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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。
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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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