();
    mutable Vector6d b = Vector6d::Zero();
    mutable double cost = 0;

public:
    JacobianAccumulator(
            const cv::Mat &img1_,
            const cv::Mat &img2_,
            const VecVector2d &px_ref_,
            const vector<double> depth_ref_,
            Sophus::SE3d &T21_) :
            img1(img1_), img2(img2_), px_ref(px_ref_), depth_ref(depth_ref_), T21(T21_)
            {
        projection = VecVector2d(px_ref.size(), Eigen::Vector2d(0, 0));
    }

    /// accumulate jacobians in a range在一个范围内累加雅可比矩阵
//    void accumulate_jacobian(const cv::Range &range);


    /// get hessian matrix
    Matrix6d hessian() const { return H; }

    /// get bias
    Vector6d bias() const { return b; }

    /// get total cost
    double cost_func() const { return cost; }

    /// get projected points
    VecVector2d projected_points() const { return projection; }

    /// reset h, b, cost to zero
    void reset() {
        H = Matrix6d::Zero();
        b = Vector6d::Zero();
        cost = 0;
    }

    virtual void operator()(const cv::Range& range) const {

        // parameters
        const int half_patch_size = 1;
        int cnt_good = 0;
        Matrix6d hessian = Matrix6d::Zero();
        Vector6d bias = Vector6d::Zero();
        double cost_tmp = 0;

        for (size_t i = range.start; i < range.end; i++)
        {

            // compute the projection in the second image计算第二幅图像中的投影
            Eigen::Vector3d point_ref =
                    depth_ref[i] * Eigen::Vector3d((px_ref[i][0] - cx) / fx, (px_ref[i][1] - cy) / fy, 1);
            Eigen::Vector3d point_cur = T21 * point_ref;
            if (point_cur[2] < 0)   // depth invalid
                continue;

            float u = fx * point_cur[0] / point_cur[2] + cx, v = fy * point_cur[1] / point_cur[2] + cy;
            if (u < half_patch_size || u > img2.cols - half_patch_size || v < half_patch_size ||
                v > img2.rows - half_patch_size)
                continue;

            projection[i] = Eigen::Vector2d(u, v);
            double X = point_cur[0], Y = point_cur[1], Z = point_cur[2],
                    Z2 = Z * Z, Z_inv = 1.0 / Z, Z2_inv = Z_inv * Z_inv;
            cnt_good++;

            // and compute error and jacobian
            for (int x = -half_patch_size; x <= half_patch_size; x++)
                for (int y = -half_patch_size; y <= half_patch_size; y++) {

                    double error = GetPixelValue(img1, px_ref[i][0] + x, px_ref[i][1] + y) -
                                   GetPixelValue(img2, u + x, v + y);
                    Matrix26d J_pixel_xi;
                    Eigen::Vector2d J_img_pixel;

                    J_pixel_xi(0, 0) = fx * Z_inv;
                    J_pixel_xi(0, 1) = 0;
                    J_pixel_xi(0, 2) = -fx * X * Z2_inv;
                    J_pixel_xi(0, 3) = -fx * X * Y * Z2_inv;
                    J_pixel_xi(0, 4) = fx + fx * X * X * Z2_inv;
                    J_pixel_xi(0, 5) = -fx * Y * Z_inv;

                    J_pixel_xi(1, 0) = 0;
                    J_pixel_xi(1, 1) = fy * Z_inv;
                    J_pixel_xi(1, 2) = -fy * Y * Z2_inv;
                    J_pixel_xi(1, 3) = -fy - fy * Y * Y * Z2_inv;
                    J_pixel_xi(1, 4) = fy * X * Y * Z2_inv;
                    J_pixel_xi(1, 5) = fy * X * Z_inv;

                    J_img_pixel = Eigen::Vector2d(
                            0.5 * (GetPixelValue(img2, u + 1 + x, v + y) - GetPixelValue(img2, u - 1 + x, v + y)),
                            0.5 * (GetPixelValue(img2, u + x, v + 1 + y) - GetPixelValue(img2, u + x, v - 1 + y))
                    );

                    // total jacobian
                    Vector6d J = -1.0 * (J_img_pixel.transpose() * J_pixel_xi).transpose();

                    hessian += J * J.transpose();
                    bias += -error * J;
                    cost_tmp += error * error;
                }
        }

        if (cnt_good)
        {
            // set hessian, bias and cost
            unique_lock<mutex> lck(hessian_mutex);
            H += hessian;
            b += bias;
            cost += cost_tmp / cnt_good;
        }
    }


};



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

    cv::Mat left_img = cv::imread(left_file, 0);
    cv::Mat disparity_img = cv::imread(disparity_file, 0);
    if (left_img.empty() || disparity_img.empty())
    {
        std::cout << "!!! Failed imread(): image not found" << std::endl;
        return 1;
    }
    // let's randomly pick pixels in the first image and generate some 3d points in the first image's frame
    //让我们在第一个图像中随机选取像素，并在第一个图像的帧中生成一些3d点
    cv::RNG rng;
    int nPoints = 2000;
    int boarder = 20;
    VecVector2d pixels_ref;
    vector<double> depth_ref;
    cout << "left_img.cols" << left_img.cols << endl;
    //cout << "left_img: " << left_img << endl;
    // generate pixels in ref and load depth data在ref和加载深度数据中生成像素
    for (int i = 0; i < nPoints; i++)
    {
        int x = rng.uniform(boarder, left_img.cols - boarder);  // don't pick pixels close to boarder不要选择靠近边框的像素
        int y = rng.uniform(boarder, left_img.rows - boarder);  // don't pick pixels close to boarder
        int disparity = disparity_img.at<uchar>(y, x);
        double depth = fx * baseline / disparity; // you know this is disparity to depth 这是深度差  p104
        depth_ref.push_back(depth);
        pixels_ref.push_back(Eigen::Vector2d(x, y));
    }

    // estimates 01~05.png's pose using this information 利用这些信息估计01~05.png的姿势
    Sophus::SE3d T_cur_ref_multi;


    for (int i = 1; i < 6; i++) {  // 1~10
        cv::Mat img = cv::imread((fmt_others % i).str(), 0);
        // try single layer by uncomment this line 尝试取消这行注释的单层
        // DirectPoseEstimationSingleLayer(left_img, img, pixels_ref, depth_ref, T_cur_ref);
        DirectPoseEstimationMultiLayer(left_img, img, pixels_ref, depth_ref, T_cur_ref_multi);
    }

    /*
    //单层直接法
    Sophus::SE3d T_cur_ref_single;
    for (int i = 1; i < 6; i++) {  // 1~10
        cv::Mat img = cv::imread((fmt_others % i).str(), 0);
        // try single layer by uncomment this line 尝试取消这行注释的单层
        DirectPoseEstimationSingleLayer(left_img, img, pixels_ref, depth_ref, T_cur_ref_single);
        //DirectPoseEstimationMultiLayer(left_img, img, pixels_ref, depth_ref, T_cur_ref_multi);
    }
    */
    return 0;
}

void DirectPoseEstimationSingleLayer(
        const cv::Mat &img1,
        const cv::Mat &img2,
        const VecVector2d &px_ref,
        const vector<double> depth_ref,
        Sophus::SE3d &T21) {

    const int iterations = 10;
    double cost = 0, lastCost = 0;
    auto t1 = chrono::steady_clock::now();
    JacobianAccumulator jaco_accu(img1, img2, px_ref, depth_ref, T21);

    for (int iter = 0; iter < iterations; iter++)
    {
        jaco_accu.reset();
        cv::parallel_for_(cv::Range(0, px_ref.size()), jaco_accu);
        Matrix6d H = jaco_accu.hessian();
        Vector6d b = jaco_accu.bias();

        // solve update and put it into estimation 解决更新，并将其放入估计
        Vector6d update = H.ldlt().solve(b);;
        T21 = Sophus::SE3d::exp(update) * T21;
        cost = jaco_accu.cost_func();

        if (std::isnan(update[0])) {
            // sometimes occurred when we have a black or white patch and H is irreversible
            cout << "update is nan" << endl;
            break;
        }
        if (iter > 0 && cost > lastCost) {
            cout << "cost increased: " << cost << ", " << lastCost << endl;
            break;
        }
        if (update.norm() < 1e-3) {
            // converge
            break;
        }

        lastCost = cost;
        cout << "iteration: " << iter << ", cost: " << cost << endl;
    }

    cout << "T21 = \n" << T21.matrix() << endl;
    auto t2 = chrono::steady_clock::now();
    auto time_used = chrono::duration_cast<chrono::duration<double>>(t2 - t1);
    cout << "direct method for single layer: " << time_used.count() << endl;

    // plot the projected pixels here
    cv::Mat img2_show;
    cv::cvtColor(img2, img2_show, CV_GRAY2BGR);
    VecVector2d projection = jaco_accu.projected_points();
    for (size_t i = 0; i < px_ref.size(); ++i) {
        auto p_ref = px_ref[i];
        auto p_cur = projection[i];
        if (p_cur[0] > 0 && p_cur[1] > 0) {
            cv::circle(img2_show, cv::Point2f(p_cur[0], p_cur[1]), 2, cv::Scalar(0, 250, 0), 2);
            cv::line(img2_show, cv::Point2f(p_ref[0], p_ref[1]), cv::Point2f(p_cur[0], p_cur[1]),
                     cv::Scalar(0, 250, 0));
        }
    }
    cv::imshow("current", img2_show);
    cv::waitKey();
}


void DirectPoseEstimationMultiLayer(
        const cv::Mat &img1,
        const cv::Mat &img2,
        const VecVector2d &px_ref,
        const vector<double> depth_ref,
        Sophus::SE3d &T21) {

    // parameters
    int pyramids = 4;
    double pyramid_scale = 0.5;
    double scales[] = {1.0, 0.5, 0.25, 0.125};

    // create pyramids
    vector<cv::Mat> pyr1, pyr2; // image pyramids
    for (int i = 0; i < pyramids; i++) {
        if (i == 0) {
            pyr1.push_back(img1);
            pyr2.push_back(img2);
        } else {
            cv::Mat img1_pyr, img2_pyr;
            cv::resize(pyr1[i - 1], img1_pyr,
                       cv::Size(pyr1[i - 1].cols * pyramid_scale, pyr1[i - 1].rows * pyramid_scale));
            cv::resize(pyr2[i - 1], img2_pyr,
                       cv::Size(pyr2[i - 1].cols * pyramid_scale, pyr2[i - 1].rows * pyramid_scale));
            pyr1.push_back(img1_pyr);
            pyr2.push_back(img2_pyr);
        }
    }

    double fxG = fx, fyG = fy, cxG = cx, cyG = cy;  // backup the old values
    for (int level = pyramids - 1; level >= 0; level--)
    {
        VecVector2d px_ref_pyr; // set the keypoints in this pyramid level 设置这个金字塔级别的关键点
        for (auto &px: px_ref)
        {
            px_ref_pyr.push_back(scales[level] * px);
        }

        // scale fx, fy, cx, cy in different pyramid levels 将fx, fy, cx, cy在不同的金字塔层次上进行缩放
        fx = fxG * scales[level];
        fy = fyG * scales[level];
        cx = cxG * scales[level];
        cy = cyG * scales[level];
        DirectPoseEstimationSingleLayer(pyr1[level], pyr2[level], px_ref_pyr, depth_ref, T21);
    }

}

2 CMakeLists

cmake_minimum_required(VERSION 2.8)
project(direct_method)

set(CMAKE_BUILD_TYPE "Release")
add_definitions("-DENABLE_SSE")
set(CMAKE_CXX_STANDARD 14 )

find_package(OpenCV 3 REQUIRED)
find_package(Sophus REQUIRED)
find_package(Pangolin REQUIRED)

include_directories(
        ${OpenCV_INCLUDE_DIRS}
        ${Sophus_INCLUDE_DIRS}
        "/usr/include/eigen3/"
        ${Pangolin_INCLUDE_DIRS}
)

add_executable(direct_method src/direct_method.cpp)
target_link_libraries(direct_method
        ${OpenCV_LIBS}
        ${Pangolin_LIBRARIES}
        ${Sophus_LIBRARIES} fmt
        )