从 2 张图像进行 3D 重建，无需有关相机的信息

Question

我是这个领域的新手，我正在尝试在 2D 图像中的 3D 中建模一个简单的场景，但我没有任何有关相机的信息。我知道有3个选项：

• 我有两张图像，并且我知道我从 XML 加载的相机型号（内部），例如 loadXMLFromFile() => stereoRectify() =>; reprojectImageTo3D()

• 我没有它们，但我可以校准我的相机=> stereoCalibrate() =>; stereoRectify() =>; reprojectImageTo3D()

• 我无法校准相机（这是我的情况，因为我没有拍摄两张图像的相机，那么我需要在两张图片上找到成对的关键点例如，使用 SURF、SIFT 处理图像（我实际上可以使用任何斑点检测器），然后计算这些关键点的描述符，然后根据它们的描述符匹配图像右侧和图像左侧的关键点，然后从中找到基本矩阵进行处理。更难，就像这样：

  1. 检测关键点（SURF、SIFT）=>
  2. 提取描述符（SURF、SIFT）=>
  3. 比较和匹配描述符（BruteForce、基于 Flann 的方法）=>
  4. 从这些对中找到基本垫（findFundamentalMat()）=>
  5. stereoRectifyUncaliblated() =>;
  6. reprojectImageTo3D()

我正在使用最后一种方法和我的问题是：

1）是吗？

2）如果可以的话，我对最后一步stereoRectifyUncaliberated() =>有疑问reprojectImageTo3D()。 reprojectImageTo3D() 函数的签名为：

void reprojectImageTo3D(InputArray disparity, OutputArray _3dImage, InputArray Q, bool handleMissingValues=false, int depth=-1 )

cv::reprojectImageTo3D(imgDisparity8U, xyz, Q, true) (in my code)

参数：

• disparity – 输入单通道 8 位无符号、16 位有符号、32 位有符号或 32 位浮点点视差图像。
• _3dImage – 输出与视差大小相同的 3 通道浮点图像。 _3dImage(x,y) 的每个元素都包含根据视差图计算出的点 (x,y) 的 3D 坐标。
• Q – 4x4 透视变换矩阵，可以通过 stereoRectify() 获得。
• handleMissingValues – 指示函数是否应处理缺失值（即未计算差异的点）。如果handleMissingValues=true，则与异常值相对应的具有最小视差的像素（请参阅StereoBM::operator()）将转换为具有非常大的 Z 值的 3D 点（当前设置为 10000）。
• ddepth – 可选的输出数组深度。如果为 -1，输出图像将具有 CV_32F 深度。 ddepth 还可以设置为 CV_16S、CV_32S 或 `CV_32F'。

如何获得Q矩阵？是否可以用F、H1和H2或其他方式获得Q矩阵？

3）是否有另一种方法可以在不校准相机的情况下获得xyz坐标？

我的代码是：

#include <opencv2/core/core.hpp>
#include <opencv2/calib3d/calib3d.hpp>
#include <opencv2/imgproc/imgproc.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/contrib/contrib.hpp>
#include <opencv2/features2d/features2d.hpp>
#include <stdio.h>
#include <iostream>
#include <vector>
#include <conio.h>
#include <opencv/cv.h>
#include <opencv/cxcore.h>
#include <opencv/cvaux.h>


using namespace cv;
using namespace std;

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

    // Read the images
    Mat imgLeft = imread( argv[1], CV_LOAD_IMAGE_GRAYSCALE );
    Mat imgRight = imread( argv[2], CV_LOAD_IMAGE_GRAYSCALE );

    // check
    if (!imgLeft.data || !imgRight.data)
            return 0;

    // 1] find pair keypoints on both images (SURF, SIFT):::::::::::::::::::::::::::::

    // vector of keypoints
    std::vector<cv::KeyPoint> keypointsLeft;
    std::vector<cv::KeyPoint> keypointsRight;

    // Construct the SURF feature detector object
    cv::SiftFeatureDetector sift(
            0.01, // feature threshold
            10); // threshold to reduce
                // sensitivity to lines
                // Detect the SURF features

    // Detection of the SIFT features
    sift.detect(imgLeft,keypointsLeft);
    sift.detect(imgRight,keypointsRight);

    std::cout << "Number of SURF points (1): " << keypointsLeft.size() << std::endl;
    std::cout << "Number of SURF points (2): " << keypointsRight.size() << std::endl;

    // 2] compute descriptors of these keypoints (SURF,SIFT) ::::::::::::::::::::::::::

    // Construction of the SURF descriptor extractor
    cv::SurfDescriptorExtractor surfDesc;

    // Extraction of the SURF descriptors
    cv::Mat descriptorsLeft, descriptorsRight;
    surfDesc.compute(imgLeft,keypointsLeft,descriptorsLeft);
    surfDesc.compute(imgRight,keypointsRight,descriptorsRight);

    std::cout << "descriptor matrix size: " << descriptorsLeft.rows << " by " << descriptorsLeft.cols << std::endl;

    // 3] matching keypoints from image right and image left according to their descriptors (BruteForce, Flann based approaches)

    // Construction of the matcher
    cv::BruteForceMatcher<cv::L2<float> > matcher;

    // Match the two image descriptors
    std::vector<cv::DMatch> matches;
    matcher.match(descriptorsLeft,descriptorsRight, matches);

    std::cout << "Number of matched points: " << matches.size() << std::endl;


    // 4] find the fundamental mat ::::::::::::::::::::::::::::::::::::::::::::::::::::

    // Convert 1 vector of keypoints into
    // 2 vectors of Point2f for compute F matrix
    // with cv::findFundamentalMat() function
    std::vector<int> pointIndexesLeft;
    std::vector<int> pointIndexesRight;
    for (std::vector<cv::DMatch>::const_iterator it= matches.begin(); it!= matches.end(); ++it) {

         // Get the indexes of the selected matched keypoints
         pointIndexesLeft.push_back(it->queryIdx);
         pointIndexesRight.push_back(it->trainIdx);
    }

    // Convert keypoints into Point2f
    std::vector<cv::Point2f> selPointsLeft, selPointsRight;
    cv::KeyPoint::convert(keypointsLeft,selPointsLeft,pointIndexesLeft);
    cv::KeyPoint::convert(keypointsRight,selPointsRight,pointIndexesRight);

    /* check by drawing the points
    std::vector<cv::Point2f>::const_iterator it= selPointsLeft.begin();
    while (it!=selPointsLeft.end()) {

            // draw a circle at each corner location
            cv::circle(imgLeft,*it,3,cv::Scalar(255,255,255),2);
            ++it;
    }

    it= selPointsRight.begin();
    while (it!=selPointsRight.end()) {

            // draw a circle at each corner location
            cv::circle(imgRight,*it,3,cv::Scalar(255,255,255),2);
            ++it;
    } */

    // Compute F matrix from n>=8 matches
    cv::Mat fundemental= cv::findFundamentalMat(
            cv::Mat(selPointsLeft), // points in first image
            cv::Mat(selPointsRight), // points in second image
            CV_FM_RANSAC);       // 8-point method

    std::cout << "F-Matrix size= " << fundemental.rows << "," << fundemental.cols << std::endl;

    /* draw the left points corresponding epipolar lines in right image
    std::vector<cv::Vec3f> linesLeft;
    cv::computeCorrespondEpilines(
            cv::Mat(selPointsLeft), // image points
            1,                      // in image 1 (can also be 2)
            fundemental,            // F matrix
            linesLeft);             // vector of epipolar lines

    // for all epipolar lines
    for (vector<cv::Vec3f>::const_iterator it= linesLeft.begin(); it!=linesLeft.end(); ++it) {

        // draw the epipolar line between first and last column
        cv::line(imgRight,cv::Point(0,-(*it)[2]/(*it)[1]),cv::Point(imgRight.cols,-((*it)[2]+(*it)[0]*imgRight.cols)/(*it)[1]),cv::Scalar(255,255,255));
    }

    // draw the left points corresponding epipolar lines in left image
    std::vector<cv::Vec3f> linesRight;
    cv::computeCorrespondEpilines(cv::Mat(selPointsRight),2,fundemental,linesRight);
    for (vector<cv::Vec3f>::const_iterator it= linesRight.begin(); it!=linesRight.end(); ++it) {

        // draw the epipolar line between first and last column
        cv::line(imgLeft,cv::Point(0,-(*it)[2]/(*it)[1]), cv::Point(imgLeft.cols,-((*it)[2]+(*it)[0]*imgLeft.cols)/(*it)[1]), cv::Scalar(255,255,255));
    }

    // Display the images with points and epipolar lines
    cv::namedWindow("Right Image Epilines");
    cv::imshow("Right Image Epilines",imgRight);
    cv::namedWindow("Left Image Epilines");
    cv::imshow("Left Image Epilines",imgLeft);
    */

    // 5] stereoRectifyUncalibrated()::::::::::::::::::::::::::::::::::::::::::::::::::

    //H1, H2 – The output rectification homography matrices for the first and for the second images.
    cv::Mat H1(4,4, imgRight.type());
    cv::Mat H2(4,4, imgRight.type());
    cv::stereoRectifyUncalibrated(selPointsRight, selPointsLeft, fundemental, imgRight.size(), H1, H2);


    // create the image in which we will save our disparities
    Mat imgDisparity16S = Mat( imgLeft.rows, imgLeft.cols, CV_16S );
    Mat imgDisparity8U = Mat( imgLeft.rows, imgLeft.cols, CV_8UC1 );

    // Call the constructor for StereoBM
    int ndisparities = 16*5;      // < Range of disparity >
    int SADWindowSize = 5;        // < Size of the block window > Must be odd. Is the 
                                  // size of averaging window used to match pixel  
                                  // blocks(larger values mean better robustness to
                                  // noise, but yield blurry disparity maps)

    StereoBM sbm( StereoBM::BASIC_PRESET,
        ndisparities,
        SADWindowSize );

    // Calculate the disparity image
    sbm( imgLeft, imgRight, imgDisparity16S, CV_16S );

    // Check its extreme values
    double minVal; double maxVal;

    minMaxLoc( imgDisparity16S, &minVal, &maxVal );

    printf("Min disp: %f Max value: %f \n", minVal, maxVal);

    // Display it as a CV_8UC1 image
    imgDisparity16S.convertTo( imgDisparity8U, CV_8UC1, 255/(maxVal - minVal));

    namedWindow( "windowDisparity", CV_WINDOW_NORMAL );
    imshow( "windowDisparity", imgDisparity8U );


    // 6] reprojectImageTo3D() :::::::::::::::::::::::::::::::::::::::::::::::::::::

    //Mat xyz;
    //cv::reprojectImageTo3D(imgDisparity8U, xyz, Q, true);

    //How can I get the Q matrix? Is possibile to obtain the Q matrix with 
    //F, H1 and H2 or in another way?
    //Is there another way for obtain the xyz coordinates?

    cv::waitKey();
    return 0;
}

Answer 1

StereoRectifyUncaliblated 仅计算平面透视变换，而不是对象空间中的校正变换。有必要将此平面变换转换为物体空间变换以提取 Q 矩阵，并且我认为它需要一些相机校准参数（例如相机内在函数）。该主题可能正在进行一些研究课题。

您可能添加了一些步骤来估计相机内在参数，并提取相机的相对方向，以使您的流程正常工作。我认为，如果没有使用主动照明方法，相机校准参数对于提取场景的正确 3D 结构至关重要。

此外，还需要基于束块调整的解决方案来将所有估计值细化为更准确的值。

Answer 2

1. 这个过程对我来说看起来不错。

2. 据我所知，对于基于图像的3D建模，相机是显式校准或隐式校准的。您不想明确校准相机。无论如何你都会利用这些东西。匹配对应点对绝对是一种常用的方法。

Answer 3

我认为你需要使用 StereoRectify 来校正你的图像并获得 Q。
该函数需要两个参数（R 和 T）来表示两个相机之间的旋转和平移。
因此您可以使用solvePnP 计算参数。该函数需要某些物体的3D真实坐标和图像中的2D点及其对应点