OpenCV相机标定函数calibrateCamera无法收敛到正确的解决方案（投影仪标定）。

Question

OpenCV相机标定函数calibrateCamera无法收敛到正确的解决方案（投影仪标定）。

3

我正在尝试使用cv::calibrateCamera对相机+投影仪系统进行校准。虽然有时它似乎有效，但在许多情况下，估计的解决方案与正确的解决方案相差甚远。

以下是一个代码示例，显示了该问题（包括所有数据 - 因此它非常大）。

#include <opencv2/core/core.hpp>
#include <opencv2/calib3d/calib3d.hpp>

#include <iostream>
#include <vector>

cv::Mat calculateTransformation(cv::Mat translationVec, cv::Mat rotationVec) {
    cv::Mat rotationMat3x3;
    cv::Rodrigues(rotationVec, rotationMat3x3);
    cv::Mat rotationMat = cv::Mat::eye(4, 4, CV_64F);
    rotationMat3x3.copyTo(rotationMat(cv::Rect(0, 0, 3, 3)));

    cv::Mat translationMat = cv::Mat::eye(4, 4, CV_64F);
    translationVec.copyTo(translationMat(cv::Rect(3, 0, 1, 3)));

    return translationMat * rotationMat;
}

int main() {
    std::vector<cv::Point2f> image_points;
    std::vector<cv::Point3f> object_points;

    image_points.push_back(cv::Point2f(400.0f, 940.0f));
    image_points.push_back(cv::Point2f(480.0f, 940.0f));
    image_points.push_back(cv::Point2f(560.0f, 940.0f));
    image_points.push_back(cv::Point2f(640.0f, 940.0f));
    image_points.push_back(cv::Point2f(720.0f, 940.0f));
    image_points.push_back(cv::Point2f(800.0f, 940.0f));
    image_points.push_back(cv::Point2f(880.0f, 940.0f));
    image_points.push_back(cv::Point2f(960.0f, 940.0f));
    image_points.push_back(cv::Point2f(1040.0f, 940.0f));
    image_points.push_back(cv::Point2f(1120.0f, 940.0f));
    image_points.push_back(cv::Point2f(1200.0f, 940.0f));
    image_points.push_back(cv::Point2f(1280.0f, 940.0f));
    image_points.push_back(cv::Point2f(400.0f, 860.0f));
    image_points.push_back(cv::Point2f(480.0f, 860.0f));
    image_points.push_back(cv::Point2f(560.0f, 860.0f));
    image_points.push_back(cv::Point2f(640.0f, 860.0f));
    image_points.push_back(cv::Point2f(720.0f, 860.0f));
    image_points.push_back(cv::Point2f(800.0f, 860.0f));
    image_points.push_back(cv::Point2f(880.0f, 860.0f));
    image_points.push_back(cv::Point2f(960.0f, 860.0f));
    image_points.push_back(cv::Point2f(1040.0f, 860.0f));
    image_points.push_back(cv::Point2f(1120.0f, 860.0f));
    image_points.push_back(cv::Point2f(1200.0f, 860.0f));
    image_points.push_back(cv::Point2f(1280.0f, 860.0f));
    image_points.push_back(cv::Point2f(400.0f, 780.0f));
    image_points.push_back(cv::Point2f(480.0f, 780.0f));
    image_points.push_back(cv::Point2f(560.0f, 780.0f));
    image_points.push_back(cv::Point2f(640.0f, 780.0f));
    image_points.push_back(cv::Point2f(720.0f, 780.0f));
    image_points.push_back(cv::Point2f(800.0f, 780.0f));
    image_points.push_back(cv::Point2f(880.0f, 780.0f));
    image_points.push_back(cv::Point2f(960.0f, 780.0f));
    image_points.push_back(cv::Point2f(1040.0f, 780.0f));
    image_points.push_back(cv::Point2f(1120.0f, 780.0f));
    image_points.push_back(cv::Point2f(1200.0f, 780.0f));
    image_points.push_back(cv::Point2f(1280.0f, 780.0f));
    image_points.push_back(cv::Point2f(400.0f, 700.0f));
    image_points.push_back(cv::Point2f(480.0f, 700.0f));
    image_points.push_back(cv::Point2f(560.0f, 700.0f));
    image_points.push_back(cv::Point2f(640.0f, 700.0f));
    image_points.push_back(cv::Point2f(720.0f, 700.0f));
    image_points.push_back(cv::Point2f(800.0f, 700.0f));
    image_points.push_back(cv::Point2f(880.0f, 700.0f));
    image_points.push_back(cv::Point2f(960.0f, 700.0f));
    image_points.push_back(cv::Point2f(1040.0f, 700.0f));
    image_points.push_back(cv::Point2f(1120.0f, 700.0f));
    image_points.push_back(cv::Point2f(1200.0f, 700.0f));
    image_points.push_back(cv::Point2f(1280.0f, 700.0f));
    image_points.push_back(cv::Point2f(400.0f, 620.0f));
    image_points.push_back(cv::Point2f(480.0f, 620.0f));
    image_points.push_back(cv::Point2f(560.0f, 620.0f));
    image_points.push_back(cv::Point2f(640.0f, 620.0f));
    image_points.push_back(cv::Point2f(720.0f, 620.0f));
    image_points.push_back(cv::Point2f(800.0f, 620.0f));
    image_points.push_back(cv::Point2f(880.0f, 620.0f));
    image_points.push_back(cv::Point2f(960.0f, 620.0f));
    image_points.push_back(cv::Point2f(1120.0f, 620.0f));
    image_points.push_back(cv::Point2f(1040.0f, 620.0f));
    image_points.push_back(cv::Point2f(1200.0f, 620.0f));
    image_points.push_back(cv::Point2f(1280.0f, 620.0f));
    image_points.push_back(cv::Point2f(400.0f, 540.0f));
    image_points.push_back(cv::Point2f(480.0f, 540.0f));
    image_points.push_back(cv::Point2f(560.0f, 540.0f));
    image_points.push_back(cv::Point2f(640.0f, 540.0f));
    image_points.push_back(cv::Point2f(720.0f, 540.0f));
    image_points.push_back(cv::Point2f(800.0f, 540.0f));
    image_points.push_back(cv::Point2f(880.0f, 540.0f));
    image_points.push_back(cv::Point2f(1200.0f, 540.0f));
    image_points.push_back(cv::Point2f(1120.0f, 540.0f));
    image_points.push_back(cv::Point2f(480.0f, 460.0f));
    image_points.push_back(cv::Point2f(400.0f, 460.0f));
    image_points.push_back(cv::Point2f(560.0f, 460.0f));
    image_points.push_back(cv::Point2f(720.0f, 460.0f));
    image_points.push_back(cv::Point2f(640.0f, 460.0f));
    image_points.push_back(cv::Point2f(800.0f, 460.0f));
    image_points.push_back(cv::Point2f(1120.0f, 460.0f));
    image_points.push_back(cv::Point2f(880.0f, 460.0f));
    image_points.push_back(cv::Point2f(1040.0f, 460.0f));
    image_points.push_back(cv::Point2f(1280.0f, 460.0f));
    image_points.push_back(cv::Point2f(1120.0f, 380.0f));
    image_points.push_back(cv::Point2f(1280.0f, 380.0f));
    image_points.push_back(cv::Point2f(1200.0f, 380.0f));
    image_points.push_back(cv::Point2f(1040.0f, 380.0f));
    image_points.push_back(cv::Point2f(880.0f, 380.0f));
    image_points.push_back(cv::Point2f(800.0f, 380.0f));
    image_points.push_back(cv::Point2f(960.0f, 380.0f));
    image_points.push_back(cv::Point2f(640.0f, 380.0f));
    image_points.push_back(cv::Point2f(720.0f, 380.0f));
    image_points.push_back(cv::Point2f(560.0f, 380.0f));
    image_points.push_back(cv::Point2f(400.0f, 380.0f));
    image_points.push_back(cv::Point2f(480.0f, 380.0f));
    image_points.push_back(cv::Point2f(1120.0f, 300.0f));
    image_points.push_back(cv::Point2f(1040.0f, 300.0f));
    image_points.push_back(cv::Point2f(960.0f, 300.0f));
    image_points.push_back(cv::Point2f(880.0f, 300.0f));
    image_points.push_back(cv::Point2f(800.0f, 300.0f));
    image_points.push_back(cv::Point2f(720.0f, 300.0f));
    image_points.push_back(cv::Point2f(640.0f, 300.0f));
    image_points.push_back(cv::Point2f(560.0f, 300.0f));
    image_points.push_back(cv::Point2f(480.0f, 300.0f));
    image_points.push_back(cv::Point2f(400.0f, 300.0f));
    image_points.push_back(cv::Point2f(1280.0f, 220.0f));
    image_points.push_back(cv::Point2f(1200.0f, 220.0f));
    image_points.push_back(cv::Point2f(1120.0f, 220.0f));
    image_points.push_back(cv::Point2f(1040.0f, 220.0f));
    image_points.push_back(cv::Point2f(960.0f, 220.0f));
    image_points.push_back(cv::Point2f(800.0f, 220.0f));
    image_points.push_back(cv::Point2f(720.0f, 220.0f));
    image_points.push_back(cv::Point2f(640.0f, 220.0f));
    image_points.push_back(cv::Point2f(560.0f, 220.0f));
    image_points.push_back(cv::Point2f(480.0f, 220.0f));
    image_points.push_back(cv::Point2f(400.0f, 220.0f));
    image_points.push_back(cv::Point2f(1280.0f, 140.0f));
    image_points.push_back(cv::Point2f(1200.0f, 140.0f));
    image_points.push_back(cv::Point2f(1040.0f, 140.0f));
    image_points.push_back(cv::Point2f(960.0f, 140.0f));
    image_points.push_back(cv::Point2f(800.0f, 140.0f));
    image_points.push_back(cv::Point2f(720.0f, 140.0f));
    image_points.push_back(cv::Point2f(640.0f, 140.0f));
    image_points.push_back(cv::Point2f(560.0f, 140.0f));
    image_points.push_back(cv::Point2f(480.0f, 140.0f));
    image_points.push_back(cv::Point2f(400.0f, 140.0f));
    image_points.push_back(cv::Point2f(960.0f, 540.0f));
    image_points.push_back(cv::Point2f(1040.0f, 540.0f));
    image_points.push_back(cv::Point2f(960.0f, 460.0f));

    object_points.push_back(cv::Point3f(-0.0671159000000000f, -0.0530089000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0572335000000000f, -0.0531021000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0473920000000000f, -0.0531268000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0375422000000000f, -0.0531293000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0277093000000000f, -0.0532232000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0179416000000000f, -0.0532900000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00818986000000000f, -0.0533080000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00159555000000000f, -0.0533734000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0113126000000000f, -0.0534102000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0210113000000000f, -0.0534688000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0307716000000000f, -0.0535300000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0404079000000000f, -0.0535600000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0668703000000000f, -0.0429498000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0569997000000000f, -0.0430325000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0471452000000000f, -0.0430930000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0373059000000000f, -0.0431530000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0274813000000000f, -0.0432117000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0176713000000000f, -0.0432687000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00790218000000000f, -0.0433224000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00190183000000000f, -0.0433762000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0116116000000000f, -0.0434242000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0213028000000000f, -0.0434700000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0310283000000000f, -0.0435404000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0406556000000000f, -0.0436058000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0666877000000000f, -0.0329366000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0568031000000000f, -0.0329860000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0469101000000000f, -0.0330818000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0370300000000000f, -0.0331543000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0272122000000000f, -0.0332004000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0173840000000000f, -0.0332688000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00759575000000000f, -0.0333343000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00215042000000000f, -0.0334201000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0119054000000000f, -0.0334816000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0215901000000000f, -0.0335390000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0313087000000000f, -0.0336208000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0409288000000000f, -0.0336740000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0664698000000000f, -0.0228786000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0565702000000000f, -0.0229386000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0466851000000000f, -0.0230437000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0367625000000000f, -0.0230813000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0269267000000000f, -0.0231839000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0171296000000000f, -0.0232845000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00732099000000000f, -0.0232912000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00244503000000000f, -0.0234120000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0121943000000000f, -0.0235079000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0218997000000000f, -0.0235779000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0316661000000000f, -0.0236490000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0413080000000000f, -0.0237153000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0662403000000000f, -0.0127937000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0563243000000000f, -0.0128856000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0464450000000000f, -0.0129539000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0365046000000000f, -0.0130461000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0266992000000000f, -0.0131572000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0168820000000000f, -0.0132217000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00702858000000000f, -0.0133096000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00273311000000000f, -0.0134175000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0222048000000000f, -0.0135829000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0124779000000000f, -0.0135008000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0319668000000000f, -0.0136414000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0416578000000000f, -0.0137210000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0660230000000000f, -0.00272328000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0560886000000000f, -0.00280125000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0461911000000000f, -0.00292352000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0362558000000000f, -0.00302379000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0264298000000000f, -0.00309841000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0165924000000000f, -0.00321897000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00674314000000000f, -0.00331641000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0322628000000000f, -0.00369330000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0225310000000000f, -0.00360024000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0558388000000000f, 0.00733873000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0657448000000000f, 0.00744612000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0458967000000000f, 0.00723106000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0261183000000000f, 0.00701760000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0359654000000000f, 0.00710082000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0162843000000000f, 0.00688856000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0228789000000000f, 0.00646718000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00641300000000000f, 0.00678188000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0131059000000000f, 0.00657206000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0422672000000000f, 0.00628497000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0231953000000000f, 0.0165035000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0425539000000000f, 0.0162757000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0328968000000000f, 0.0163892000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0133982000000000f, 0.0166424000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00611577000000000f, 0.0168486000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0160094000000000f, 0.0169642000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00368791000000000f, 0.0167334000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0357336000000000f, 0.0171710000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0258655000000000f, 0.0170562000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0456858000000000f, 0.0173090000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0655273000000000f, 0.0175171000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0555765000000000f, 0.0174012000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0235599000000000f, 0.0266047000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0137369000000000f, 0.0267060000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00400251000000000f, 0.0268771000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.00579988000000000f, 0.0269546000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0156666000000000f, 0.0270784000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0255455000000000f, 0.0272245000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0354855000000000f, 0.0273244000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0454115000000000f, 0.0274243000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0553239000000000f, 0.0275921000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0652735000000000f, 0.0276931000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0432836000000000f, 0.0364607000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0335970000000000f, 0.0365698000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0239205000000000f, 0.0367035000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0140970000000000f, 0.0368368000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00436217000000000f, 0.0369936000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0152808000000000f, 0.0372578000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0252343000000000f, 0.0373656000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0351242000000000f, 0.0374961000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0450986000000000f, 0.0376261000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0550835000000000f, 0.0377566000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0649853000000000f, 0.0379110000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0436747000000000f, 0.0466393000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0339311000000000f, 0.0467559000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0144269000000000f, 0.0470150000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00466523000000000f, 0.0471564000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0150279000000000f, 0.0474823000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0248820000000000f, 0.0475522000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0348463000000000f, 0.0476901000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0447968000000000f, 0.0478509000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0547835000000000f, 0.0479670000000000f, 0.0f));
    object_points.push_back(cv::Point3f(-0.0647592000000000f, 0.0481078000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00301477000000000f, -0.00341146000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.0128075000000000f, -0.00350684000000000f, 0.0f));
    object_points.push_back(cv::Point3f(0.00336785000000000f, 0.00670002000000000f, 0.0f));

    std::vector<std::vector<cv::Point2f>> all_image_points;
    all_image_points.push_back(image_points);
    std::vector<std::vector<cv::Point3f>> all_object_points;
    all_object_points.push_back(object_points);

    cv::Mat camera_mat = cv::Mat::eye(3, 3, CV_64F);
    cv::Mat dist_coeffs = cv::Mat::zeros(4, 1, CV_64F);
    std::vector<cv::Mat> rvecs;
    std::vector<cv::Mat> tvecs;

    double reprojection_error = cv::calibrateCamera(all_object_points, all_image_points, cv::Size(1920, 1080), camera_mat, dist_coeffs, rvecs, tvecs);
    std::cout << "Reprojection error: " << reprojection_error << std::endl;

    cv::Mat transformation = calculateTransformation(tvecs.front(), rvecs.front());
    cv::Mat origin = cv::Mat::zeros(4, 1, CV_64F);
    origin.at<double>(3, 0) = 1.0;
    std::cout << "distance to board: " << cv::norm(transformation * origin) << std::endl;

    return 0;
}

物体点的测量单位是米
板子距离应该大约为0.64米(估计为1.7米)
径向畸变参数k2的值高于200，有点奇怪
我使用matlab可视化了我的输入数据以验证对应关系是否正确
我知道用多个采集获得更强健的解决方案，但发布的数据似乎对解决方案产生了很大影响。我进行了两次捕捉，得到了一个正确的解决方案，添加了另一个捕捉（发布的数据），导致了错误的解决方案。
我猜数据比常规校准数据要更嘈杂，因为我不能直接捕捉数据（它是投影机校准），但需要使用检测投射的图案的相机

如果有人想使用matlab可视化数据：我简单地使用了

plot3([image_points(1,:);object_points(1,:) * 10000], [image_points(2,:);object_points(2,:) * -10000], [zeros(1, 125); ones(1, 125)], 'b-')

因此，每个对象和图像点之间的对应关系都将获得一行。

如果需要更多信息，请发布评论。

- Daniel

2

所以你有时候能得到正确的参数吗？你试过用一个猜测来初始化相机矩阵并使用CV_CALIB_USE_INTRINSIC_GUESS吗？我过去在Matlab相机标定工具箱中也取得了更多的成功，也许可以将结果与那里得到的进行比较。 - Sean

有时我会得到正确的参数（内参和外参）。在我的实际实现中，我使用initCameraMatrix2D作为初始猜测-这似乎在某些情况下有所改善，但仍然经常发生。我还尝试将其行为与Matlab校准工具箱进行比较，但无法弄清楚如何直接输入我的对应关系（如果您能给我一个提示，那也太棒了）。 - Daniel

"所以你有时候会获得正确的参数？" - 经过思考后：我有时候会在不同的数据下获得正确的参数 - 希望这样不那么模棱两可。 - Daniel

1

如果我理解正确的话，您正在尝试仅使用一个支架（一个表面）来校准相机？如果是这样，恐怕您需要至少两个非平面表面及其投影才能成功进行校准。从理论上讲，一个支架是不够的。因此，问题不在于点数（例如您的示例中的125个点），而在于使用不同的视角。离题了：+1，因为该示例可以直接粘贴到Visual Studio中以测试该问题。 - marol

@marol：感谢您的评论。实际上，这是我正在考虑的一件事情——有一个明确的答案是很好的。但我仍然想知道为什么当我试图从不同的距离捕捉图案时，校准没有起作用。由于景深，我只能将其移动约10厘米。我猜更多的移动会带来更好的结果？我一定会在周一尝试并给您反馈——如果这解决了问题，您也可以将其发布为答案，以便我接受它。 - Daniel

1个回答

网页内容由stack overflow 提供, 点击上面的

可以查看英文原文，
原文链接

- marol · Accepted Answer

我的建议是在相机校准过程中使用不同的非共面装置（表面）。OpenCV算法肯定需要至少两个不同视角才能进行良好的校准。如果可能的话，请提供几个具有不同角度的视角（2只是一个起点，10是理想的）。我现在不确定百分之百，但我认为非平面要求是必要条件，也就是说，你不能通过共面视图获得良好的结果（因为实际上它们仅根据比例因子不同，因此从某种意义上说，我们可以说它们在投影几何方面是同构的）。

对于投影误差的一个评论-在测试的情况下约为0.65，这似乎是准确的...但这里有一个棘手的部分-因为我们仅使用一个装置来校准相机，所以按定义，当OpenCV重新投影点时，它只有一个表面可以重新投影到。换句话说，校准误差很小，仅因存在给出点的投影的噪声而大于零。