cv2.imread函数_cv2.imread函数

cv2.imread函数_cv2.imread函数cvCalcMatMulDeriv://reimplementationofdAB.m/*这个矩阵求导和传统的矩阵求导不太一样求dcda假设a:M*Nc:I*J最后生成矩阵IJ*MN-PQ求得的元素是将c按行主序展

cv2.imread函数_cv2.imread函数"

cvCalcMatMulDeriv:


// reimplementation of dAB.m
/*这个矩阵求导和传统的矩阵求导不太一样  求dcda 假设a:M*N  c:I*J   最后生成矩阵  IJ * MN -> PQ
求得的元素是  将c按行主序 展开成向量C,C(0,0) ~ C(0,I*J) , a也 按行主序 展开成向量A,A(0,0) ~ A(0,M*N ) 
那么   dcda = D = d(p,q) = 
dC(0,0)/dA(0,0) dC(0,0)/dA(0,1) dC(0,0)/dA(0,2) ... dC(0,0)/dA(0,MN)
dC(0,1)/dA(0,0) dC(0,1)/dA(0,1) dC(0,1)/dA(0,2) ... dC(0,1)/dA(0,MN)
...
...
dC(0,IJ)/dA(0,0) dC(0,IJ)/dA(0,1) dC(0,IJ)/dA(0,2) ... dC(0,IJ)/dA(0,MN)
*/
CV_IMPL void cvCalcMatMulDeriv( const CvMat* A, const CvMat* B, CvMat* dABdA, CvMat* dABdB )
{
    //矩阵对矩阵求偏导:相当于被偏导的矩阵每个位置上的元素 对 求导矩阵的每个值求偏导。  若A m*n  B:n*k  AB:m*k    dABdA = m*
    int i, j, M, N, L;
    int bstep;

    CV_Assert( CV_IS_MAT(A) && CV_IS_MAT(B) );
    CV_Assert( CV_ARE_TYPES_EQ(A, B) &&
        (CV_MAT_TYPE(A->type) == CV_32F || CV_MAT_TYPE(A->type) == CV_64F) );
    CV_Assert( A->cols == B->rows );

    M = A->rows;
    L = A->cols;
    N = B->cols;
    bstep = B->step/CV_ELEM_SIZE(B->type);//B行有多少个

    if( dABdA )
    {
        CV_Assert( CV_ARE_TYPES_EQ(A, dABdA) &&
            dABdA->rows == A->rows*B->cols && dABdA->cols == A->rows*A->cols );
    }

    if( dABdB )
    {
        CV_Assert( CV_ARE_TYPES_EQ(A, dABdB) &&
            dABdB->rows == A->rows*B->cols && dABdB->cols == B->rows*B->cols );
    }

    if( CV_MAT_TYPE(A->type) == CV_32F )
    {
        for( i = 0; i < M*N; i++ )
        {
            int i1 = i / N,  i2 = i % N;

            if( dABdA )
            {
                float* dcda = (float*)(dABdA->data.ptr + dABdA->step*i);
                const float* b = (const float*)B->data.ptr + i2;

                for( j = 0; j < M*L; j++ )
                    dcda[j] = 0;
                for( j = 0; j < L; j++ )
                    dcda[i1*L + j] = b[j*bstep];//实际上是列
            }

            if( dABdB )
            {
                float* dcdb = (float*)(dABdB->data.ptr + dABdB->step*i);//step行的长度  dcdb 实际上指的是这一列
                const float* a = (const float*)(A->data.ptr + A->step*i1);

                for( j = 0; j < L*N; j++ )
                    dcdb[j] = 0;
                for( j = 0; j < L; j++ )
                    dcdb[j*N + i2] = a[j];
            }
        }
    }
    else
    {
        for( i = 0; i < M*N; i++ )
        {
            int i1 = i / N,  i2 = i % N;

            if( dABdA )
            {
                double* dcda = (double*)(dABdA->data.ptr + dABdA->step*i);
                const double* b = (const double*)B->data.ptr + i2;

                for( j = 0; j < M*L; j++ )
                    dcda[j] = 0;
                for( j = 0; j < L; j++ )
                    dcda[i1*L + j] = b[j*bstep];
            }

            if( dABdB )
            {
                double* dcdb = (double*)(dABdB->data.ptr + dABdB->step*i);
                const double* a = (const double*)(A->data.ptr + A->step*i1);

                for( j = 0; j < L*N; j++ )
                    dcdb[j] = 0;
                for( j = 0; j < L; j++ )
                    dcdb[j*N + i2] = a[j];
            }
        }
    }
}

cvComposeRT:


// reimplementation of compose_motion.m
/*R3 = R2 * R1   Rrw = Rrl * Rlw 
t3 = R2t1 + t2   trw = Rrl * tlw + trl
*/
CV_IMPL void cvComposeRT( const CvMat* _rvec1, const CvMat* _tvec1,
             const CvMat* _rvec2, const CvMat* _tvec2,
             CvMat* _rvec3, CvMat* _tvec3,
             CvMat* dr3dr1, CvMat* dr3dt1,
             CvMat* dr3dr2, CvMat* dr3dt2,
             CvMat* dt3dr1, CvMat* dt3dt1,
             CvMat* dt3dr2, CvMat* dt3dt2 )
{
    double _r1[3], _r2[3];
    double _R1[9], _d1[9*3], _R2[9], _d2[9*3];
    CvMat r1 = cvMat(3,1,CV_64F,_r1), r2 = cvMat(3,1,CV_64F,_r2);
    CvMat R1 = cvMat(3,3,CV_64F,_R1), R2 = cvMat(3,3,CV_64F,_R2);
    CvMat dR1dr1 = cvMat(9,3,CV_64F,_d1), dR2dr2 = cvMat(9,3,CV_64F,_d2);

    CV_Assert( CV_IS_MAT(_rvec1) && CV_IS_MAT(_rvec2) );

    CV_Assert( CV_MAT_TYPE(_rvec1->type) == CV_32F ||
               CV_MAT_TYPE(_rvec1->type) == CV_64F );

    CV_Assert( _rvec1->rows == 3 && _rvec1->cols == 1 && CV_ARE_SIZES_EQ(_rvec1, _rvec2) );

    cvConvert( _rvec1, &r1 );
    cvConvert( _rvec2, &r2 );
    //旋转向量 变 旋转矩阵 dR1dr1  dR2dr2 是对应偏导数
    cvRodrigues2( &r1, &R1, &dR1dr1 );
    cvRodrigues2( &r2, &R2, &dR2dr2 );
    //
    if( _rvec3 || dr3dr1 || dr3dr2 )
    {
        //参数绑定
        double _r3[3], _R3[9], _dR3dR1[9*9], _dR3dR2[9*9], _dr3dR3[9*3];
        double _W1[9*3], _W2[3*3];
        CvMat r3 = cvMat(3,1,CV_64F,_r3), R3 = cvMat(3,3,CV_64F,_R3);
        CvMat dR3dR1 = cvMat(9,9,CV_64F,_dR3dR1), dR3dR2 = cvMat(9,9,CV_64F,_dR3dR2);
        CvMat dr3dR3 = cvMat(3,9,CV_64F,_dr3dR3);
        CvMat W1 = cvMat(3,9,CV_64F,_W1), W2 = cvMat(3,3,CV_64F,_W2);
        //矩阵乘法 dst=src1*src2
        cvMatMul( &R2, &R1, &R3 );
        //求偏导
        cvCalcMatMulDeriv( &R2, &R1, &dR3dR2, &dR3dR1 );
        //罗德里格斯公式 将旋转矩阵变为旋转向量 
        cvRodrigues2( &R3, &r3, &dr3dR3 );

        if( _rvec3 )
            cvConvert( &r3, _rvec3 );
        //链式法则
        if( dr3dr1 )
        {
            cvMatMul( &dr3dR3, &dR3dR1, &W1 );
            cvMatMul( &W1, &dR1dr1, &W2 );
            cvConvert( &W2, dr3dr1 );
        }

        if( dr3dr2 )
        {
            cvMatMul( &dr3dR3, &dR3dR2, &W1 );
            cvMatMul( &W1, &dR2dr2, &W2 );
            cvConvert( &W2, dr3dr2 );
        }
    }

    if( dr3dt1 )
        cvZero( dr3dt1 );
    if( dr3dt2 )
        cvZero( dr3dt2 );
    //原理基本同上
    if( _tvec3 || dt3dr2 || dt3dt1 )
    {
        double _t1[3], _t2[3], _t3[3], _dxdR2[3*9], _dxdt1[3*3], _W3[3*3];
        CvMat t1 = cvMat(3,1,CV_64F,_t1), t2 = cvMat(3,1,CV_64F,_t2);
        CvMat t3 = cvMat(3,1,CV_64F,_t3);
        CvMat dxdR2 = cvMat(3, 9, CV_64F, _dxdR2);
        CvMat dxdt1 = cvMat(3, 3, CV_64F, _dxdt1);
        CvMat W3 = cvMat(3, 3, CV_64F, _W3);

        CV_Assert( CV_IS_MAT(_tvec1) && CV_IS_MAT(_tvec2) );
        CV_Assert( CV_ARE_SIZES_EQ(_tvec1, _tvec2) && CV_ARE_SIZES_EQ(_tvec1, _rvec1) );

        cvConvert( _tvec1, &t1 );
        cvConvert( _tvec2, &t2 );
        cvMatMulAdd( &R2, &t1, &t2, &t3 );

        if( _tvec3 )
            cvConvert( &t3, _tvec3 );

        if( dt3dr2 || dt3dt1 )
        {
            cvCalcMatMulDeriv( &R2, &t1, &dxdR2, &dxdt1 );
            if( dt3dr2 )
            {
                cvMatMul( &dxdR2, &dR2dr2, &W3 );
                cvConvert( &W3, dt3dr2 );
            }
            if( dt3dt1 )
                cvConvert( &dxdt1, dt3dt1 );
        }
    }
    //基本同上
    if( dt3dt2 )
        cvSetIdentity( dt3dt2 );
    if( dt3dr1 )
        cvZero( dt3dr1 );
}

 cvProjectPoints2Internal:

//计算 3d点到2d点的映射, 并且计算 点p关于外参r t,焦距f,偏置c,畸变k的偏导
static void cvProjectPoints2Internal( const CvMat* objectPoints,
                  const CvMat* r_vec,
                  const CvMat* t_vec,
                  const CvMat* A,
                  const CvMat* distCoeffs,
                  CvMat* imagePoints, CvMat* dpdr CV_DEFAULT(NULL),
                  CvMat* dpdt CV_DEFAULT(NULL), CvMat* dpdf CV_DEFAULT(NULL),
                  CvMat* dpdc CV_DEFAULT(NULL), CvMat* dpdk CV_DEFAULT(NULL),
                  CvMat* dpdo CV_DEFAULT(NULL),
                  double aspectRatio CV_DEFAULT(0) )
{
    //设定不同指针
    Ptr<CvMat> matM, _m;
    Ptr<CvMat> _dpdr, _dpdt, _dpdc, _dpdf, _dpdk;
    Ptr<CvMat> _dpdo;
    //计数
    int i, j, count;
    int calc_derivatives;
    //点指针
    const CvPoint3D64f* M;
    CvPoint2D64f* m;
    //绑定内存
    double r[3], R[9], dRdr[27], t[3], a[9], k[14] = {0,0,0,0,0,0,0,0,0,0,0,0,0,0}, fx, fy, cx, cy;
    Matx33d matTilt = Matx33d::eye();
    Matx33d dMatTiltdTauX(0,0,0,0,0,0,0,-1,0);
    Matx33d dMatTiltdTauY(0,0,0,0,0,0,1,0,0);
    CvMat _r, _t, _a = cvMat( 3, 3, CV_64F, a ), _k;
    CvMat matR = cvMat( 3, 3, CV_64F, R ), _dRdr = cvMat( 3, 9, CV_64F, dRdr );
    double *dpdr_p = 0, *dpdt_p = 0, *dpdk_p = 0, *dpdf_p = 0, *dpdc_p = 0;
    double* dpdo_p = 0;
    int dpdr_step = 0, dpdt_step = 0, dpdk_step = 0, dpdf_step = 0, dpdc_step = 0;
    int dpdo_step = 0;
    //是否固定横纵比
    bool fixedAspectRatio = aspectRatio > FLT_EPSILON;
    //检查参数
    if( !CV_IS_MAT(objectPoints) || !CV_IS_MAT(r_vec) ||
        !CV_IS_MAT(t_vec) || !CV_IS_MAT(A) ||
        /*!CV_IS_MAT(distCoeffs) ||*/ !CV_IS_MAT(imagePoints) )
        CV_Error( CV_StsBadArg, "One of required arguments is not a valid matrix" );
    //要求输入的是非其次坐标
    int total = objectPoints->rows * objectPoints->cols * CV_MAT_CN(objectPoints->type);
    if(total % 3 != 0)
    {
        //we have stopped support of homogeneous coordinates because it cause ambiguity in interpretation of the input data
        CV_Error( CV_StsBadArg, "Homogeneous coordinates are not supported" );
    }
    //点数目
    count = total / 3;
    //参数类型检查 matM是3d点
    if( CV_IS_CONT_MAT(objectPoints->type) &&
        (CV_MAT_DEPTH(objectPoints->type) == CV_32F || CV_MAT_DEPTH(objectPoints->type) == CV_64F)&&
        ((objectPoints->rows == 1 && CV_MAT_CN(objectPoints->type) == 3) ||
        (objectPoints->rows == count && CV_MAT_CN(objectPoints->type)*objectPoints->cols == 3) ||
        (objectPoints->rows == 3 && CV_MAT_CN(objectPoints->type) == 1 && objectPoints->cols == count)))
    {
        matM.reset(cvCreateMat( objectPoints->rows, objectPoints->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(objectPoints->type)) ));
        cvConvert(objectPoints, matM);
    }
    else
    {
//        matM = cvCreateMat( 1, count, CV_64FC3 );
//        cvConvertPointsHomogeneous( objectPoints, matM );
        CV_Error( CV_StsBadArg, "Homogeneous coordinates are not supported" );
    }
    //_m是2d点
    if( CV_IS_CONT_MAT(imagePoints->type) &&
        (CV_MAT_DEPTH(imagePoints->type) == CV_32F || CV_MAT_DEPTH(imagePoints->type) == CV_64F) &&
        ((imagePoints->rows == 1 && CV_MAT_CN(imagePoints->type) == 2) ||
        (imagePoints->rows == count && CV_MAT_CN(imagePoints->type)*imagePoints->cols == 2) ||
        (imagePoints->rows == 2 && CV_MAT_CN(imagePoints->type) == 1 && imagePoints->cols == count)))
    {
        _m.reset(cvCreateMat( imagePoints->rows, imagePoints->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(imagePoints->type)) ));
        cvConvert(imagePoints, _m);
    }
    else
    {
//        _m = cvCreateMat( 1, count, CV_64FC2 );
        CV_Error( CV_StsBadArg, "Homogeneous coordinates are not supported" );
    }
    //3d点 和 2d点指针
    M = (CvPoint3D64f*)matM->data.db;
    m = (CvPoint2D64f*)_m->data.db;

    if( (CV_MAT_DEPTH(r_vec->type) != CV_64F && CV_MAT_DEPTH(r_vec->type) != CV_32F) ||
        (((r_vec->rows != 1 && r_vec->cols != 1) ||
        r_vec->rows*r_vec->cols*CV_MAT_CN(r_vec->type) != 3) &&
        ((r_vec->rows != 3 && r_vec->cols != 3) || CV_MAT_CN(r_vec->type) != 1)))
        CV_Error( CV_StsBadArg, "Rotation must be represented by 1x3 or 3x1 "
                  "floating-point rotation vector, or 3x3 rotation matrix" );
    //这里把旋转矩阵转向量,再转回来,是为了要求旋转矩阵对旋转向量的偏导
    if( r_vec->rows == 3 && r_vec->cols == 3 )
    {
        _r = cvMat( 3, 1, CV_64FC1, r );
        cvRodrigues2( r_vec, &_r );
        cvRodrigues2( &_r, &matR, &_dRdr );
        cvCopy( r_vec, &matR );
    }
    else
    {
        _r = cvMat( r_vec->rows, r_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(r_vec->type)), r );
        cvConvert( r_vec, &_r );
        cvRodrigues2( &_r, &matR, &_dRdr );
    }
    //参数检查
    if( (CV_MAT_DEPTH(t_vec->type) != CV_64F && CV_MAT_DEPTH(t_vec->type) != CV_32F) ||
        (t_vec->rows != 1 && t_vec->cols != 1) ||
        t_vec->rows*t_vec->cols*CV_MAT_CN(t_vec->type) != 3 )
        CV_Error( CV_StsBadArg,
            "Translation vector must be 1x3 or 3x1 floating-point vector" );
    //平移
    _t = cvMat( t_vec->rows, t_vec->cols, CV_MAKETYPE(CV_64F,CV_MAT_CN(t_vec->type)), t );
    cvConvert( t_vec, &_t );

    if( (CV_MAT_TYPE(A->type) != CV_64FC1 && CV_MAT_TYPE(A->type) != CV_32FC1) ||
        A->rows != 3 || A->cols != 3 )
        CV_Error( CV_StsBadArg, "Instrinsic parameters must be 3x3 floating-point matrix" );
    //内参
    cvConvert( A, &_a );
    fx = a[0]; fy = a[4];
    cx = a[2]; cy = a[5];
    //固定比例
    if( fixedAspectRatio )
        fx = fy*aspectRatio;
    //参数检查
    if( distCoeffs )
    {
        if( !CV_IS_MAT(distCoeffs) ||
            (CV_MAT_DEPTH(distCoeffs->type) != CV_64F &&
            CV_MAT_DEPTH(distCoeffs->type) != CV_32F) ||
            (distCoeffs->rows != 1 && distCoeffs->cols != 1) ||
            (distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 4 &&
            distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 5 &&
            distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 8 &&
            distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 12 &&
            distCoeffs->rows*distCoeffs->cols*CV_MAT_CN(distCoeffs->type) != 14) )
            CV_Error( CV_StsBadArg, cvDistCoeffErr );

        _k = cvMat( distCoeffs->rows, distCoeffs->cols,
                    CV_MAKETYPE(CV_64F,CV_MAT_CN(distCoeffs->type)), k );
        cvConvert( distCoeffs, &_k );
        /*
        计算传感器倾斜矩阵,(倾斜参数x,倾斜参数y,倾斜矩阵Tilt,偏导) 
        */
        if(k[12] != 0 || k[13] != 0)
        {
          detail::computeTiltProjectionMatrix(k[12], k[13],
            &matTilt, &dMatTiltdTauX, &dMatTiltdTauY);
        }
    }
    //做类型检测,然后指针初始化,并获取每行的元素个数
    if( dpdr )
    {
        if( !CV_IS_MAT(dpdr) ||
            (CV_MAT_TYPE(dpdr->type) != CV_32FC1 &&
            CV_MAT_TYPE(dpdr->type) != CV_64FC1) ||
            dpdr->rows != count*2 || dpdr->cols != 3 )
            CV_Error( CV_StsBadArg, "dp/drot must be 2Nx3 floating-point matrix" );

        if( CV_MAT_TYPE(dpdr->type) == CV_64FC1 )
        {
            _dpdr.reset(cvCloneMat(dpdr));
        }
        else
            _dpdr.reset(cvCreateMat( 2*count, 3, CV_64FC1 ));
        dpdr_p = _dpdr->data.db;
        dpdr_step = _dpdr->step/sizeof(dpdr_p[0]);
    }

    if( dpdt )
    {
        if( !CV_IS_MAT(dpdt) ||
            (CV_MAT_TYPE(dpdt->type) != CV_32FC1 &&
            CV_MAT_TYPE(dpdt->type) != CV_64FC1) ||
            dpdt->rows != count*2 || dpdt->cols != 3 )
            CV_Error( CV_StsBadArg, "dp/dT must be 2Nx3 floating-point matrix" );

        if( CV_MAT_TYPE(dpdt->type) == CV_64FC1 )
        {
            _dpdt.reset(cvCloneMat(dpdt));
        }
        else
            _dpdt.reset(cvCreateMat( 2*count, 3, CV_64FC1 ));
        dpdt_p = _dpdt->data.db;
        dpdt_step = _dpdt->step/sizeof(dpdt_p[0]);
    }

    if( dpdf )
    {
        if( !CV_IS_MAT(dpdf) ||
            (CV_MAT_TYPE(dpdf->type) != CV_32FC1 && CV_MAT_TYPE(dpdf->type) != CV_64FC1) ||
            dpdf->rows != count*2 || dpdf->cols != 2 )
            CV_Error( CV_StsBadArg, "dp/df must be 2Nx2 floating-point matrix" );

        if( CV_MAT_TYPE(dpdf->type) == CV_64FC1 )
        {
            _dpdf.reset(cvCloneMat(dpdf));
        }
        else
            _dpdf.reset(cvCreateMat( 2*count, 2, CV_64FC1 ));
        dpdf_p = _dpdf->data.db;
        dpdf_step = _dpdf->step/sizeof(dpdf_p[0]);
    }

    if( dpdc )
    {
        if( !CV_IS_MAT(dpdc) ||
            (CV_MAT_TYPE(dpdc->type) != CV_32FC1 && CV_MAT_TYPE(dpdc->type) != CV_64FC1) ||
            dpdc->rows != count*2 || dpdc->cols != 2 )
            CV_Error( CV_StsBadArg, "dp/dc must be 2Nx2 floating-point matrix" );

        if( CV_MAT_TYPE(dpdc->type) == CV_64FC1 )
        {
            _dpdc.reset(cvCloneMat(dpdc));
        }
        else
            _dpdc.reset(cvCreateMat( 2*count, 2, CV_64FC1 ));
        dpdc_p = _dpdc->data.db;
        dpdc_step = _dpdc->step/sizeof(dpdc_p[0]);
    }

    if( dpdk )
    {
        if( !CV_IS_MAT(dpdk) ||
            (CV_MAT_TYPE(dpdk->type) != CV_32FC1 && CV_MAT_TYPE(dpdk->type) != CV_64FC1) ||
            dpdk->rows != count*2 || (dpdk->cols != 14 && dpdk->cols != 12 && dpdk->cols != 8 && dpdk->cols != 5 && dpdk->cols != 4 && dpdk->cols != 2) )
            CV_Error( CV_StsBadArg, "dp/df must be 2Nx14, 2Nx12, 2Nx8, 2Nx5, 2Nx4 or 2Nx2 floating-point matrix" );

        if( !distCoeffs )
            CV_Error( CV_StsNullPtr, "distCoeffs is NULL while dpdk is not" );

        if( CV_MAT_TYPE(dpdk->type) == CV_64FC1 )
        {
            _dpdk.reset(cvCloneMat(dpdk));
        }
        else
            _dpdk.reset(cvCreateMat( dpdk->rows, dpdk->cols, CV_64FC1 ));
        dpdk_p = _dpdk->data.db;
        dpdk_step = _dpdk->step/sizeof(dpdk_p[0]);
    }

    if( dpdo )
    {
        if( !CV_IS_MAT( dpdo ) || ( CV_MAT_TYPE( dpdo->type ) != CV_32FC1
                                    && CV_MAT_TYPE( dpdo->type ) != CV_64FC1 )
            || dpdo->rows != count * 2 || dpdo->cols != count * 3 )
            CV_Error( CV_StsBadArg, "dp/do must be 2Nx3N floating-point matrix" );

        if( CV_MAT_TYPE( dpdo->type ) == CV_64FC1 )
        {
            _dpdo.reset( cvCloneMat( dpdo ) );
        }
        else
            _dpdo.reset( cvCreateMat( 2 * count, 3 * count, CV_64FC1 ) );
        cvZero(_dpdo);
        dpdo_p = _dpdo->data.db;
        dpdo_step = _dpdo->step / sizeof( dpdo_p[0] );
    }
    //要不要算偏导
    calc_derivatives = dpdr || dpdt || dpdf || dpdc || dpdk || dpdo;
    //遍历所有点进行运算
    for( i = 0; i < count; i++ )
    {
        //X Y Z 是3d点坐标
        double X = M[i].x, Y = M[i].y, Z = M[i].z;
        //利用外参R t ,对齐坐标系:世界坐标系 和 相机坐标系,xyz是相机坐标系下点坐标
        double x = R[0]*X + R[1]*Y + R[2]*Z + t[0];
        double y = R[3]*X + R[4]*Y + R[5]*Z + t[1];
        double z = R[6]*X + R[7]*Y + R[8]*Z + t[2];
        double r2, r4, r6, a1, a2, a3, cdist, icdist2;
        double xd, yd, xd0, yd0, invProj;
        Vec3d vecTilt;
        Vec3d dVecTilt;
        Matx22d dMatTilt;
        Vec2d dXdYd;
        //逆深度 z不是0 就取倒数
        double z0 = z;
        z = z ? 1./z : 1;
        //投影到单位平面
        x *= z; y *= z;
        //准备畸变叠加
        r2 = x*x + y*y;
        r4 = r2*r2;
        r6 = r4*r2;
        a1 = 2*x*y;
        a2 = r2 + 2*x*x;
        a3 = r2 + 2*y*y;
        cdist = 1 + k[0]*r2 + k[1]*r4 + k[4]*r6;
        icdist2 = 1./(1 + k[5]*r2 + k[6]*r4 + k[7]*r6);
        //加入畸变
        xd0 = x*cdist*icdist2 + k[2]*a1 + k[3]*a2 + k[8]*r2+k[9]*r4;
        yd0 = y*cdist*icdist2 + k[2]*a3 + k[3]*a1 + k[10]*r2+k[11]*r4;

        // 去除沙氏镜头的失真
        vecTilt = matTilt*Vec3d(xd0, yd0, 1);
        invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
        xd = invProj * vecTilt(0);
        yd = invProj * vecTilt(1);
        // 考虑内参,投影到像素平面
        m[i].x = xd*fx + cx;
        m[i].y = yd*fy + cy;
        //计算各个偏导   暂时略过,这个需要动笔算算
        if( calc_derivatives )
        {
            if( dpdc_p )
            {
                dpdc_p[0] = 1; dpdc_p[1] = 0; // dp_xdc_x; dp_xdc_y
                dpdc_p[dpdc_step] = 0;
                dpdc_p[dpdc_step+1] = 1;
                dpdc_p += dpdc_step*2;
            }

            if( dpdf_p )
            {
                if( fixedAspectRatio )
                {
                    dpdf_p[0] = 0; dpdf_p[1] = xd*aspectRatio; // dp_xdf_x; dp_xdf_y
                    dpdf_p[dpdf_step] = 0;
                    dpdf_p[dpdf_step+1] = yd;
                }
                else
                {
                    dpdf_p[0] = xd; dpdf_p[1] = 0;
                    dpdf_p[dpdf_step] = 0;
                    dpdf_p[dpdf_step+1] = yd;
                }
                dpdf_p += dpdf_step*2;
            }
            for (int row = 0; row < 2; ++row)
                for (int col = 0; col < 2; ++col)
                    dMatTilt(row,col) = matTilt(row,col)*vecTilt(2)
                      - matTilt(2,col)*vecTilt(row);
            double invProjSquare = (invProj*invProj);
            dMatTilt *= invProjSquare;
            if( dpdk_p )
            {
                dXdYd = dMatTilt*Vec2d(x*icdist2*r2, y*icdist2*r2);
                dpdk_p[0] = fx*dXdYd(0);
                dpdk_p[dpdk_step] = fy*dXdYd(1);
                dXdYd = dMatTilt*Vec2d(x*icdist2*r4, y*icdist2*r4);
                dpdk_p[1] = fx*dXdYd(0);
                dpdk_p[dpdk_step+1] = fy*dXdYd(1);
                if( _dpdk->cols > 2 )
                {
                    dXdYd = dMatTilt*Vec2d(a1, a3);
                    dpdk_p[2] = fx*dXdYd(0);
                    dpdk_p[dpdk_step+2] = fy*dXdYd(1);
                    dXdYd = dMatTilt*Vec2d(a2, a1);
                    dpdk_p[3] = fx*dXdYd(0);
                    dpdk_p[dpdk_step+3] = fy*dXdYd(1);
                    if( _dpdk->cols > 4 )
                    {
                        dXdYd = dMatTilt*Vec2d(x*icdist2*r6, y*icdist2*r6);
                        dpdk_p[4] = fx*dXdYd(0);
                        dpdk_p[dpdk_step+4] = fy*dXdYd(1);

                        if( _dpdk->cols > 5 )
                        {
                            dXdYd = dMatTilt*Vec2d(
                              x*cdist*(-icdist2)*icdist2*r2, y*cdist*(-icdist2)*icdist2*r2);
                            dpdk_p[5] = fx*dXdYd(0);
                            dpdk_p[dpdk_step+5] = fy*dXdYd(1);
                            dXdYd = dMatTilt*Vec2d(
                              x*cdist*(-icdist2)*icdist2*r4, y*cdist*(-icdist2)*icdist2*r4);
                            dpdk_p[6] = fx*dXdYd(0);
                            dpdk_p[dpdk_step+6] = fy*dXdYd(1);
                            dXdYd = dMatTilt*Vec2d(
                              x*cdist*(-icdist2)*icdist2*r6, y*cdist*(-icdist2)*icdist2*r6);
                            dpdk_p[7] = fx*dXdYd(0);
                            dpdk_p[dpdk_step+7] = fy*dXdYd(1);
                            if( _dpdk->cols > 8 )
                            {
                                dXdYd = dMatTilt*Vec2d(r2, 0);
                                dpdk_p[8] = fx*dXdYd(0); //s1
                                dpdk_p[dpdk_step+8] = fy*dXdYd(1); //s1
                                dXdYd = dMatTilt*Vec2d(r4, 0);
                                dpdk_p[9] = fx*dXdYd(0); //s2
                                dpdk_p[dpdk_step+9] = fy*dXdYd(1); //s2
                                dXdYd = dMatTilt*Vec2d(0, r2);
                                dpdk_p[10] = fx*dXdYd(0);//s3
                                dpdk_p[dpdk_step+10] = fy*dXdYd(1); //s3
                                dXdYd = dMatTilt*Vec2d(0, r4);
                                dpdk_p[11] = fx*dXdYd(0);//s4
                                dpdk_p[dpdk_step+11] = fy*dXdYd(1); //s4
                                if( _dpdk->cols > 12 )
                                {
                                    dVecTilt = dMatTiltdTauX * Vec3d(xd0, yd0, 1);
                                    dpdk_p[12] = fx * invProjSquare * (
                                      dVecTilt(0) * vecTilt(2) - dVecTilt(2) * vecTilt(0));
                                    dpdk_p[dpdk_step+12] = fy*invProjSquare * (
                                      dVecTilt(1) * vecTilt(2) - dVecTilt(2) * vecTilt(1));
                                    dVecTilt = dMatTiltdTauY * Vec3d(xd0, yd0, 1);
                                    dpdk_p[13] = fx * invProjSquare * (
                                      dVecTilt(0) * vecTilt(2) - dVecTilt(2) * vecTilt(0));
                                    dpdk_p[dpdk_step+13] = fy * invProjSquare * (
                                      dVecTilt(1) * vecTilt(2) - dVecTilt(2) * vecTilt(1));
                                }
                            }
                        }
                    }
                }
                dpdk_p += dpdk_step*2;
            }

            if( dpdt_p )
            {
                double dxdt[] = { z, 0, -x*z }, dydt[] = { 0, z, -y*z };
                for( j = 0; j < 3; j++ )
                {
                    double dr2dt = 2*x*dxdt[j] + 2*y*dydt[j];
                    double dcdist_dt = k[0]*dr2dt + 2*k[1]*r2*dr2dt + 3*k[4]*r4*dr2dt;
                    double dicdist2_dt = -icdist2*icdist2*(k[5]*dr2dt + 2*k[6]*r2*dr2dt + 3*k[7]*r4*dr2dt);
                    double da1dt = 2*(x*dydt[j] + y*dxdt[j]);
                    double dmxdt = (dxdt[j]*cdist*icdist2 + x*dcdist_dt*icdist2 + x*cdist*dicdist2_dt +
                                       k[2]*da1dt + k[3]*(dr2dt + 4*x*dxdt[j]) + k[8]*dr2dt + 2*r2*k[9]*dr2dt);
                    double dmydt = (dydt[j]*cdist*icdist2 + y*dcdist_dt*icdist2 + y*cdist*dicdist2_dt +
                                       k[2]*(dr2dt + 4*y*dydt[j]) + k[3]*da1dt + k[10]*dr2dt + 2*r2*k[11]*dr2dt);
                    dXdYd = dMatTilt*Vec2d(dmxdt, dmydt);
                    dpdt_p[j] = fx*dXdYd(0);
                    dpdt_p[dpdt_step+j] = fy*dXdYd(1);
                }
                dpdt_p += dpdt_step*2;
            }

            if( dpdr_p )
            {
                double dx0dr[] =
                {
                    X*dRdr[0] + Y*dRdr[1] + Z*dRdr[2],
                    X*dRdr[9] + Y*dRdr[10] + Z*dRdr[11],
                    X*dRdr[18] + Y*dRdr[19] + Z*dRdr[20]
                };
                double dy0dr[] =
                {
                    X*dRdr[3] + Y*dRdr[4] + Z*dRdr[5],
                    X*dRdr[12] + Y*dRdr[13] + Z*dRdr[14],
                    X*dRdr[21] + Y*dRdr[22] + Z*dRdr[23]
                };
                double dz0dr[] =
                {
                    X*dRdr[6] + Y*dRdr[7] + Z*dRdr[8],
                    X*dRdr[15] + Y*dRdr[16] + Z*dRdr[17],
                    X*dRdr[24] + Y*dRdr[25] + Z*dRdr[26]
                };
                for( j = 0; j < 3; j++ )
                {
                    double dxdr = z*(dx0dr[j] - x*dz0dr[j]);
                    double dydr = z*(dy0dr[j] - y*dz0dr[j]);
                    double dr2dr = 2*x*dxdr + 2*y*dydr;
                    double dcdist_dr = (k[0] + 2*k[1]*r2 + 3*k[4]*r4)*dr2dr;
                    double dicdist2_dr = -icdist2*icdist2*(k[5] + 2*k[6]*r2 + 3*k[7]*r4)*dr2dr;
                    double da1dr = 2*(x*dydr + y*dxdr);
                    double dmxdr = (dxdr*cdist*icdist2 + x*dcdist_dr*icdist2 + x*cdist*dicdist2_dr +
                                       k[2]*da1dr + k[3]*(dr2dr + 4*x*dxdr) + (k[8] + 2*r2*k[9])*dr2dr);
                    double dmydr = (dydr*cdist*icdist2 + y*dcdist_dr*icdist2 + y*cdist*dicdist2_dr +
                                       k[2]*(dr2dr + 4*y*dydr) + k[3]*da1dr + (k[10] + 2*r2*k[11])*dr2dr);
                    dXdYd = dMatTilt*Vec2d(dmxdr, dmydr);
                    dpdr_p[j] = fx*dXdYd(0);
                    dpdr_p[dpdr_step+j] = fy*dXdYd(1);
                }
                dpdr_p += dpdr_step*2;
            }

            if( dpdo_p )
            {
                double dxdo[] = { z * ( R[0] - x * z * z0 * R[6] ),
                                  z * ( R[1] - x * z * z0 * R[7] ),
                                  z * ( R[2] - x * z * z0 * R[8] ) };
                double dydo[] = { z * ( R[3] - y * z * z0 * R[6] ),
                                  z * ( R[4] - y * z * z0 * R[7] ),
                                  z * ( R[5] - y * z * z0 * R[8] ) };
                for( j = 0; j < 3; j++ )
                {
                    double dr2do = 2 * x * dxdo[j] + 2 * y * dydo[j];
                    double dr4do = 2 * r2 * dr2do;
                    double dr6do = 3 * r4 * dr2do;
                    double da1do = 2 * y * dxdo[j] + 2 * x * dydo[j];
                    double da2do = dr2do + 4 * x * dxdo[j];
                    double da3do = dr2do + 4 * y * dydo[j];
                    double dcdist_do
                        = k[0] * dr2do + k[1] * dr4do + k[4] * dr6do;
                    double dicdist2_do = -icdist2 * icdist2
                        * ( k[5] * dr2do + k[6] * dr4do + k[7] * dr6do );
                    double dxd0_do = cdist * icdist2 * dxdo[j]
                        + x * icdist2 * dcdist_do + x * cdist * dicdist2_do
                        + k[2] * da1do + k[3] * da2do + k[8] * dr2do
                        + k[9] * dr4do;
                    double dyd0_do = cdist * icdist2 * dydo[j]
                        + y * icdist2 * dcdist_do + y * cdist * dicdist2_do
                        + k[2] * da3do + k[3] * da1do + k[10] * dr2do
                        + k[11] * dr4do;
                    dXdYd = dMatTilt * Vec2d( dxd0_do, dyd0_do );
                    dpdo_p[i * 3 + j] = fx * dXdYd( 0 );
                    dpdo_p[dpdo_step + i * 3 + j] = fy * dXdYd( 1 );
                }
                dpdo_p += dpdo_step * 2;
            }
        }
    }

    if( _m != imagePoints )
        cvConvert( _m, imagePoints );

    if( _dpdr != dpdr )
        cvConvert( _dpdr, dpdr );

    if( _dpdt != dpdt )
        cvConvert( _dpdt, dpdt );

    if( _dpdf != dpdf )
        cvConvert( _dpdf, dpdf );

    if( _dpdc != dpdc )
        cvConvert( _dpdc, dpdc );

    if( _dpdk != dpdk )
        cvConvert( _dpdk, dpdk );

    if( _dpdo != dpdo )
        cvConvert( _dpdo, dpdo );
}

cvFindExtrinsicCameraParams2

//获取外参,获取相机坐标系和世界坐标系下之间的旋转向量和平移向量  本质上和pnp差不多   //给初值,然后LM优化
CV_IMPL void cvFindExtrinsicCameraParams2( const CvMat* objectPoints,
                  const CvMat* imagePoints, const CvMat* A,
                  const CvMat* distCoeffs, CvMat* rvec, CvMat* tvec,
                  int useExtrinsicGuess )
{
    const int max_iter = 20;
    Ptr<CvMat> matM, _Mxy, _m, _mn, matL;
    //变量初始定义
    int i, count;
    double a[9], ar[9]={1,0,0,0,1,0,0,0,1}, R[9];
    double MM[9], U[9], V[9], W[3];
    cv::Scalar Mc;
    double param[6];
    CvMat matA = cvMat( 3, 3, CV_64F, a );
    CvMat _Ar = cvMat( 3, 3, CV_64F, ar );
    CvMat matR = cvMat( 3, 3, CV_64F, R );
    CvMat _r = cvMat( 3, 1, CV_64F, param );
    CvMat _t = cvMat( 3, 1, CV_64F, param + 3 );
    CvMat _Mc = cvMat( 1, 3, CV_64F, Mc.val );
    CvMat _MM = cvMat( 3, 3, CV_64F, MM );
    CvMat matU = cvMat( 3, 3, CV_64F, U );
    CvMat matV = cvMat( 3, 3, CV_64F, V );
    CvMat matW = cvMat( 3, 1, CV_64F, W );
    CvMat _param = cvMat( 6, 1, CV_64F, param );
    CvMat _dpdr, _dpdt;
    //变量类型检测
    CV_Assert( CV_IS_MAT(objectPoints) && CV_IS_MAT(imagePoints) &&
        CV_IS_MAT(A) && CV_IS_MAT(rvec) && CV_IS_MAT(tvec) );

    count = MAX(objectPoints->cols, objectPoints->rows);
    matM.reset(cvCreateMat( 1, count, CV_64FC3 ));
    _m.reset(cvCreateMat( 1, count, CV_64FC2 ));
    //转成齐次坐标
    cvConvertPointsHomogeneous( objectPoints, matM );
    cvConvertPointsHomogeneous( imagePoints, _m );
    cvConvert( A, &matA );
    //变量类型检测
    CV_Assert( (CV_MAT_DEPTH(rvec->type) == CV_64F || CV_MAT_DEPTH(rvec->type) == CV_32F) &&
        (rvec->rows == 1 || rvec->cols == 1) && rvec->rows*rvec->cols*CV_MAT_CN(rvec->type) == 3 );

    CV_Assert( (CV_MAT_DEPTH(tvec->type) == CV_64F || CV_MAT_DEPTH(tvec->type) == CV_32F) &&
        (tvec->rows == 1 || tvec->cols == 1) && tvec->rows*tvec->cols*CV_MAT_CN(tvec->type) == 3 );

    CV_Assert((count >= 4) || (count == 3 && useExtrinsicGuess)); // it is unsafe to call LM optimisation without an extrinsic guess in the case of 3 points. This is because there is no guarantee that it will converge on the correct solution.

    _mn.reset(cvCreateMat( 1, count, CV_64FC2 ));
    _Mxy.reset(cvCreateMat( 1, count, CV_64FC2 ));

    // normalize image points
    // (unapply the intrinsic matrix transformation and distortion)
    //将点去除畸变,同时放到归一化坐标系(Ar是单位阵) 待解读
    cvUndistortPoints( _m, _mn, &matA, distCoeffs, 0, &_Ar );
    //如果给定了预先的外参
    if( useExtrinsicGuess )
    {
        CvMat _r_temp = cvMat(rvec->rows, rvec->cols,
            CV_MAKETYPE(CV_64F,CV_MAT_CN(rvec->type)), param );
        CvMat _t_temp = cvMat(tvec->rows, tvec->cols,
            CV_MAKETYPE(CV_64F,CV_MAT_CN(tvec->type)), param + 3);
        cvConvert( rvec, &_r_temp );
        cvConvert( tvec, &_t_temp );
    }
    //没有给外参 就算一个外参  
    else 
    {
        //求所有3d点的中心   均值   这里实际上把所有点的变换到,点中心是【0,0,0】的xy平面上,求了一个icp  ref:Least-Squares Fitting of Two 3-D Point Sets
        Mc = cvAvg(matM);
        cvReshape( matM, matM, 1, count );
        // Calculates _MM = (matM-_Mc)^T*(matM-_Mc) 
        cvMulTransposed( matM, &_MM, 1, &_Mc );
        //svd 将_MM进行分解, _MM = UWV  其中U不输出, CV_SVD_MODIFY_A指定后_MM将改变 CV_SVD_V_T表示V是转置后生成的  (A,W,U,V,) 目的是看一看这些点的自由度是几维度的
        cvSVD( &_MM, &matW, 0, &matV, CV_SVD_MODIFY_A + CV_SVD_V_T );
       
        // 比较特征值
        // 因为  我们相当于求的是 每个点相对于均值点的偏差,如果所有点位于同一个平面上,它们的差值将会只在x,y两个方向上存在数值,即只在这两个尺度上发生变化,SVD分解后,特征值对角上由于3d上的点(取了个根号),只在两个方向上存在自由度,所以只存在两个有意义的特征值,因此第三个特征值数量级很小很小。
        if( W[2]/W[1] < 1e-3)
        {
            // a planar structure case (all M's lie in the same plane)
            double tt[3], h[9], h1_norm, h2_norm;
            CvMat* R_transform = &matV;
            CvMat T_transform = cvMat( 3, 1, CV_64F, tt );
            CvMat matH = cvMat( 3, 3, CV_64F, h );
            CvMat _h1, _h2, _h3;
            //这里求解要求A满秩,如果V最后一列为0,呢么A必不满秩,所有点在一条线上,线平移即可,不需要旋转
            if( V[2]*V[2] + V[5]*V[5] < 1e-10 )
                cvSetIdentity( R_transform );
            //求行列式,如果行列式小于0,就将R_transform取负
            if( cvDet(R_transform) < 0 )
                cvScale( R_transform, R_transform, -1 );
            //dst = (alpha*src1)*src2+(beta*src3)  CV_GEMM_B_T表示转置 src2    T_transform = - R_transform * _Mc.T
            cvGEMM( R_transform, &_Mc, -1, 0, 0, &T_transform, CV_GEMM_B_T );
            //_Mxy 就是点平移后的阵,这时候是2d的,丢掉了第三维度
            for( i = 0; i < count; i++ )
            {
                const double* Rp = R_transform->data.db;
                const double* Tp = T_transform.data.db;
                const double* src = matM->data.db + i*3;
                double* dst = _Mxy->data.db + i*2;

                dst[0] = Rp[0]*src[0] + Rp[1]*src[1] + Rp[2]*src[2] + Tp[0];
                dst[1] = Rp[3]*src[0] + Rp[4]*src[1] + Rp[5]*src[2] + Tp[1];
            }
            //找到物体平面和图像(视图)平面之间的透视变换  matH是透视变换矩阵  本质是这个函数实现的 findHomography  /calib3d/src/fundam.cpp
            cvFindHomography( _Mxy, _mn, &matH );
            //判断这个值怎么样,如果太大或者不合法,就把matR设置为单位阵,否则会给一个R   这块操作没看懂  我感觉 这里是一个归一化的过程,把点映射到归一化平面上
            if( cvCheckArr(&matH, CV_CHECK_QUIET) )
            {
                //将_h1定义为h的第一列,_h2是第二列,_h3第三列
                cvGetCol( &matH, &_h1, 0 );
                _h2 = _h1; _h2.data.db++;
                _h3 = _h2; _h3.data.db++;
                h1_norm = std::sqrt(h[0]*h[0] + h[3]*h[3] + h[6]*h[6]);
                h2_norm = std::sqrt(h[1]*h[1] + h[4]*h[4] + h[7]*h[7]);
                //线性变换  cvConvertScale( const CvArr* src, CvArr* dst, double scale CV_DEFAULT(1), double shift CV_DEFAULT(0) ) dst = scale * src + shift
                cvScale( &_h1, &_h1, 1./MAX(h1_norm, DBL_EPSILON) );
                cvScale( &_h2, &_h2, 1./MAX(h2_norm, DBL_EPSILON) );
                cvScale( &_h3, &_t, 2./MAX(h1_norm + h2_norm, DBL_EPSILON));
                //求两个3d向量叉积
                cvCrossProduct( &_h1, &_h2, &_h3 );

                cvRodrigues2( &matH, &_r );
                cvRodrigues2( &_r, &matH );
                cvMatMulAdd( &matH, &T_transform, &_t, &_t );
                cvMatMul( &matH, R_transform, &matR );
            }
            else
            {
                cvSetIdentity( &matR );
                cvZero( &_t );
            }

            cvRodrigues2( &matR, &_r );
        }
        //畸变校准中 所有点 必位于同一个平面 不可能else 所以忽略
        else
        {
            // non-planar structure. Use DLT method
            CV_CheckGE(count, 6, "DLT algorithm needs at least 6 points for pose estimation from 3D-2D point correspondences.");
            double* L;
            double LL[12*12], LW[12], LV[12*12], sc;
            CvMat _LL = cvMat( 12, 12, CV_64F, LL );
            CvMat _LW = cvMat( 12, 1, CV_64F, LW );
            CvMat _LV = cvMat( 12, 12, CV_64F, LV );
            CvMat _RRt, _RR, _tt;
            CvPoint3D64f* M = (CvPoint3D64f*)matM->data.db;
            CvPoint2D64f* mn = (CvPoint2D64f*)_mn->data.db;

            matL.reset(cvCreateMat( 2*count, 12, CV_64F ));
            L = matL->data.db;

            for( i = 0; i < count; i++, L += 24 )
            {
                double x = -mn[i].x, y = -mn[i].y;
                L[0] = L[16] = M[i].x;
                L[1] = L[17] = M[i].y;
                L[2] = L[18] = M[i].z;
                L[3] = L[19] = 1.;
                L[4] = L[5] = L[6] = L[7] = 0.;
                L[12] = L[13] = L[14] = L[15] = 0.;
                L[8] = x*M[i].x;
                L[9] = x*M[i].y;
                L[10] = x*M[i].z;
                L[11] = x;
                L[20] = y*M[i].x;
                L[21] = y*M[i].y;
                L[22] = y*M[i].z;
                L[23] = y;
            }

            cvMulTransposed( matL, &_LL, 1 );
            cvSVD( &_LL, &_LW, 0, &_LV, CV_SVD_MODIFY_A + CV_SVD_V_T );
            _RRt = cvMat( 3, 4, CV_64F, LV + 11*12 );
            cvGetCols( &_RRt, &_RR, 0, 3 );
            cvGetCol( &_RRt, &_tt, 3 );
            if( cvDet(&_RR) < 0 )
                cvScale( &_RRt, &_RRt, -1 );
            sc = cvNorm(&_RR);
            CV_Assert(fabs(sc) > DBL_EPSILON);
            cvSVD( &_RR, &matW, &matU, &matV, CV_SVD_MODIFY_A + CV_SVD_U_T + CV_SVD_V_T );
            cvGEMM( &matU, &matV, 1, 0, 0, &matR, CV_GEMM_A_T );
            cvScale( &_tt, &_t, cvNorm(&matR)/sc );
            cvRodrigues2( &matR, &_r );
        }
    }

    cvReshape( matM, matM, 3, 1 );
    cvReshape( _mn, _mn, 2, 1 );
    //定义了一个求解器,采用LM优化R t 
    // refine extrinsic parameters using iterative algorithm     优化变量个数 样本个数  迭代停止标准 雅克比矩阵的对称原则,true 则 m_ij=m_ji   i < j
    CvLevMarq solver( 6, count*2, cvTermCriteria(CV_TERMCRIT_EPS+CV_TERMCRIT_ITER,max_iter,FLT_EPSILON), true);
    cvCopy( &_param, solver.param );
    //把所有点放进去迭代求解
    for(;;)
    {
        CvMat *matJ = 0, *_err = 0;
        const CvMat *__param = 0;
        bool proceed = solver.update( __param, matJ, _err );
        cvCopy( __param, &_param );
        if( !proceed || !_err )
            break;
        cvReshape( _err, _err, 2, 1 );
        if( matJ )
        {
            cvGetCols( matJ, &_dpdr, 0, 3 );
            cvGetCols( matJ, &_dpdt, 3, 6 );
            cvProjectPoints2( matM, &_r, &_t, &matA, distCoeffs,
                              _err, &_dpdr, &_dpdt, 0, 0, 0 );
        }
        else
        {
            cvProjectPoints2( matM, &_r, &_t, &matA, distCoeffs,
                              _err, 0, 0, 0, 0, 0 );
        }
        cvSub(_err, _m, _err);
        cvReshape( _err, _err, 1, 2*count );
    }
    cvCopy( solver.param, &_param );

    _r = cvMat( rvec->rows, rvec->cols,
        CV_MAKETYPE(CV_64F,CV_MAT_CN(rvec->type)), param );
    _t = cvMat( tvec->rows, tvec->cols,
        CV_MAKETYPE(CV_64F,CV_MAT_CN(tvec->type)), param + 3 );

    cvConvert( &_r, rvec );
    cvConvert( &_t, tvec );
}

HomographyEstimatorCallback   runKernel

//主要方法
    int runKernel( InputArray _m1, InputArray _m2, OutputArray _model ) const CV_OVERRIDE
    {
        //输入参数,获取点的数量
        Mat m1 = _m1.getMat(), m2 = _m2.getMat();
        int i, count = m1.checkVector(2);
        const Point2f* M = m1.ptr<Point2f>();
        const Point2f* m = m2.ptr<Point2f>();
        //变量初始化
        double LtL[9][9], W[9][1], V[9][9];
        Mat _LtL( 9, 9, CV_64F, &LtL[0][0] );
        Mat matW( 9, 1, CV_64F, W );
        Mat matV( 9, 9, CV_64F, V );
        Mat _H0( 3, 3, CV_64F, V[8] );
        Mat _Htemp( 3, 3, CV_64F, V[7] );
        Point2d cM(0,0), cm(0,0), sM(0,0), sm(0,0);
        //求和
        for( i = 0; i < count; i++ )
        {
            cm.x += m[i].x; cm.y += m[i].y;
            cM.x += M[i].x; cM.y += M[i].y;
        }
        //求平均
        cm.x /= count;
        cm.y /= count;
        cM.x /= count;
        cM.y /= count;
        //求每个点相对于平均点的偏差
        for( i = 0; i < count; i++ )
        {
            sm.x += fabs(m[i].x - cm.x);
            sm.y += fabs(m[i].y - cm.y);
            sM.x += fabs(M[i].x - cM.x);
            sM.y += fabs(M[i].y - cM.y);
        }
        //如果所有点在一条线上,就没有意义
        if( fabs(sm.x) < DBL_EPSILON || fabs(sm.y) < DBL_EPSILON ||
            fabs(sM.x) < DBL_EPSILON || fabs(sM.y) < DBL_EPSILON )
            return 0;
        //求所有点相对于中心点偏差 的倒数sm 是么m2  sM 是 m1
        sm.x = count/sm.x; sm.y = count/sm.y;
        sM.x = count/sM.x; sM.y = count/sM.y;

        double invHnorm[9] = { 1./sm.x, 0, cm.x, 0, 1./sm.y, cm.y, 0, 0, 1 };
        double Hnorm2[9] = { sM.x, 0, -cM.x*sM.x, 0, sM.y, -cM.y*sM.y, 0, 0, 1 };
        Mat _invHnorm( 3, 3, CV_64FC1, invHnorm );
        Mat _Hnorm2( 3, 3, CV_64FC1, Hnorm2 );

        _LtL.setTo(Scalar::all(0));
        for( i = 0; i < count; i++ )
        {
            double x = (m[i].x - cm.x)*sm.x, y = (m[i].y - cm.y)*sm.y;
            double X = (M[i].x - cM.x)*sM.x, Y = (M[i].y - cM.y)*sM.y;
            double Lx[] = { X, Y, 1, 0, 0, 0, -x*X, -x*Y, -x };
            double Ly[] = { 0, 0, 0, X, Y, 1, -y*X, -y*Y, -y };
            int j, k;
            for( j = 0; j < 9; j++ )
                for( k = j; k < 9; k++ )
                    LtL[j][k] += Lx[j]*Lx[k] + Ly[j]*Ly[k];
        }
        completeSymm( _LtL );

        eigen( _LtL, matW, matV );
        _Htemp = _invHnorm*_H0;
        _H0 = _Htemp*_Hnorm2;
        _H0.convertTo(_model, _H0.type(), 1./_H0.at<double>(2,2) );

        return 1;
    }

代码阅读基本到这里结束,省掉了3d到2d映射的求导检查以及n点透视变换的代码阅读。接下来会对omni的双目标定进行检查,重写相关代码。

今天的文章cv2.imread函数_cv2.imread函数分享到此就结束了,感谢您的阅读。

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