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在初中物理课堂上，我们可能都见过一个蜡烛投影实验：在一个暗箱的前方放着一支点燃的蜡烛，蜡烛的光透过暗箱上的一个小孔投影在暗箱的后方平面上，并在这个平面上形成一个倒立的蜡
烛图像。在这个过程中，小孔模型能够把三维世界中的蜡烛投影到一个二维成像平面。同理，我们可以用这个简单的模型来解释相机的成像过程

 

 

 

 

 

我们可以把一个世界坐标点先转换到相机坐标系，再除掉它最后一维的数值（即该点距离相机成像平面的深度），这相当于把最后一维进行归一化处理，得到点 P 在相机归一化平面上的投影：

归一化坐标可看成相机前方`z = 1 处的平面上的一个点，这个 z = 1 平面也称为归一化平面。归一化坐标再左乘内参就得到了像素坐标，所以我们可以把像素坐标 [u; v]^T 看成对归一化平面上的点进
行量化测量的结果。从这个模型中也可以看出，如果对相机坐标同时乘以任意非零常数，归一化坐标都是一样的，这说明点的深度在投影过程中被丢失了，所以单目视觉中没法得到像素点的深度值。

 

 

//
// Created by Qian.
//

#include <opencv2/opencv.hpp>
#include <string>

using namespace std;

string image_file = "../test.png";   // 请确保路径正确

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

    // 本程序需要你自己实现去畸变部分的代码。尽管我们可以调用OpenCV的去畸变，但自己实现一遍有助于理解。
    // 畸变参数
    double k1 = -0.28340811, k2 = 0.07395907, p1 = 0.00019359, p2 = 1.76187114e-05;
    // 内参
    double fx = 458.654, fy = 457.296, cx = 367.215, cy = 248.375;

    cv::Mat image = cv::imread(image_file,CV_8UC1);   // 图像是灰度图，CV_8UC1
    int rows = image.rows, cols = image.cols;
    cv::Mat image_undistort = cv::Mat(rows, cols, CV_8UC1);   // 去畸变以后的图

    // 计算去畸变后图像的内容
    for (int v = 0; v < rows; v++)
        for (int u = 0; u < cols; u++) {

            double u_distorted = 0, v_distorted = 0;
            // TODO 按照公式，计算点(u,v)对应到畸变图像中的坐标(u_distorted, v_distorted) (~6 lines)
            // start your code here
            //首先转化成归一化坐标
            double x=(u-cx)/fx;
            double y=(v-cy)/fy;
            double r2=x*x+y*y;

            double x_distorted = x * (1 + k1 * r2 + k2 * r2 * r2)+2*p1*x*y+p2*(r2+2*x*x);
            double y_distorted= y * (1 + k1 * r2 + k2 * r2 * r2)+p1*(r2+2*y*y)+2*p2*x*y;
//            double x_distorted = x * (1 + k1 * r2 + k2 * r2 * r2);
//            double y_distorted= y * (1 + k1 * r2 + k2 * r2 * r2);

            //还原为像素坐标
            u_distorted = fx * x_distorted + cx;
            v_distorted = fy * y_distorted + cy;
            // end your code here

            // 赋值 (最近邻插值)
            if (u_distorted >= 0 && v_distorted >= 0 && u_distorted < cols && v_distorted < rows) {
                image_undistort.at<uchar>(v, u) = image.at<uchar>((int) v_distorted, (int) u_distorted);
            } else {
                image_undistort.at<uchar>(v, u) = 0;
            }
        }

    // 画图去畸变后图像
    cv::imshow("image undistorted", image_undistort);
    cv::waitKey();
}

    return 0;
}

 

 

 

 双目视觉

#include <opencv2/opencv.hpp>
#include <vector>
#include <string>
#include <Eigen/Core>
#include <pangolin/pangolin.h>
#include <unistd.h>

using namespace std;
using namespace Eigen;

// 文件路径
string left_file = "/home/qian/slambook2/ch5/stereo/left.png";
string right_file = "/home/qian/slambook2/ch5/stereo/right.png";

// 在pangolin中画图，已写好，无需调整
void showPointCloud(
    const vector<Vector4d, Eigen::aligned_allocator<Vector4d>> &pointcloud); //使用eigen库中的变量Vector、matrix等时需要这样写

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

    // 内参
    double fx = 718.856, fy = 718.856, cx = 607.1928, cy = 185.2157;
    // 基线
    double b = 0.573;

    // 读取图像
    cv::Mat left = cv::imread(left_file, 0);
    cv::Mat right = cv::imread(right_file, 0);
    cv::Ptr<cv::StereoSGBM> sgbm = cv::StereoSGBM::create(
        0, 96, 9, 8 * 9 * 9, 32 * 9 * 9, 1, 63, 10, 100, 32);    // 神奇的参数
    cv::Mat disparity_sgbm, disparity;
    sgbm->compute(left, right, disparity_sgbm);
    disparity_sgbm.convertTo(disparity, CV_32F, 1.0 / 16.0f);

    // 生成点云
    vector<Vector4d, Eigen::aligned_allocator<Vector4d>> pointcloud;

    // 如果你的机器慢，请把后面的v++和u++改成v+=2, u+=2
    for (int v = 0; v < left.rows; v++)
        for (int u = 0; u < left.cols; u++) {
            if (disparity.at<float>(v, u) <= 0.0 || disparity.at<float>(v, u) >= 96.0) continue;

            Vector4d point(0, 0, 0, left.at<uchar>(v, u) / 255.0); // 前三维为xyz,第四维为颜色

            // 根据双目模型计算 point 的位置
            double x = (u - cx) / fx;
            double y = (v - cy) / fy;
            double depth = fx * b / (disparity.at<float>(v, u));
            point[0] = x * depth;
            point[1] = y * depth;
            point[2] = depth;

            pointcloud.push_back(point);
        }

    cv::imshow("disparity", disparity / 96.0);
    cv::waitKey(0);
    // 画出点云
    showPointCloud(pointcloud);
    return 0;
}

void showPointCloud(const vector<Vector4d, Eigen::aligned_allocator<Vector4d>> &pointcloud) {

    if (pointcloud.empty()) {
        cerr << "Point cloud is empty!" << endl;
        return;
    }

    pangolin::CreateWindowAndBind("Point Cloud Viewer", 1024, 768);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

    pangolin::OpenGlRenderState s_cam(
        pangolin::ProjectionMatrix(1024, 768, 500, 500, 512, 389, 0.1, 1000),
        pangolin::ModelViewLookAt(0, -0.1, -1.8, 0, 0, 0, 0.0, -1.0, 0.0)
    );

    pangolin::View &d_cam = pangolin::CreateDisplay()
        .SetBounds(0.0, 1.0, pangolin::Attach::Pix(175), 1.0, -1024.0f / 768.0f)
        .SetHandler(new pangolin::Handler3D(s_cam));

    while (pangolin::ShouldQuit() == false) {
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        d_cam.Activate(s_cam);
        glClearColor(1.0f, 1.0f, 1.0f, 1.0f);

        glPointSize(2);
        glBegin(GL_POINTS);
        for (auto &p: pointcloud) {
            glColor3f(p[3], p[3], p[3]);
            glVertex3d(p[0], p[1], p[2]);
        }
        glEnd();
        pangolin::FinishFrame();
        usleep(5000);   // sleep 5 ms
    }
    return;
}

深度摄像头点云拼接

#include <iostream>
#include <fstream>
#include <opencv2/opencv.hpp>
#include <boost/format.hpp>  // for formating strings
#include <sophus/se3.hpp>
#include <pangolin/pangolin.h>

using namespace std;
typedef vector<Sophus::SE3d, Eigen::aligned_allocator<Sophus::SE3d>> TrajectoryType;
typedef Eigen::Matrix<double, 6, 1> Vector6d;

// 在pangolin中画图，已写好，无需调整
void showPointCloud(
    const vector<Vector6d, Eigen::aligned_allocator<Vector6d>> &pointcloud);

int main(int argc, char **argv) {
    vector<cv::Mat> colorImgs, depthImgs;    // 彩色图和深度图
    TrajectoryType poses;         // 相机位姿

    ifstream fin("./pose.txt");
    if (!fin) {
        cerr << "请在有pose.txt的目录下运行此程序" << endl;
        return 1;
    }

    for (int i = 0; i < 5; i++) {
        boost::format fmt("./%s/%d.%s"); //图像文件格式
        colorImgs.push_back(cv::imread((fmt % "color" % (i + 1) % "png").str()));
        depthImgs.push_back(cv::imread((fmt % "depth" % (i + 1) % "pgm").str(), -1)); // 使用-1读取原始图像

        double data[7] = {0};
        for (auto &d:data)
            fin >> d;
        Sophus::SE3d pose(Eigen::Quaterniond(data[6], data[3], data[4], data[5]),
                          Eigen::Vector3d(data[0], data[1], data[2]));
        poses.push_back(pose);
    }

    // 计算点云并拼接
    // 相机内参 
    double cx = 325.5;
    double cy = 253.5;
    double fx = 518.0;
    double fy = 519.0;
    double depthScale = 1000.0;
    vector<Vector6d, Eigen::aligned_allocator<Vector6d>> pointcloud;
    pointcloud.reserve(1000000);

    for (int i = 0; i < 5; i++) {
        cout << "转换图像中: " << i + 1 << endl;
        cv::Mat color = colorImgs[i];
        cv::Mat depth = depthImgs[i];
        Sophus::SE3d T = poses[i];
        for (int v = 0; v < color.rows; v++)
            for (int u = 0; u < color.cols; u++) {
                unsigned int d = depth.ptr<unsigned short>(v)[u]; // 深度值
                if (d == 0) continue; // 为0表示没有测量到
                Eigen::Vector3d point;
                point[2] = double(d) / depthScale;
                point[0] = (u - cx) * point[2] / fx;
                point[1] = (v - cy) * point[2] / fy;
                Eigen::Vector3d pointWorld = T * point;

                Vector6d p;
                p.head<3>() = pointWorld;
                p[5] = color.data[v * color.step + u * color.channels()];   // blue
                p[4] = color.data[v * color.step + u * color.channels() + 1]; // green
                p[3] = color.data[v * color.step + u * color.channels() + 2]; // red
                pointcloud.push_back(p);
            }
    }

    cout << "点云共有" << pointcloud.size() << "个点." << endl;
    showPointCloud(pointcloud);
    return 0;
}

void showPointCloud(const vector<Vector6d, Eigen::aligned_allocator<Vector6d>> &pointcloud) {

    if (pointcloud.empty()) {
        cerr << "Point cloud is empty!" << endl;
        return;
    }

    pangolin::CreateWindowAndBind("Point Cloud Viewer", 1024, 768);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_BLEND);
    glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);

    pangolin::OpenGlRenderState s_cam(
        pangolin::ProjectionMatrix(1024, 768, 500, 500, 512, 389, 0.1, 1000),
        pangolin::ModelViewLookAt(0, -0.1, -1.8, 0, 0, 0, 0.0, -1.0, 0.0)
    );

    pangolin::View &d_cam = pangolin::CreateDisplay()
        .SetBounds(0.0, 1.0, pangolin::Attach::Pix(175), 1.0, -1024.0f / 768.0f)
        .SetHandler(new pangolin::Handler3D(s_cam));

    while (pangolin::ShouldQuit() == false) {
        glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

        d_cam.Activate(s_cam);
        glClearColor(1.0f, 1.0f, 1.0f, 1.0f);

        glPointSize(2);
        glBegin(GL_POINTS);
        for (auto &p: pointcloud) {
            glColor3d(p[3] / 255.0, p[4] / 255.0, p[5] / 255.0);
            glVertex3d(p[0], p[1], p[2]);
        }
        glEnd();
        pangolin::FinishFrame();
        usleep(5000);   // sleep 5 ms
    }
    return;
}