OpenCV："camera calibrate" 为什么非平面校准平台需要初始猜测？

Question

根据 OpenCV 文档，“对于非平面校准装置，必须指定初始内在矩阵”的原因在于“内在参数的初始化”

OPENCV：校准相机（）latest-doc：

Currently, initialization of intrinsic parameters (when CALIB_USE_INTRINSIC_GUESS is not set) is only implemented for planar calibration patterns (where Z-coordinates of the object points must be all zeros). 3D calibration rigs can also be used as long as initial cameraMatrix is provided.

“内部参数初始化”中发生了什么？为什么 3D 钻机不能（或很难）？

初始猜测对相机校准的影响有多大？

Answer 1

根据opencv源代码，cvInitIntrinsicParams2D使用消失点和单应性来估计焦距。单应性仅适用于平面场景。由于失真等原因，它仍然会有错误。也许你可以将你的 3D 校准图案映射到平面上？我不知道初始猜测的质量对于校准过程的其余部分有多重要。

可能，如果 3D 装备中有清晰的 2D 平面（例如，大量点的相同 z 坐标），则可以很容易地调整算法以首先从 3D 装备中提取 2D 平面。如果您能够提取这样的平面但无法调整代码：使用高级 intrinsicGuess 函数，它在 API 中公开，并将猜测的内在矩阵输入到您的校准中。

这是源代码，在 modules/calib3d/src/calibration.cpp (opencv 4.5.2) 中可用：

    CV_IMPL void cvInitIntrinsicParams2D( const CvMat* objectPoints,
                         const CvMat* imagePoints, const CvMat* npoints,
                         CvSize imageSize, CvMat* cameraMatrix,
                         double aspectRatio )
{
    Ptr<CvMat> matA, _b, _allH;

    int i, j, pos, nimages, ni = 0;
    double a[9] = { 0, 0, 0, 0, 0, 0, 0, 0, 1 };
    double H[9] = {0}, f[2] = {0};
    CvMat _a = cvMat( 3, 3, CV_64F, a );
    CvMat matH = cvMat( 3, 3, CV_64F, H );
    CvMat _f = cvMat( 2, 1, CV_64F, f );

    CV_Assert(npoints);
    CV_Assert(CV_MAT_TYPE(npoints->type) == CV_32SC1);
    CV_Assert(CV_IS_MAT_CONT(npoints->type));
    nimages = npoints->rows + npoints->cols - 1;

    if( (CV_MAT_TYPE(objectPoints->type) != CV_32FC3 &&
        CV_MAT_TYPE(objectPoints->type) != CV_64FC3) ||
        (CV_MAT_TYPE(imagePoints->type) != CV_32FC2 &&
        CV_MAT_TYPE(imagePoints->type) != CV_64FC2) )
        CV_Error( CV_StsUnsupportedFormat, "Both object points and image points must be 2D" );

    if( objectPoints->rows != 1 || imagePoints->rows != 1 )
        CV_Error( CV_StsBadSize, "object points and image points must be a single-row matrices" );

    matA.reset(cvCreateMat( 2*nimages, 2, CV_64F ));
    _b.reset(cvCreateMat( 2*nimages, 1, CV_64F ));
    a[2] = (!imageSize.width) ? 0.5 : (imageSize.width - 1)*0.5;
    a[5] = (!imageSize.height) ? 0.5 : (imageSize.height - 1)*0.5;
    _allH.reset(cvCreateMat( nimages, 9, CV_64F ));

    // extract vanishing points in order to obtain initial value for the focal length
    for( i = 0, pos = 0; i < nimages; i++, pos += ni )
    {
        CV_DbgAssert(npoints->data.i);
        CV_DbgAssert(matA && matA->data.db);
        CV_DbgAssert(_b && _b->data.db);
        double* Ap = matA->data.db + i*4;
        double* bp = _b->data.db + i*2;
        ni = npoints->data.i[i];
        double h[3], v[3], d1[3], d2[3];
        double n[4] = {0,0,0,0};
        CvMat _m, matM;
        cvGetCols( objectPoints, &matM, pos, pos + ni );
        cvGetCols( imagePoints, &_m, pos, pos + ni );

        cvFindHomography( &matM, &_m, &matH );
        CV_DbgAssert(_allH && _allH->data.db);
        memcpy( _allH->data.db + i*9, H, sizeof(H) );

        H[0] -= H[6]*a[2]; H[1] -= H[7]*a[2]; H[2] -= H[8]*a[2];
        H[3] -= H[6]*a[5]; H[4] -= H[7]*a[5]; H[5] -= H[8]*a[5];

        for( j = 0; j < 3; j++ )
        {
            double t0 = H[j*3], t1 = H[j*3+1];
            h[j] = t0; v[j] = t1;
            d1[j] = (t0 + t1)*0.5;
            d2[j] = (t0 - t1)*0.5;
            n[0] += t0*t0; n[1] += t1*t1;
            n[2] += d1[j]*d1[j]; n[3] += d2[j]*d2[j];
        }

        for( j = 0; j < 4; j++ )
            n[j] = 1./std::sqrt(n[j]);

        for( j = 0; j < 3; j++ )
        {
            h[j] *= n[0]; v[j] *= n[1];
            d1[j] *= n[2]; d2[j] *= n[3];
        }

        Ap[0] = h[0]*v[0]; Ap[1] = h[1]*v[1];
        Ap[2] = d1[0]*d2[0]; Ap[3] = d1[1]*d2[1];
        bp[0] = -h[2]*v[2]; bp[1] = -d1[2]*d2[2];
    }

    cvSolve( matA, _b, &_f, CV_NORMAL + CV_SVD );
    a[0] = std::sqrt(fabs(1./f[0]));
    a[4] = std::sqrt(fabs(1./f[1]));
    if( aspectRatio != 0 )
    {
        double tf = (a[0] + a[4])/(aspectRatio + 1.);
        a[0] = aspectRatio*tf;
        a[4] = tf;
    }

    cvConvert( &_a, cameraMatrix );
}

OpenCV："camera calibrate" 为什么非平面校准平台需要初始猜测？

OpenCV: "camera calibrate" Why non-planar calibration rigs need initial guess?

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