c++ - OpenCV >>摄像机相对姿态估计

环境

使用3DS Max生成的3D场景

摄像机视场为45度

使用同一相机以800x600分辨率

渲染两个图像

摄像机Z旋转== 0度的图像A

摄像机Z旋转== 25度的图像B

8个对应点(手动驱动)，没有异常

手头的任务

解析图像A和图像B(上图)之间的相对相机姿态，以期望导致Z轴旋转25度

实现

选项A:

手动生成信函，以确保没有异常值(请参见下面的代码段，请参见“rotZ0”和“rotZ25”)

根据this link，使用图像分辨率和FOV得出像素分辨率的相机焦距

由图像分辨率和相机FOV构成的相机固有矩阵(根据this link)组成

基本矩阵是使用'cv::findFundamentalMat'得出的

基本矩阵由相机固有矩阵'K'和基本矩阵'F'组成(根据this link)，其方式如下:'Kt()* F * K'*其中'Kt()'是固有矩阵转置。

在基本矩阵'matE'上执行SVD

解决4种可能的解决方案:[U * W * Vt]，[U * Wt()* Vt]，[U * Wt()* Vt.t()]和[U * W * Vt.t()]

选项B:

手动生成信函，以确保没有异常值(请参见“rotZ0”和“rotZ25”)

Essential Matrix使用'cv::findEssentialMat'

组成

使用'cv::recoverPose'

估计相机姿势


结果

以上两个选项均无法正确恢复相机的相对姿态(预计Z轴旋转25度)

我究竟做错了什么？相机的相对姿势如何正确解决？

任何帮助，将不胜感激。

完整代码

#define RAD2DEG(rad) (((rad) * 180)/M_PI)
#define DEG2RAD(deg) (((deg) * M_PI)/180)
#define FOV2FOCAL(pixelssensorsize, fov) ((pixelssensorsize) / (2 * tan((fov) / 2)))// http://books.google.co.il/books?id=bXzAlkODwa8C&pg=PA48&lpg=PA48&dq=expressing+focal+length+in+pixels&source=bl&ots=gY4972kxAC&sig=U1BUeNHhOHmYIrDrO0YDb1DrNng&hl=en&sa=X&ei=45dLU9u9DIyv7QbN2oGIDA&ved=0CGsQ6AEwCA#v=onepage&q=expressing%20focal%20length%20in%20pixels&f=false

// http://nghiaho.com/?page_id=846
void DecomposeRotation(IN const cv::Mat& R, OUT float& fX, OUT float& fY, OUT float& fZ) {// Taken from MatLab
    fX = (float)atan2(R.at<double>(2, 1), R.at<double>(2, 2));
    fY = (float)atan2(-R.at<double>(2, 0), sqrt(R.at<double>(2, 1)*R.at<double>(2, 1) + R.at<double>(2, 2)*R.at<double>(2, 2)));
    fZ = (float)atan2(R.at<double>(1, 0), R.at<double>(0, 0));
}

int _tmain(int argc, _TCHAR* argv[])
{
    // 25 deg rotation in the Z axis (800x600)
    const cv::Point2f rotZ0[] = { { 109, 250 }, { 175, 266 }, { 204, 279 }, { 221, 253 }, { 324, 281 }, { 312, 319 }, { 328, 352 }, { 322, 365 } };
    const cv::Point2f rotZ25[] = { { 510, 234 }, { 569, 622 }, { 593, 278 }, { 616, 257 }, { 716, 303 }, { 698, 340 }, { 707, 377 }, { 697, 390 } };
    const cv::Point2f rotZminus15[] = { { 37, 260 }, { 106, 275 }, { 135, 286 }, { 152, 260 }, { 258, 284 }, { 248, 324 }, { 266, 356 }, { 260, 370 } };


    const double        dFOV = DEG2RAD(45);
    const cv::Point2d   res(800, 600);
    const cv::Point2d   pntPriciplePoint(res.x / 2, res.y / 2);
    const cv::Point2d   pntFocal(FOV2FOCAL(res.x, dFOV), FOV2FOCAL(res.y, dFOV));

    //transfer the vector of points to the appropriate opencv matrix structures
    const int                numPoints = sizeof(rotZ0) / sizeof(rotZ0[0]);
    std::vector<cv::Point2f> vecPnt1(numPoints);
    std::vector<cv::Point2f> vecPnt2(numPoints);

    for (int i = 0; i < numPoints; i++) {
        vecPnt2[i] = rotZ0[i];
        //vecPnt2[i] = rotZminus15[i];
        vecPnt1[i] = rotZ25[i];
    }

    //// Normalize points
    //for (int i = 0; i < numPoints; i++) {
    //  vecPnt1[i].x = (vecPnt1[i].x - pntPriciplePoint.x) / pntFocal.x;
    //  vecPnt1[i].y = (vecPnt1[i].y - pntPriciplePoint.y) / pntFocal.y;

    //  vecPnt2[i].x = (vecPnt2[i].x - pntPriciplePoint.x) / pntFocal.x;
    //  vecPnt2[i].y = (vecPnt2[i].y - pntPriciplePoint.y) / pntFocal.y;
    //}

    try {
        // http://docs.opencv.org/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
        cv::Mat matK = cv::Mat::zeros(3, 3, CV_64F);
        matK.at<double>(0, 0) = pntFocal.x;
        matK.at<double>(1, 1) = pntFocal.y;
        matK.at<double>(0, 2) = pntPriciplePoint.x;
        matK.at<double>(1, 2) = pntPriciplePoint.y;
        matK.at<double>(2, 2) = 1;

        float x, y, z;
        cv::Mat R1, R2, R3, R4;
        cv::Mat t;
        cv::Mat matE;

#if 1 // Option [A]
        cv::Mat matF = cv::findFundamentalMat(vecPnt1, vecPnt2);
        matE = matK.t() * matF * matK; // http://en.wikipedia.org/wiki/Essential_matrix

        cv::Mat _tmp;
        cv::Mat U;
        cv::Mat Vt;

        cv::SVD::compute(matE, _tmp, U, Vt);

        cv::Matx33d W(0, -1, 0,
                      1,  0, 0,
                      0,  0, 1);

        R1 = U*cv::Mat(W)*Vt; // See http://stackoverflow.com/questions/14150152/extract-translation-and-rotation-from-fundamental-matrix for details
        R2 = U*cv::Mat(W)*Vt.t();
        R3 = U*cv::Mat(W).t()*Vt;
        R4 = U*cv::Mat(W).t()*Vt.t();
#else // Option [B]
        matE = cv::findEssentialMat(vecPnt1, vecPnt2, pntFocal.x, pntPriciplePoint);// http://docs.opencv.org/trunk/modules/calib3d/doc/camera_calibration_and_3d_reconstruction.html
        cv::decomposeEssentialMat(matE, R1, R2, t);
        int iInliers = cv::recoverPose(matE, vecPnt1, vecPnt2, R4, t);// , pntFocal.x, pntPriciplePoint);
        R3 = cv::Mat::zeros(3, 3, CV_64F);
#endif

        DecomposeRotation(R1, x, y, z);
        std::cout << "Euler Angles R1 (X,Y,Z): " << RAD2DEG(x) << ", " << RAD2DEG(y) << ", " << RAD2DEG(z) << std::endl;
        DecomposeRotation(R2, x, y, z);
        std::cout << "             R2 (X,Y,Z): " << RAD2DEG(x) << ", " << RAD2DEG(y) << ", " << RAD2DEG(z) << std::endl;
        DecomposeRotation(R3, x, y, z);
        std::cout << "             R3 (X,Y,Z): " << RAD2DEG(x) << ", " << RAD2DEG(y) << ", " << RAD2DEG(z) << std::endl;
        DecomposeRotation(R4, x, y, z);
        std::cout << "             R4 (X,Y,Z): " << RAD2DEG(x) << ", " << RAD2DEG(y) << ", " << RAD2DEG(z) << std::endl;

        //cv::Mat res = matFrom.t() * matF * matTo;// Results in a null vector ( as it should ) http://en.wikipedia.org/wiki/Fundamental_matrix_(computer_vision)
        //res = matFrom.t() * matE * matTo;// Results in a null vector ( as it should )
    }
    catch (cv::Exception e) {
        _ASSERT(FALSE);
    }
    return 0;
}

执行结果

选项A:

Euler Angles R1 (X,Y,Z): -26.2625, 8.70029, 163.643
             R2 (X,Y,Z): 16.6929, -29.9901, -3.81642
             R3 (X,Y,Z): 5.59033, -20.841, -19.9316
             R4 (X,Y,Z): -5.76906, 7.25413, -179.086

选项B:

Euler Angles R1 (X,Y,Z): -13.8355, 3.0098, 171.451
             R2 (X,Y,Z): 2.22802, -22.3479, -11.332
             R3 (X,Y,Z): 0, -0, 0
             R4 (X,Y,Z): 2.22802, -22.3479, -11.332

最佳答案

首先，请校准相机，而不要使用预定义的值。它总是会产生很大的影响。
由8点或5点计算出的相对姿势会受到很大的干扰，决不是暗示最后一个词。话虽如此，重建点然后 bundle 调整整个场景将是一个好主意。优化您的外在性，您应该提出一个更好的姿势。

关于c++ - OpenCV >>摄像机相对姿态估计，我们在Stack Overflow上找到一个类似的问题：https://stackoverflow.com/questions/23114047/