opencv迭代去畸变算法(含源码分析)

时间:2024-04-13 18:58:17
  • 函数简介

opencv中函数undistortPoints()用于对图像点坐标进行去畸变,以下为该函数解释:

void undistortPoints(InputArray src, OutputArray dst, InputArray cameraMatrix, InputArray distCoeffs, InputArray R=noArray(), InputArray P=noArray())

src-原图像坐标;dst-输出图像坐标;cameraMatrix-相机内参矩阵;distCoeffs-畸变系数,有四种畸变模型,分别含有4,5,8个元素,通常使用具有4/5个参数的模型,如果该向量为NULL,那么设定该图像没有畸变;R-相机坐标系的矫正矩阵(即对相机坐标系的位姿调整,见stereoRectify函数中的Rl,Rr),如果矩阵为空,那么默认使用单位矩阵;P-新的相机矩阵(3x3)或者新的投影矩阵(3x4,包含相机坐标系相对世界坐标系的相对位姿,见stereoRectify函数中的Pl,Pr),如该矩阵为空的话,将设置该矩阵为单位阵。

  • 源码分析

void cvUndistortPointsInternal( const CvMat* _src, CvMat* _dst, const CvMat* _cameraMatrix,
                   const CvMat* _distCoeffs,
                   const CvMat* matR, const CvMat* matP, cv::TermCriteria criteria)
{
	// 判断迭代条件是否有效
    CV_Assert(criteria.isValid());
	// 定义中间变量--A相机内参数组,和matA共享内存;RR-矫正变换数组,和_RR共享内存
	// k-畸变系数数组
    double A[3][3], RR[3][3], k[14]={0,0,0,0,0,0,0,0,0,0,0,0,0,0};
    CvMat matA=cvMat(3, 3, CV_64F, A), _Dk;
    CvMat _RR=cvMat(3, 3, CV_64F, RR);
    cv::Matx33d invMatTilt = cv::Matx33d::eye();
    cv::Matx33d matTilt = cv::Matx33d::eye();
	
	// 检查输入变量是否有效
    CV_Assert( CV_IS_MAT(_src) && CV_IS_MAT(_dst) &&
        (_src->rows == 1 || _src->cols == 1) &&
        (_dst->rows == 1 || _dst->cols == 1) &&
        _src->cols + _src->rows - 1 == _dst->rows + _dst->cols - 1 &&
        (CV_MAT_TYPE(_src->type) == CV_32FC2 || CV_MAT_TYPE(_src->type) == CV_64FC2) &&
        (CV_MAT_TYPE(_dst->type) == CV_32FC2 || CV_MAT_TYPE(_dst->type) == CV_64FC2));

    CV_Assert( CV_IS_MAT(_cameraMatrix) &&
        _cameraMatrix->rows == 3 && _cameraMatrix->cols == 3 );

    cvConvert( _cameraMatrix, &matA );// _cameraMatrix <--> matA / A

	// 判断输入的畸变系数是否有效
    if( _distCoeffs )
    {
        CV_Assert( CV_IS_MAT(_distCoeffs) &&
            (_distCoeffs->rows == 1 || _distCoeffs->cols == 1) &&
            (_distCoeffs->rows*_distCoeffs->cols == 4 ||
             _distCoeffs->rows*_distCoeffs->cols == 5 ||
             _distCoeffs->rows*_distCoeffs->cols == 8 ||
             _distCoeffs->rows*_distCoeffs->cols == 12 ||
             _distCoeffs->rows*_distCoeffs->cols == 14));

        _Dk = cvMat( _distCoeffs->rows, _distCoeffs->cols,
            CV_MAKETYPE(CV_64F,CV_MAT_CN(_distCoeffs->type)), k);// _Dk和数组k共享内存指针

        cvConvert( _distCoeffs, &_Dk );
        if (k[12] != 0 || k[13] != 0)
        {
            cv::detail::computeTiltProjectionMatrix<double>(k[12], k[13], NULL, NULL, NULL, &invMatTilt);
            cv::detail::computeTiltProjectionMatrix<double>(k[12], k[13], &matTilt, NULL, NULL);
        }
    }

    if( matR )
    {
        CV_Assert( CV_IS_MAT(matR) && matR->rows == 3 && matR->cols == 3 );
        cvConvert( matR, &_RR );// matR和_RR共享内存指针
    }
    else
        cvSetIdentity(&_RR);

    if( matP )
    {
        double PP[3][3];
        CvMat _P3x3, _PP=cvMat(3, 3, CV_64F, PP);
        CV_Assert( CV_IS_MAT(matP) && matP->rows == 3 && (matP->cols == 3 || matP->cols == 4));
        cvConvert( cvGetCols(matP, &_P3x3, 0, 3), &_PP );// _PP和数组PP共享内存指针
        cvMatMul( &_PP, &_RR, &_RR );// _RR=_PP*_RR 放在一起计算比较高效
    }

    const CvPoint2D32f* srcf = (const CvPoint2D32f*)_src->data.ptr;
    const CvPoint2D64f* srcd = (const CvPoint2D64f*)_src->data.ptr;
    CvPoint2D32f* dstf = (CvPoint2D32f*)_dst->data.ptr;
    CvPoint2D64f* dstd = (CvPoint2D64f*)_dst->data.ptr;
    int stype = CV_MAT_TYPE(_src->type);
    int dtype = CV_MAT_TYPE(_dst->type);
    int sstep = _src->rows == 1 ? 1 : _src->step/CV_ELEM_SIZE(stype);
    int dstep = _dst->rows == 1 ? 1 : _dst->step/CV_ELEM_SIZE(dtype);

    double fx = A[0][0];
    double fy = A[1][1];
    double ifx = 1./fx;
    double ify = 1./fy;
    double cx = A[0][2];
    double cy = A[1][2];

    int n = _src->rows + _src->cols - 1;
	// 开始对所有点开始遍历
    for( int i = 0; i < n; i++ )
    {
        double x, y, x0 = 0, y0 = 0, u, v;
        if( stype == CV_32FC2 )
        {
            x = srcf[i*sstep].x;
            y = srcf[i*sstep].y;
        }
        else
        {
            x = srcd[i*sstep].x;
            y = srcd[i*sstep].y;
        }
        u = x; v = y;
        x = (x - cx)*ifx;//转换到归一化图像坐标系(含有畸变)
        y = (y - cy)*ify;

		//进行畸变矫正
        if( _distCoeffs ) {
            // compensate tilt distortion--该部分系数用来弥补沙氏镜头畸变??
			// 如果不懂也没管,因为普通镜头中没有这些畸变系数
            cv::Vec3d vecUntilt = invMatTilt * cv::Vec3d(x, y, 1);
            double invProj = vecUntilt(2) ? 1./vecUntilt(2) : 1;
            x0 = x = invProj * vecUntilt(0);
            y0 = y = invProj * vecUntilt(1);

            double error = std::numeric_limits<double>::max();// error设定为系统最大值
            // compensate distortion iteratively
			// 迭代去除镜头畸变
			// 迭代公式    x′= (x−2p1 xy−p2 (r^2 + 2x^2))∕( 1 + k1*r^2 + k2*r^4 + k3*r^6)
			//             y′= (y−2p2 xy−p1 (r^2 + 2y^2))∕( 1 + k1*r^2 + k2*r^4 + k3*r^6)

            for( int j = 0; ; j++ )
            {
                if ((criteria.type & cv::TermCriteria::COUNT) && j >= criteria.maxCount)// 迭代最大次数为5次
                    break;
                if ((criteria.type & cv::TermCriteria::EPS) && error < criteria.epsilon)// 迭代误差阈值为0.01
                    break;
                double r2 = x*x + y*y;
                double icdist = (1 + ((k[7]*r2 + k[6])*r2 + k[5])*r2)/(1 + ((k[4]*r2 + k[1])*r2 + k[0])*r2);
                double deltaX = 2*k[2]*x*y + k[3]*(r2 + 2*x*x)+ k[8]*r2+k[9]*r2*r2;
                double deltaY = k[2]*(r2 + 2*y*y) + 2*k[3]*x*y+ k[10]*r2+k[11]*r2*r2;
                x = (x0 - deltaX)*icdist;
                y = (y0 - deltaY)*icdist;

				// 对当前迭代的坐标加畸变,计算误差error用于判断迭代条件
                if(criteria.type & cv::TermCriteria::EPS)
                {
                    double r4, r6, a1, a2, a3, cdist, icdist2;
                    double xd, yd, xd0, yd0;
                    cv::Vec3d vecTilt;

                    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);
                    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;

                    vecTilt = matTilt*cv::Vec3d(xd0, yd0, 1);
                    invProj = vecTilt(2) ? 1./vecTilt(2) : 1;
                    xd = invProj * vecTilt(0);
                    yd = invProj * vecTilt(1);

                    double x_proj = xd*fx + cx;
                    double y_proj = yd*fy + cy;

                    error = sqrt( pow(x_proj - u, 2) + pow(y_proj - v, 2) );
                }
            }
        }
		// 将坐标从归一化图像坐标系转换到成像平面坐标系
        double xx = RR[0][0]*x + RR[0][1]*y + RR[0][2];
        double yy = RR[1][0]*x + RR[1][1]*y + RR[1][2];
        double ww = 1./(RR[2][0]*x + RR[2][1]*y + RR[2][2]);
        x = xx*ww;
        y = yy*ww;

        if( dtype == CV_32FC2 )
        {
            dstf[i*dstep].x = (float)x;
            dstf[i*dstep].y = (float)y;
        }
        else
        {
            dstd[i*dstep].x = x;
            dstd[i*dstep].y = y;
        }
    }
}

该函数所实现的迭代算法很简单,只要了解相机的畸变模型就可以很容易理解函数的实现过程了。

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opencv迭代去畸变算法(含源码分析)

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