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omnidir.cpp
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omnidir.cpp
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/*M///////////////////////////////////////////////////////////////////////////////////////
//
// IMPORTANT: READ BEFORE DOWNLOADING, COPYING, INSTALLING OR USING.
//
// By downloading, copying, installing or using the software you agree to this license.
// If you do not agree to this license, do not download, install,
// copy or use the software.
//
//
// License Agreement
// For Open Source Computer Vision Library
//
// Copyright (C) 2015, Baisheng Lai (laibaisheng@gmail.com), Zhejiang University,
// all rights reserved.
//
// Redistribution and use in source and binary forms, with or without modification,
// are permitted provided that the following conditions are met:
//
// * Redistribution's of source code must retain the above copyright notice,
// this list of conditions and the following disclaimer.
//
// * Redistribution's in binary form must reproduce the above copyright notice,
// this list of conditions and the following disclaimer in the documentation
// and/or other materials provided with the distribution.
//
// * The name of the copyright holders may not be used to endorse or promote products
// derived from this software without specific prior written permission.
//
// This software is provided by the copyright holders and contributors "as is" and
// any express or implied warranties, including, but not limited to, the implied
// warranties of merchantability and fitness for a particular purpose are disclaimed.
// In no event shall the Intel Corporation or contributors be liable for any direct,
// indirect, incidental, special, exemplary, or consequential damages
// (including, but not limited to, procurement of substitute goods or services;
// loss of use, data, or profits; or business interruption) however caused
// and on any theory of liability, whether in contract, strict liability,
// or tort (including negligence or otherwise) arising in any way out of
// the use of this software, even if advised of the possibility of such damage.
//
//M*/
/**
* This module was accepted as a GSoC 2015 project for OpenCV, authored by
* Baisheng Lai, mentored by Bo Li.
*
* The omnidirectional camera in this module is denoted by the catadioptric
* model. Please refer to Mei's paper for details of the camera model:
*
* C. Mei and P. Rives, "Single view point omnidirectional camera
* calibration from planar grids", in ICRA 2007.
*
* The implementation of the calibration part is based on Li's calibration
* toolbox:
*
* B. Li, L. Heng, K. Kevin and M. Pollefeys, "A Multiple-Camera System
* Calibration Toolbox Using A Feature Descriptor-Based Calibration
* Pattern", in IROS 2013.
*/
#include "precomp.hpp"
#include "opencv2/ccalib/omnidir.hpp"
#include <fstream>
#include <iostream>
namespace cv { namespace
{
struct JacobianRow
{
Matx13d dom,dT;
Matx12d df;
double ds;
Matx12d dc;
double dxi;
Matx14d dkp; // distortion k1,k2,p1,p2
};
}}
/////////////////////////////////////////////////////////////////////////////
//////// projectPoints
void cv::omnidir::projectPoints(InputArray objectPoints, OutputArray imagePoints,
const Affine3d& affine, InputArray K, double xi, InputArray D, OutputArray jacobian)
{
projectPoints(objectPoints, imagePoints, affine.rvec(), affine.translation(), K, xi, D, jacobian);
}
void cv::omnidir::projectPoints(InputArray objectPoints, OutputArray imagePoints,
InputArray rvec, InputArray tvec, InputArray K, double xi, InputArray D, OutputArray jacobian)
{
CV_Assert(objectPoints.type() == CV_64FC3 || objectPoints.type() == CV_32FC3);
CV_Assert((rvec.depth() == CV_64F || rvec.depth() == CV_32F) && rvec.total() == 3);
CV_Assert((tvec.depth() == CV_64F || tvec.depth() == CV_32F) && tvec.total() == 3);
CV_Assert((K.type() == CV_64F || K.type() == CV_32F) && K.size() == Size(3,3));
CV_Assert((D.type() == CV_64F || D.type() == CV_32F) && D.total() == 4);
imagePoints.create(objectPoints.size(), CV_MAKETYPE(objectPoints.depth(), 2));
int n = (int)objectPoints.total();
Vec3d om = rvec.depth() == CV_32F ? (Vec3d)*rvec.getMat().ptr<Vec3f>() : *rvec.getMat().ptr<Vec3d>();
Vec3d T = tvec.depth() == CV_32F ? (Vec3d)*tvec.getMat().ptr<Vec3f>() : *tvec.getMat().ptr<Vec3d>();
Vec2d f,c;
double s;
if (K.depth() == CV_32F)
{
Matx33f Kc = K.getMat();
f = Vec2f(Kc(0,0), Kc(1,1));
c = Vec2f(Kc(0,2),Kc(1,2));
s = (double)Kc(0,1);
}
else
{
Matx33d Kc = K.getMat();
f = Vec2d(Kc(0,0), Kc(1,1));
c = Vec2d(Kc(0,2),Kc(1,2));
s = Kc(0,1);
}
Vec4d kp = D.depth() == CV_32F ? (Vec4d)*D.getMat().ptr<Vec4f>() : *D.getMat().ptr<Vec4d>();
//Vec<double, 4> kp= (Vec<double,4>)*D.getMat().ptr<Vec<double,4> >();
const Vec3d* Xw_alld = objectPoints.getMat().ptr<Vec3d>();
const Vec3f* Xw_allf = objectPoints.getMat().ptr<Vec3f>();
Vec2d* xpd = imagePoints.getMat().ptr<Vec2d>();
Vec2f* xpf = imagePoints.getMat().ptr<Vec2f>();
Matx33d R;
Matx<double, 3, 9> dRdom;
Rodrigues(om, R, dRdom);
JacobianRow *Jn = 0;
if (jacobian.needed())
{
int nvars = 2+2+1+4+3+3+1; // f,c,s,kp,om,T,xi
jacobian.create(2*int(n), nvars, CV_64F);
Jn = jacobian.getMat().ptr<JacobianRow>(0);
}
double k1=kp[0],k2=kp[1];
double p1 = kp[2], p2 = kp[3];
for (int i = 0; i < n; i++)
{
// convert to camera coordinate
Vec3d Xw = objectPoints.depth() == CV_32F ? (Vec3d)Xw_allf[i] : Xw_alld[i];
Vec3d Xc = (Vec3d)(R*Xw + T);
// convert to unit sphere
Vec3d Xs = Xc/cv::norm(Xc);
// convert to normalized image plane
Vec2d xu = Vec2d(Xs[0]/(Xs[2]+xi), Xs[1]/(Xs[2]+xi));
// add distortion
Vec2d xd;
double r2 = xu[0]*xu[0]+xu[1]*xu[1];
double r4 = r2*r2;
xd[0] = xu[0]*(1+k1*r2+k2*r4) + 2*p1*xu[0]*xu[1] + p2*(r2+2*xu[0]*xu[0]);
xd[1] = xu[1]*(1+k1*r2+k2*r4) + p1*(r2+2*xu[1]*xu[1]) + 2*p2*xu[0]*xu[1];
// convert to pixel coordinate
Vec2d final;
final[0] = f[0]*xd[0]+s*xd[1]+c[0];
final[1] = f[1]*xd[1]+c[1];
if (objectPoints.depth() == CV_32F)
{
xpf[i] = final;
}
else
{
xpd[i] = final;
}
/*xpd[i][0] = f[0]*xd[0]+s*xd[1]+c[0];
xpd[i][1] = f[1]*xd[1]+c[1];*/
if (jacobian.needed())
{
double dXcdR_a[] = {Xw[0],Xw[1],Xw[2],0,0,0,0,0,0,
0,0,0,Xw[0],Xw[1],Xw[2],0,0,0,
0,0,0,0,0,0,Xw[0],Xw[1],Xw[2]};
Matx<double,3, 9> dXcdR(dXcdR_a);
Matx33d dXcdom = dXcdR * dRdom.t();
double r_1 = 1.0/norm(Xc);
double r_3 = pow(r_1,3);
Matx33d dXsdXc(r_1-Xc[0]*Xc[0]*r_3, -(Xc[0]*Xc[1])*r_3, -(Xc[0]*Xc[2])*r_3,
-(Xc[0]*Xc[1])*r_3, r_1-Xc[1]*Xc[1]*r_3, -(Xc[1]*Xc[2])*r_3,
-(Xc[0]*Xc[2])*r_3, -(Xc[1]*Xc[2])*r_3, r_1-Xc[2]*Xc[2]*r_3);
Matx23d dxudXs(1/(Xs[2]+xi), 0, -Xs[0]/(Xs[2]+xi)/(Xs[2]+xi),
0, 1/(Xs[2]+xi), -Xs[1]/(Xs[2]+xi)/(Xs[2]+xi));
// pre-compute some reusable things
double temp1 = 2*k1*xu[0] + 4*k2*xu[0]*r2;
double temp2 = 2*k1*xu[1] + 4*k2*xu[1]*r2;
Matx22d dxddxu(k2*r4+6*p2*xu[0]+2*p1*xu[1]+xu[0]*temp1+k1*r2+1, 2*p1*xu[0]+2*p2*xu[1]+xu[0]*temp2,
2*p1*xu[0]+2*p2*xu[1]+xu[1]*temp1, k2*r4+2*p2*xu[0]+6*p1*xu[1]+xu[1]*temp2+k1*r2+1);
Matx22d dxpddxd(f[0], s,
0, f[1]);
Matx23d dxpddXc = dxpddxd * dxddxu * dxudXs * dXsdXc;
// derivative of xpd respect to om
Matx23d dxpddom = dxpddXc * dXcdom;
Matx33d dXcdT(1.0,0.0,0.0,
0.0,1.0,0.0,
0.0,0.0,1.0);
// derivative of xpd respect to T
Matx23d dxpddT = dxpddXc * dXcdT;
Matx21d dxudxi(-Xs[0]/(Xs[2]+xi)/(Xs[2]+xi),
-Xs[1]/(Xs[2]+xi)/(Xs[2]+xi));
// derivative of xpd respect to xi
Matx21d dxpddxi = dxpddxd * dxddxu * dxudxi;
Matx<double,2,4> dxddkp(xu[0]*r2, xu[0]*r4, 2*xu[0]*xu[1], r2+2*xu[0]*xu[0],
xu[1]*r2, xu[1]*r4, r2+2*xu[1]*xu[1], 2*xu[0]*xu[1]);
// derivative of xpd respect to kp
Matx<double,2,4> dxpddkp = dxpddxd * dxddkp;
// derivative of xpd respect to f
Matx22d dxpddf(xd[0], 0,
0, xd[1]);
// derivative of xpd respect to c
Matx22d dxpddc(1, 0,
0, 1);
Jn[0].dom = dxpddom.row(0);
Jn[1].dom = dxpddom.row(1);
Jn[0].dT = dxpddT.row(0);
Jn[1].dT = dxpddT.row(1);
Jn[0].dkp = dxpddkp.row(0);
Jn[1].dkp = dxpddkp.row(1);
Jn[0].dxi = dxpddxi(0,0);
Jn[1].dxi = dxpddxi(1,0);
Jn[0].df = dxpddf.row(0);
Jn[1].df = dxpddf.row(1);
Jn[0].dc = dxpddc.row(0);
Jn[1].dc = dxpddc.row(1);
Jn[0].ds = xd[1];
Jn[1].ds = 0;
Jn += 2;
}
}
}
/////////////////////////////////////////////////////////////////////////////
//////// undistortPoints
void cv::omnidir::undistortPoints( InputArray distorted, OutputArray undistorted,
InputArray K, InputArray D, InputArray xi, InputArray R)
{
CV_Assert(distorted.type() == CV_64FC2 || distorted.type() == CV_32FC2);
CV_Assert(R.empty() || (!R.empty() && (R.size() == Size(3, 3) || R.total() * R.channels() == 3)
&& (R.depth() == CV_64F || R.depth() == CV_32F)));
CV_Assert((D.depth() == CV_64F || D.depth() == CV_32F) && D.total() == 4);
CV_Assert(K.size() == Size(3, 3) && (K.depth() == CV_64F || K.depth() == CV_32F));
CV_Assert(xi.total() == 1 && (xi.depth() == CV_64F || xi.depth() == CV_32F));
undistorted.create(distorted.size(), distorted.type());
cv::Vec2d f, c;
double s = 0.0;
if (K.depth() == CV_32F)
{
Matx33f camMat = K.getMat();
f = Vec2f(camMat(0,0), camMat(1,1));
c = Vec2f(camMat(0,2), camMat(1,2));
s = (double)camMat(0,1);
}
else if (K.depth() == CV_64F)
{
Matx33d camMat = K.getMat();
f = Vec2d(camMat(0,0), camMat(1,1));
c = Vec2d(camMat(0,2), camMat(1,2));
s = camMat(0,1);
}
Vec4d kp = D.depth()==CV_32F ? (Vec4d)*D.getMat().ptr<Vec4f>():(Vec4d)*D.getMat().ptr<Vec4d>();
Vec2d k = Vec2d(kp[0], kp[1]);
Vec2d p = Vec2d(kp[2], kp[3]);
double _xi = xi.depth() == CV_32F ? (double)*xi.getMat().ptr<float>() : *xi.getMat().ptr<double>();
cv::Matx33d RR = cv::Matx33d::eye();
// R is om
if(!R.empty() && R.total()*R.channels() == 3)
{
cv::Vec3d rvec;
R.getMat().convertTo(rvec, CV_64F);
cv::Rodrigues(rvec, RR);
}
else if (!R.empty() && R.size() == Size(3,3))
{
R.getMat().convertTo(RR, CV_64F);
}
const cv::Vec2d *srcd = distorted.getMat().ptr<cv::Vec2d>();
const cv::Vec2f *srcf = distorted.getMat().ptr<cv::Vec2f>();
cv::Vec2d *dstd = undistorted.getMat().ptr<cv::Vec2d>();
cv::Vec2f *dstf = undistorted.getMat().ptr<cv::Vec2f>();
int n = (int)distorted.total();
for (int i = 0; i < n; i++)
{
Vec2d pi = distorted.depth() == CV_32F ? (Vec2d)srcf[i]:(Vec2d)srcd[i]; // image point
Vec2d pp((pi[0]*f[1]-c[0]*f[1]-s*(pi[1]-c[1]))/(f[0]*f[1]), (pi[1]-c[1])/f[1]); //plane
Vec2d pu = pp; // points without distortion
// remove distortion iteratively
for (int j = 0; j < 20; j++)
{
double r2 = pu[0]*pu[0] + pu[1]*pu[1];
double r4 = r2*r2;
pu[0] = (pp[0] - 2*p[0]*pu[0]*pu[1] - p[1]*(r2+2*pu[0]*pu[0])) / (1 + k[0]*r2 + k[1]*r4);
pu[1] = (pp[1] - 2*p[1]*pu[0]*pu[1] - p[0]*(r2+2*pu[1]*pu[1])) / (1 + k[0]*r2 + k[1]*r4);
}
// project to unit sphere
double r2 = pu[0]*pu[0] + pu[1]*pu[1];
double a = (r2 + 1);
double b = 2*_xi*r2;
double cc = r2*_xi*_xi-1;
double Zs = (-b + sqrt(b*b - 4*a*cc))/(2*a);
Vec3d Xw = Vec3d(pu[0]*(Zs + _xi), pu[1]*(Zs +_xi), Zs);
// rotate
Xw = RR * Xw;
// project back to sphere
Vec3d Xs = Xw / cv::norm(Xw);
// reproject to camera plane
Vec3d ppu = Vec3d(Xs[0]/Xs[2], Xs[1]/Xs[2], 1.0);
if (undistorted.depth() == CV_32F)
{
dstf[i] = Vec2f((float)ppu[0], (float)ppu[1]);
}
else if (undistorted.depth() == CV_64F)
{
dstd[i] = Vec2d(ppu[0], ppu[1]);
}
}
}
/////////////////////////////////////////////////////////////////////////////
//////// cv::omnidir::initUndistortRectifyMap
void cv::omnidir::initUndistortRectifyMap(InputArray K, InputArray D, InputArray xi, InputArray R, InputArray P,
const cv::Size& size, int m1type, OutputArray map1, OutputArray map2, int flags)
{
CV_Assert( m1type == CV_16SC2 || m1type == CV_32F || m1type <=0 );
map1.create( size, m1type <= 0 ? CV_16SC2 : m1type );
map2.create( size, map1.type() == CV_16SC2 ? CV_16UC1 : CV_32F );
CV_Assert((K.depth() == CV_32F || K.depth() == CV_64F) && (D.depth() == CV_32F || D.depth() == CV_64F));
CV_Assert(K.size() == Size(3, 3) && (D.empty() || D.total() == 4));
CV_Assert(P.empty()|| (P.depth() == CV_32F || P.depth() == CV_64F));
CV_Assert(P.empty() || P.size() == Size(3, 3) || P.size() == Size(4, 3));
CV_Assert(R.empty() || (R.depth() == CV_32F || R.depth() == CV_64F));
CV_Assert(R.empty() || R.size() == Size(3, 3) || R.total() * R.channels() == 3);
CV_Assert(flags == RECTIFY_PERSPECTIVE || flags == RECTIFY_CYLINDRICAL || flags == RECTIFY_LONGLATI
|| flags == RECTIFY_STEREOGRAPHIC);
CV_Assert(xi.total() == 1 && (xi.depth() == CV_32F || xi.depth() == CV_64F));
cv::Vec2d f, c;
double s;
if (K.depth() == CV_32F)
{
Matx33f camMat = K.getMat();
f = Vec2f(camMat(0, 0), camMat(1, 1));
c = Vec2f(camMat(0, 2), camMat(1, 2));
s = (double)camMat(0,1);
}
else
{
Matx33d camMat = K.getMat();
f = Vec2d(camMat(0, 0), camMat(1, 1));
c = Vec2d(camMat(0, 2), camMat(1, 2));
s = camMat(0,1);
}
Vec4d kp = Vec4d::all(0);
if (!D.empty())
kp = D.depth() == CV_32F ? (Vec4d)*D.getMat().ptr<Vec4f>(): *D.getMat().ptr<Vec4d>();
double _xi = xi.depth() == CV_32F ? (double)*xi.getMat().ptr<float>() : *xi.getMat().ptr<double>();
Vec2d k = Vec2d(kp[0], kp[1]);
Vec2d p = Vec2d(kp[2], kp[3]);
cv::Matx33d RR = cv::Matx33d::eye();
if (!R.empty() && R.total() * R.channels() == 3)
{
cv::Vec3d rvec;
R.getMat().convertTo(rvec, CV_64F);
cv::Rodrigues(rvec, RR);
}
else if (!R.empty() && R.size() == Size(3, 3))
R.getMat().convertTo(RR, CV_64F);
cv::Matx33d PP = cv::Matx33d::eye();
if (!P.empty())
P.getMat().colRange(0, 3).convertTo(PP, CV_64F);
else
PP = K.getMat();
cv::Matx33d iKR = (PP*RR).inv(cv::DECOMP_SVD);
cv::Matx33d iK = PP.inv(cv::DECOMP_SVD);
cv::Matx33d iR = RR.inv(cv::DECOMP_SVD);
if (flags == omnidir::RECTIFY_PERSPECTIVE)
{
for (int i = 0; i < size.height; ++i)
{
float* m1f = map1.getMat().ptr<float>(i);
float* m2f = map2.getMat().ptr<float>(i);
short* m1 = (short*)m1f;
ushort* m2 = (ushort*)m2f;
double _x = i*iKR(0, 1) + iKR(0, 2),
_y = i*iKR(1, 1) + iKR(1, 2),
_w = i*iKR(2, 1) + iKR(2, 2);
for(int j = 0; j < size.width; ++j, _x+=iKR(0,0), _y+=iKR(1,0), _w+=iKR(2,0))
{
// project back to unit sphere
double r = sqrt(_x*_x + _y*_y + _w*_w);
double Xs = _x / r;
double Ys = _y / r;
double Zs = _w / r;
// project to image plane
double xu = Xs / (Zs + _xi),
yu = Ys / (Zs + _xi);
// add distortion
double r2 = xu*xu + yu*yu;
double r4 = r2*r2;
double xd = (1+k[0]*r2+k[1]*r4)*xu + 2*p[0]*xu*yu + p[1]*(r2+2*xu*xu);
double yd = (1+k[0]*r2+k[1]*r4)*yu + p[0]*(r2+2*yu*yu) + 2*p[1]*xu*yu;
// to image pixel
double u = f[0]*xd + s*yd + c[0];
double v = f[1]*yd + c[1];
if( m1type == CV_16SC2 )
{
int iu = cv::saturate_cast<int>(u*cv::INTER_TAB_SIZE);
int iv = cv::saturate_cast<int>(v*cv::INTER_TAB_SIZE);
m1[j*2+0] = (short)(iu >> cv::INTER_BITS);
m1[j*2+1] = (short)(iv >> cv::INTER_BITS);
m2[j] = (ushort)((iv & (cv::INTER_TAB_SIZE-1))*cv::INTER_TAB_SIZE + (iu & (cv::INTER_TAB_SIZE-1)));
}
else if( m1type == CV_32FC1 )
{
m1f[j] = (float)u;
m2f[j] = (float)v;
}
}
}
}
else if(flags == omnidir::RECTIFY_CYLINDRICAL || flags == omnidir::RECTIFY_LONGLATI ||
flags == omnidir::RECTIFY_STEREOGRAPHIC)
{
for (int i = 0; i < size.height; ++i)
{
float* m1f = map1.getMat().ptr<float>(i);
float* m2f = map2.getMat().ptr<float>(i);
short* m1 = (short*)m1f;
ushort* m2 = (ushort*)m2f;
// for RECTIFY_LONGLATI, theta and h are longittude and latitude
double theta = i*iK(0, 1) + iK(0, 2),
h = i*iK(1, 1) + iK(1, 2);
for (int j = 0; j < size.width; ++j, theta+=iK(0,0), h+=iK(1,0))
{
double _xt = 0.0, _yt = 0.0, _wt = 0.0;
if (flags == omnidir::RECTIFY_CYLINDRICAL)
{
//_xt = std::sin(theta);
//_yt = h;
//_wt = std::cos(theta);
_xt = std::cos(theta);
_yt = std::sin(theta);
_wt = h;
}
else if (flags == omnidir::RECTIFY_LONGLATI)
{
_xt = -std::cos(theta);
_yt = -std::sin(theta) * std::cos(h);
_wt = std::sin(theta) * std::sin(h);
}
else if (flags == omnidir::RECTIFY_STEREOGRAPHIC)
{
double a = theta*theta + h*h + 4;
double b = -2*theta*theta - 2*h*h;
double c2 = theta*theta + h*h -4;
_yt = (-b-std::sqrt(b*b - 4*a*c2))/(2*a);
_xt = theta*(1 - _yt) / 2;
_wt = h*(1 - _yt) / 2;
}
double _x = iR(0,0)*_xt + iR(0,1)*_yt + iR(0,2)*_wt;
double _y = iR(1,0)*_xt + iR(1,1)*_yt + iR(1,2)*_wt;
double _w = iR(2,0)*_xt + iR(2,1)*_yt + iR(2,2)*_wt;
double r = sqrt(_x*_x + _y*_y + _w*_w);
double Xs = _x / r;
double Ys = _y / r;
double Zs = _w / r;
// project to image plane
double xu = Xs / (Zs + _xi),
yu = Ys / (Zs + _xi);
// add distortion
double r2 = xu*xu + yu*yu;
double r4 = r2*r2;
double xd = (1+k[0]*r2+k[1]*r4)*xu + 2*p[0]*xu*yu + p[1]*(r2+2*xu*xu);
double yd = (1+k[0]*r2+k[1]*r4)*yu + p[0]*(r2+2*yu*yu) + 2*p[1]*xu*yu;
// to image pixel
double u = f[0]*xd + s*yd + c[0];
double v = f[1]*yd + c[1];
if( m1type == CV_16SC2 )
{
int iu = cv::saturate_cast<int>(u*cv::INTER_TAB_SIZE);
int iv = cv::saturate_cast<int>(v*cv::INTER_TAB_SIZE);
m1[j*2+0] = (short)(iu >> cv::INTER_BITS);
m1[j*2+1] = (short)(iv >> cv::INTER_BITS);
m2[j] = (ushort)((iv & (cv::INTER_TAB_SIZE-1))*cv::INTER_TAB_SIZE + (iu & (cv::INTER_TAB_SIZE-1)));
}
else if( m1type == CV_32FC1 )
{
m1f[j] = (float)u;
m2f[j] = (float)v;
}
}
}
}
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// cv::omnidir::undistortImage
void cv::omnidir::undistortImage(InputArray distorted, OutputArray undistorted,
InputArray K, InputArray D, InputArray xi, int flags, InputArray Knew, const Size& new_size, InputArray R)
{
Size size = new_size.empty() ? distorted.size() : new_size;
cv::Mat map1, map2;
omnidir::initUndistortRectifyMap(K, D, xi, R, Knew, size, CV_16SC2, map1, map2, flags);
cv::remap(distorted, undistorted, map1, map2, INTER_LINEAR, BORDER_CONSTANT);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// cv::omnidir::internal::initializeCalibration
void cv::omnidir::internal::initializeCalibration(InputArrayOfArrays patternPoints, InputArrayOfArrays imagePoints, Size size,
OutputArrayOfArrays omAll, OutputArrayOfArrays tAll, OutputArray K, double& xi, OutputArray idx)
{
// For details please refer to Section III from Li's IROS 2013 paper
double u0 = size.width / 2;
double v0 = size.height / 2;
int n_img = (int)imagePoints.total();
std::vector<cv::Vec3d> v_omAll(n_img), v_tAll(n_img);
std::vector<double> gammaAll(n_img);
K.create(3, 3, CV_64F);
Mat _K;
for (int image_idx = 0; image_idx < n_img; ++image_idx)
{
cv::Mat objPoints, imgPoints;
patternPoints.getMat(image_idx).copyTo(objPoints);
imagePoints.getMat(image_idx).copyTo(imgPoints);
int n_point = imgPoints.rows * imgPoints.cols;
if (objPoints.rows != n_point)
objPoints = objPoints.reshape(3, n_point);
if (imgPoints.rows != n_point)
imgPoints = imgPoints.reshape(2, n_point);
// objectPoints should be 3-channel data, imagePoints should be 2-channel data
CV_Assert(objPoints.type() == CV_64FC3 && imgPoints.type() == CV_64FC2 );
std::vector<cv::Mat> xy, uv;
cv::split(objPoints, xy);
cv::split(imgPoints, uv);
cv::Mat x = xy[0].reshape(1, n_point), y = xy[1].reshape(1, n_point),
u = uv[0].reshape(1, n_point) - u0, v = uv[1].reshape(1, n_point) - v0;
cv::Mat sqrRho = u.mul(u) + v.mul(v);
// compute extrinsic parameters
cv::Mat M(n_point, 6, CV_64F);
Mat(-v.mul(x)).copyTo(M.col(0));
Mat(-v.mul(y)).copyTo(M.col(1));
Mat(u.mul(x)).copyTo(M.col(2));
Mat(u.mul(y)).copyTo(M.col(3));
Mat(-v).copyTo(M.col(4));
Mat(u).copyTo(M.col(5));
Mat W,U,V;
cv::SVD::compute(M, W, U, V,SVD::FULL_UV);
V = V.t();
double miniReprojectError = 1e5;
// the signs of r1, r2, r3 are unknown, so they can be flipped.
for (int coef = 1; coef >= -1; coef-=2)
{
double r11 = V.at<double>(0, 5) * coef;
double r12 = V.at<double>(1, 5) * coef;
double r21 = V.at<double>(2, 5) * coef;
double r22 = V.at<double>(3, 5) * coef;
double t1 = V.at<double>(4, 5) * coef;
double t2 = V.at<double>(5, 5) * coef;
Mat roots;
double r31s;
solvePoly(Matx13d(-(r11*r12+r21*r22)*(r11*r12+r21*r22), r11*r11+r21*r21-r12*r12-r22*r22, 1), roots);
if (roots.at<Vec2d>(0)[0] > 0)
r31s = sqrt(roots.at<Vec2d>(0)[0]);
else
r31s = sqrt(roots.at<Vec2d>(1)[0]);
for (int coef2 = 1; coef2 >= -1; coef2-=2)
{
double r31 = r31s * coef2;
double r32 = -(r11*r12 + r21*r22) / r31;
cv::Vec3d r1(r11, r21, r31);
cv::Vec3d r2(r12, r22, r32);
cv::Vec3d t(t1, t2, 0);
double scale = 1 / cv::norm(r1);
r1 = r1 * scale;
r2 = r2 * scale;
t = t * scale;
// compute intrisic parameters
// Form equations in Scaramuzza's paper
// A Toolbox for Easily Calibrating Omnidirectional Cameras
Mat A(n_point*2, 3, CV_64F);
Mat((r1[1]*x + r2[1]*y + t[1])/2).copyTo(A.rowRange(0, n_point).col(0));
Mat((r1[0]*x + r2[0]*y + t[0])/2).copyTo(A.rowRange(n_point, 2*n_point).col(0));
Mat(-A.col(0).rowRange(0, n_point).mul(sqrRho)).copyTo(A.col(1).rowRange(0, n_point));
Mat(-A.col(0).rowRange(n_point, 2*n_point).mul(sqrRho)).copyTo(A.col(1).rowRange(n_point, 2*n_point));
Mat(-v).copyTo(A.rowRange(0, n_point).col(2));
Mat(-u).copyTo(A.rowRange(n_point, 2*n_point).col(2));
// Operation to avoid bad numerical-condition of A
Vec3d maxA, minA;
for (int j = 0; j < A.cols; j++)
{
cv::minMaxLoc(cv::abs(A.col(j)), &minA[j], &maxA[j]);
A.col(j) = A.col(j) / maxA[j];
}
Mat B(n_point*2 , 1, CV_64F);
Mat(v.mul(r1[2]*x + r2[2]*y)).copyTo(B.rowRange(0, n_point));
Mat(u.mul(r1[2]*x + r2[2]*y)).copyTo(B.rowRange(n_point, 2*n_point));
Mat res = A.inv(DECOMP_SVD) * B;
res = res.mul(1/Mat(maxA));
double gamma = sqrt(res.at<double>(0) / res.at<double>(1));
t[2] = res.at<double>(2);
cv::Vec3d r3 = r1.cross(r2);
Matx33d R(r1[0], r2[0], r3[0],
r1[1], r2[1], r3[1],
r1[2], r2[2], r3[2]);
Vec3d om;
Rodrigues(R, om);
// project pattern points to images
Mat projedImgPoints;
Matx33d Kc(gamma, 0, u0, 0, gamma, v0, 0, 0, 1);
// reproject error
cv::omnidir::projectPoints(objPoints, projedImgPoints, om, t, Kc, 1, Matx14d(0, 0, 0, 0), cv::noArray());
double reprojectError = omnidir::internal::computeMeanReproErr(imgPoints, projedImgPoints);
// if this reproject error is smaller
if (reprojectError < miniReprojectError)
{
miniReprojectError = reprojectError;
v_omAll[image_idx] = om;
v_tAll[image_idx] = t;
gammaAll[image_idx] = gamma;
}
}
}
}
// filter initial results whose reproject errors are too large
std::vector<double> reProjErrorFilter,v_gammaFilter;
std::vector<Vec3d> omFilter, tFilter;
double gammaFinal = 0;
// choose median value
size_t n = gammaAll.size() / 2;
std::nth_element(gammaAll.begin(), gammaAll.begin()+n, gammaAll.end());
gammaFinal = gammaAll[n];
_K = Mat(Matx33d(gammaFinal, 0, u0, 0, gammaFinal, v0, 0, 0, 1));
_K.convertTo(K, CV_64F);
std::vector<int> _idx;
// recompute reproject error using the final gamma
for (int i = 0; i< n_img; i++)
{
Mat _projected;
cv::omnidir::projectPoints(patternPoints.getMat(i), _projected, v_omAll[i], v_tAll[i], _K, 1, Matx14d(0, 0, 0, 0), cv::noArray());
double _error = omnidir::internal::computeMeanReproErr(imagePoints.getMat(i), _projected);
if(_error < 100)
{
_idx.push_back(i);
omFilter.push_back(v_omAll[i]);
tFilter.push_back(v_tAll[i]);
}
}
if (idx.needed())
{
idx.create(1, (int)_idx.size(), CV_32S);
Mat idx_m = idx.getMat();
for (int j = 0; j < (int)idx_m.total(); j++)
{
idx_m.at<int>(j) = _idx[j];
}
}
if(omAll.kind() == _InputArray::STD_VECTOR_MAT)
{
for (int i = 0; i < (int)omFilter.size(); ++i)
{
omAll.getMat(i) = Mat(omFilter[i]);
tAll.getMat(i) = Mat(tFilter[i]);
}
}
else
{
cv::Mat(omFilter).convertTo(omAll, CV_64FC3);
cv::Mat(tFilter).convertTo(tAll, CV_64FC3);
}
xi = 1;
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// cv::omnidir::internal::initializeStereoCalibration
void cv::omnidir::internal::initializeStereoCalibration(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
const Size& size1, const Size& size2, OutputArray om, OutputArray T, OutputArrayOfArrays omL, OutputArrayOfArrays tL, OutputArray K1, OutputArray D1, OutputArray K2, OutputArray D2,
double &xi1, double &xi2, int flags, OutputArray idx)
{
Mat idx1, idx2;
Matx33d _K1, _K2;
Matx14d _D1, _D2;
Mat _xi1m, _xi2m;
std::vector<Vec3d> omAllTemp1, omAllTemp2, tAllTemp1, tAllTemp2;
omnidir::calibrate(objectPoints, imagePoints1, size1, _K1, _xi1m, _D1, omAllTemp1, tAllTemp1, flags, TermCriteria(3, 100, 1e-6), idx1);
omnidir::calibrate(objectPoints, imagePoints2, size2, _K2, _xi2m, _D2, omAllTemp2, tAllTemp2, flags, TermCriteria(3, 100, 1e-6), idx2);
// find the intersection idx
Mat interIdx1, interIdx2, interOri;
getInterset(idx1, idx2, interIdx1, interIdx2, interOri);
if (idx.empty())
idx.create(1, (int)interOri.total(), CV_32S);
interOri.copyTo(idx.getMat());
int n_inter = (int)interIdx1.total();
std::vector<Vec3d> omAll1(n_inter), omAll2(n_inter), tAll1(n_inter), tAll2(n_inter);
for(int i = 0; i < (int)interIdx1.total(); ++i)
{
omAll1[i] = omAllTemp1[interIdx1.at<int>(i)];
tAll1[i] = tAllTemp1[interIdx1.at<int>(i)];
omAll2[i] = omAllTemp2[interIdx2.at<int>(i)];
tAll2[i] = tAllTemp2[interIdx2.at<int>(i)];
}
// initialize R,T
Mat omEstAll(1, n_inter, CV_64FC3), tEstAll(1, n_inter, CV_64FC3);
Mat R1, R2, T1, T2, omLR, TLR, RLR;
for (int i = 0; i < n_inter; ++i)
{
Rodrigues(omAll1[i], R1);
Rodrigues(omAll2[i], R2);
T1 = Mat(tAll1[i]).reshape(1, 3);
T2 = Mat(tAll2[i]).reshape(1, 3);
RLR = R2 * R1.t();
TLR = T2 - RLR*T1;
Rodrigues(RLR, omLR);
omLR.reshape(3, 1).copyTo(omEstAll.col(i));
TLR.reshape(3, 1).copyTo(tEstAll.col(i));
}
Vec3d omEst = internal::findMedian3(omEstAll);
Vec3d tEst = internal::findMedian3(tEstAll);
Mat(omEst).copyTo(om.getMat());
Mat(tEst).copyTo(T.getMat());
if (omL.empty())
{
omL.create((int)omAll1.size(), 1, CV_64FC3);
}
if (tL.empty())
{
tL.create((int)tAll1.size(), 1, CV_64FC3);
}
if(omL.kind() == _InputArray::STD_VECTOR_MAT)
{
for(int i = 0; i < n_inter; ++i)
{
omL.create(3, 1, CV_64F, i, true);
tL.create(3, 1, CV_64F, i, true);
omL.getMat(i) = Mat(omAll1[i]);
tL.getMat(i) = Mat(tAll1[i]);
}
}
else
{
cv::Mat(omAll1).convertTo(omL, CV_64FC3);
cv::Mat(tAll1).convertTo(tL, CV_64FC3);
}
if (K1.empty())
{
K1.create(3, 3, CV_64F);
K2.create(3, 3, CV_64F);
}
if (D1.empty())
{
D1.create(1, 4, CV_64F);
D2.create(1, 4, CV_64F);
}
Mat(_K1).copyTo(K1.getMat());
Mat(_K2).copyTo(K2.getMat());
Mat(_D1).copyTo(D1.getMat());
Mat(_D2).copyTo(D2.getMat());
xi1 = _xi1m.at<double>(0);
xi2 = _xi2m.at<double>(0);
}
//////////////////////////////////////////////////////////////////////////////////////////////////////////////
/// cv::omnidir::internal::computeJacobian
void cv::omnidir::internal::computeJacobian(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints,
InputArray parameters, Mat& JTJ_inv, Mat& JTE, int flags, double epsilon)
{
CV_Assert(!objectPoints.empty() && objectPoints.type() == CV_64FC3);
CV_Assert(!imagePoints.empty() && imagePoints.type() == CV_64FC2);
int n = (int)objectPoints.total();
Mat JTJ = Mat::zeros(10 + 6*n, 10 + 6*n, CV_64F);
JTJ_inv = Mat::zeros(10 + 6*n, 10 + 6*n, CV_64F);
JTE = Mat::zeros(10 + 6*n, 1, CV_64F);
int nPointsAll = 0;
for (int i = 0; i < n; ++i)
{
nPointsAll += (int)objectPoints.getMat(i).total();
}
Mat J = Mat::zeros(2*nPointsAll, 10+6*n, CV_64F);
Mat exAll = Mat::zeros(2*nPointsAll, 10+6*n, CV_64F);
double *para = parameters.getMat().ptr<double>();
Matx33d K(para[6*n], para[6*n+2], para[6*n+3],
0, para[6*n+1], para[6*n+4],
0, 0, 1);
Matx14d D(para[6*n+6], para[6*n+7], para[6*n+8], para[6*n+9]);
double xi = para[6*n+5];
for (int i = 0; i < n; i++)
{
Mat objPoints, imgPoints, om, T;
objectPoints.getMat(i).copyTo(objPoints);
imagePoints.getMat(i).copyTo(imgPoints);
objPoints = objPoints.reshape(3, objPoints.rows*objPoints.cols);
imgPoints = imgPoints.reshape(2, imgPoints.rows*imgPoints.cols);
om = parameters.getMat().colRange(i*6, i*6+3);
T = parameters.getMat().colRange(i*6+3, (i+1)*6);
Mat imgProj, jacobian;
omnidir::projectPoints(objPoints, imgProj, om, T, K, xi, D, jacobian);
Mat projError = imgPoints - imgProj;
// The intrinsic part of Jacobian
Mat JIn(jacobian.rows, 10, CV_64F);
Mat JEx(jacobian.rows, 6, CV_64F);
jacobian.colRange(6, 16).copyTo(JIn);
jacobian.colRange(0, 6).copyTo(JEx);
JTJ(Rect(6*n, 6*n, 10, 10)) = JTJ(Rect(6*n, 6*n, 10, 10)) + JIn.t()*JIn;
JTJ(Rect(i*6, i*6, 6, 6)) = JEx.t() * JEx;
Mat JExTIn = JEx.t() * JIn;
JExTIn.copyTo(JTJ(Rect(6*n, i*6, 10, 6)));
Mat(JIn.t()*JEx).copyTo(JTJ(Rect(i*6, 6*n, 6, 10)));
JTE(Rect(0, 6*n, 1, 10)) = JTE(Rect(0, 6*n,1, 10)) + JIn.t() * projError.reshape(1, 2*(int)projError.total());
JTE(Rect(0, i*6, 1, 6)) = JEx.t() * projError.reshape(1, 2*(int)projError.total());
//int nPoints = objectPoints.getMat(i).total();
//JIn.copyTo(J(Rect(6*n, i*nPoints*2, 10, nPoints*2)));
//JEx.copyTo(J(Rect(6*i, i*nPoints*2, 6, nPoints*2)));
//projError.reshape(1, 2*projError.rows).copyTo(exAll.rowRange(i*2*nPoints, (i+1)*2*nPoints));
}
//JTJ = J.t()*J;
//JTE = J.t()*exAll;
std::vector<int> _idx(6*n+10, 1);
flags2idx(flags, _idx, n);
subMatrix(JTJ, JTJ, _idx, _idx);
subMatrix(JTE, JTE, std::vector<int>(1, 1), _idx);
// in case JTJ is singular
//SVD svd(JTJ, SVD::NO_UV);
//double cond = svd.w.at<double>(0)/svd.w.at<double>(5);
//if (cond_JTJ.needed())
//{
// cond_JTJ.create(1, 1, CV_64F);
// cond_JTJ.getMat().at<double>(0) = cond;
//}
//double epsilon = 1e-4*std::exp(cond);
JTJ_inv = Mat(JTJ+epsilon).inv();
}
void cv::omnidir::internal::computeJacobianStereo(InputArrayOfArrays objectPoints, InputArrayOfArrays imagePoints1, InputArrayOfArrays imagePoints2,
InputArray parameters, Mat& JTJ_inv, Mat& JTE, int flags, double epsilon)
{
CV_Assert(!objectPoints.empty() && objectPoints.type() == CV_64FC3);
CV_Assert(!imagePoints1.empty() && imagePoints1.type() == CV_64FC2);
CV_Assert(!imagePoints2.empty() && imagePoints2.type() == CV_64FC2);
CV_Assert((imagePoints1.total() == imagePoints2.total()) && (imagePoints1.total() == objectPoints.total()));
// compute Jacobian matrix by naive way
int n_img = (int)objectPoints.total();
int n_points = (int)objectPoints.getMat(0).total();
Mat J = Mat::zeros(4 * n_points * n_img, 20 + 6 * (n_img + 1), CV_64F);
Mat exAll = Mat::zeros(4 * n_points * n_img, 1, CV_64F);
double *para = parameters.getMat().ptr<double>();
int offset1 = (n_img + 1) * 6;
int offset2 = offset1 + 10;
Matx33d K1(para[offset1], para[offset1+2], para[offset1+3],
0, para[offset1+1], para[offset1+4],
0, 0, 1);
Matx14d D1(para[offset1+6], para[offset1+7], para[offset1+8], para[offset1+9]);
double xi1 = para[offset1+5];
Matx33d K2(para[offset2], para[offset2+2], para[offset2+3],
0, para[offset2+1], para[offset2+4],
0, 0, 1);
Matx14d D2(para[offset2+6], para[offset2+7], para[offset2+8], para[offset2+9]);
double xi2 = para[offset2+5];
Mat om = parameters.getMat().reshape(1, 1).colRange(0, 3);
Mat T = parameters.getMat().reshape(1, 1).colRange(3, 6);
for (int i = 0; i < n_img; i++)
{
Mat objPointsi, imgPoints1i, imgPoints2i, om1, T1;
objectPoints.getMat(i).copyTo(objPointsi);
imagePoints1.getMat(i).copyTo(imgPoints1i);
imagePoints2.getMat(i).copyTo(imgPoints2i);
objPointsi = objPointsi.reshape(3, objPointsi.rows*objPointsi.cols);
imgPoints1i = imgPoints1i.reshape(2, imgPoints1i.rows*imgPoints1i.cols);
imgPoints2i = imgPoints2i.reshape(2, imgPoints2i.rows*imgPoints2i.cols);
om1 = parameters.getMat().reshape(1, 1).colRange((1 + i) * 6, (1 + i) * 6 + 3);
T1 = parameters.getMat().reshape(1, 1).colRange((1 + i) * 6 + 3, (i + 1) * 6 + 6);
Mat imgProj1, imgProj2, jacobian1, jacobian2;
// jacobian for left image
cv::omnidir::projectPoints(objPointsi, imgProj1, om1, T1, K1, xi1, D1, jacobian1);
Mat projError1 = imgPoints1i - imgProj1;
//Mat JIn1(jacobian1.rows, 10, CV_64F);
//Mat JEx1(jacobian1.rows, 6, CV_64F);
jacobian1.colRange(6, 16).copyTo(J(Rect(6*(n_img+1), i*n_points*4, 10, n_points*2)));
jacobian1.colRange(0, 6).copyTo(J(Rect(6+i*6, i*n_points*4, 6, n_points*2)));
projError1.reshape(1, 2*n_points).copyTo(exAll.rowRange(i*4*n_points, (i*4+2)*n_points));
//jacobian for right image
Mat om2, T2, dom2dom1, dom2dT1, dom2dom, dom2dT, dT2dom1, dT2dT1, dT2dom, dT2dT;
cv::omnidir::internal::compose_motion(om1, T1, om, T, om2, T2, dom2dom1, dom2dT1, dom2dom, dom2dT, dT2dom1, dT2dT1, dT2dom, dT2dT);
cv::omnidir::projectPoints(objPointsi, imgProj2, om2, T2, K2, xi2, D2, jacobian2);
Mat projError2 = imgPoints2i - imgProj2;
projError2.reshape(1, 2*n_points).copyTo(exAll.rowRange((i*4+2)*n_points, (i*4+4)*n_points));
Mat dxrdom = jacobian2.colRange(0, 3) * dom2dom + jacobian2.colRange(3, 6) * dT2dom;
Mat dxrdT = jacobian2.colRange(0, 3) * dom2dT + jacobian2.colRange(3, 6) * dT2dT;