没有相机信息的 2 张图像的 3D 重建

Question

我是这个领域的新手，我正在尝试用 2d 图像在 3d 中建模一个简单的场景，但我没有任何关于相机的信息。我知道有3 options：

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

• 我没有，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 2 张​​图像的相机，那么我需要使用 SURF，SIFT 在两张图像上找到对关键点（我可以实际使用任何blob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右图和左图的关键点，然后从中找到基本矩阵。处理要困难得多，会是这样的：

  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. stereoRectifyUncalibrated() =>
  6. reprojectImageTo3D()

我正在使用最后一种方法，我的问题是：

1) 对吗？

2) 如果没问题，我对最后一步有疑问stereoRectifyUncalibrated() => reprojectImageTo3D()。 reprojectImageTo3D()函数的签名是：

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 位浮点视差图像。
• _3dImage – 输出与disparity 大小相同的三通道浮点图像。 _3dImage(x,y) 的每个元素都包含根据视差图计算得出的点 (x,y) 的 3D 坐标。
• Q – 可以使用stereoRectify() 获得的 4x4 透视变换矩阵。
• 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 Z 值（当前设置为 10000）的 3D 点。
• ddepth – 可选的输出数组深度。如果为 -1，则输出图像将具有CV_32F 深度。 ddepth 也可以设置为 CV_16S、CV_32S 或 `CV_32F'。

如何获得Q 矩阵？是否可以通过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

StereoRectifyUncalibrated 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对象空间变换以提取 Q 矩阵，我认为它需要一些相机校准参数（如相机内在函数）。可能有一些与该主题相关的研究课题。

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

还需要基于捆绑块调整的解决方案来将所有估计值精炼为更准确的值。

Answer 2

1. 我觉得这个过程没问题。

2. 据我所知，关于基于图像的 3D 建模，相机是经过显式校准或隐式校准的。您不想明确校准相机。无论如何，您都会使用这些东西。匹配对应点对绝对是一种被大量使用的方法。

Answer 3

我认为您需要使用 StereoRectify 来纠正您的图像并获得 Q。 这个函数需要两个参数（R 和 T）两个相机之间的旋转和平移。 因此，您可以使用solvePnP 计算参数。这个函数需要某个物体的一些3d真实坐标和图像中的2d点及其对应点