CCamModel.h

Go to the documentation of this file.

/* +---------------------------------------------------------------------------+
   |          The Mobile Robot Programming Toolkit (MRPT) C++ library          |
   |                                                                           |
   |                       http://www.mrpt.org/                                |
   |                                                                           |
   |   Copyright (C) 2005-2011  University of Malaga                           |
   |                                                                           |
   |    This software was written by the Machine Perception and Intelligent    |
   |      Robotics Lab, University of Malaga (Spain).                          |
   |    Contact: Jose-Luis Blanco  <jlblanco@ctima.uma.es>                     |
   |                                                                           |
   |  This file is part of the MRPT project.                                   |
   |                                                                           |
   |     MRPT is free software: you can redistribute it and/or modify          |
   |     it under the terms of the GNU General Public License as published by  |
   |     the Free Software Foundation, either version 3 of the License, or     |
   |     (at your option) any later version.                                   |
   |                                                                           |
   |   MRPT is distributed in the hope that it will be useful,                 |
   |     but WITHOUT ANY WARRANTY; without even the implied warranty of        |
   |     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the         |
   |     GNU General Public License for more details.                          |
   |                                                                           |
   |     You should have received a copy of the GNU General Public License     |
   |     along with MRPT.  If not, see <http://www.gnu.org/licenses/>.         |
   |                                                                           |
   +---------------------------------------------------------------------------+ */
#ifndef CCamModel_H
#define CCamModel_H

#include <mrpt/utils/TCamera.h>
#include <mrpt/system/os.h>
#include <mrpt/vision/utils.h>
#include <mrpt/math/lightweight_geom_data.h>

namespace mrpt
{
        namespace vision
        {
                /** This class represent a pinhole camera model for Monocular SLAM and implements some associated Jacobians
                 *
                 *  The camera parameters are accessible in the public member CCamModel::cam
                 *
                 * - Versions:
                 *    - First version: By Antonio J. Ortiz de Galistea.
                 *    - 2009-2010: Rewritten by various authors.
                 *
                 * \sa mrpt::utils::TCamera, CMonoSlam, the application <a href="http://www.mrpt.org/Application:camera-calib-gui" >camera-calib-gui</a> for calibrating a camera
                 * \ingroup mrpt_vision_grp 
                 */
                class VISION_IMPEXP  CCamModel : public mrpt::utils::CLoadableOptions
                {
                public:
                        mrpt::utils::TCamera cam;  //!< The parameters of a camera

                        /** Default Constructor */
                        CCamModel();

                        /** This method loads the options from a ".ini"-like file or memory-stored string list.
                         */
                        void  loadFromConfigFile(
                                const mrpt::utils::CConfigFileBase      &source,
                                const std::string               &section);

                        /** This method displays clearly all the contents of the structure in textual form, sending it to a CStream. */
                        void  dumpToTextStream( CStream         &out) const;

                        /** Constructor from a ini file
                         */
                        CCamModel(const mrpt::utils::CConfigFileBase &cfgIni);

                        /** Jacobian for undistortion the image coordinates */
                        void  jacob_undistor_fm(const mrpt::vision::TPixelCoordf &uvd, math::CMatrixDouble &J_undist);

                        /** Calculate the image coordinates undistorted
                         */
                        void jacob_undistor(const mrpt::vision::TPixelCoordf &p, mrpt::math::CMatrixDouble &J_undist );

                        /**     Return the pixel position distorted by the camera
                         */
                        void  distort_a_point(const mrpt::vision::TPixelCoordf &p, mrpt::vision::TPixelCoordf &distorted_p);

                        /**     Return the pixel position undistorted by the camera
                         *      The input values 'col' and 'row' will be replace for the new values (undistorted)
                         */
                        void  undistort_point(const mrpt::vision::TPixelCoordf &p, mrpt::vision::TPixelCoordf &undistorted_p);

                        /**     Return the (distorted) pixel position of a 3D point given in coordinates relative to the camera (+Z pointing forward, +X to the right)
                         * \sa unproject_3D_point
                     */
                        void  project_3D_point(const mrpt::math::TPoint3D &p3D, mrpt::vision::TPixelCoordf &distorted_p) const;

                        /**     Return the 3D location of a point (at a fixed distance z=1), for the given (distorted) pixel position
                         * \sa project_3D_point
                         * \note Of course, there is a depth ambiguity, so the returned 3D point must be considered a direction from the camera focus, or a vector, rather than a meaninful physical point.
                     */
                        void  unproject_3D_point(const mrpt::vision::TPixelCoordf &distorted_p, mrpt::math::TPoint3D &p3D) const;

                        /** Jacobian of the projection of 3D points (with distortion), as done in project_3D_point \f$ \frac{\partial h}{\partial y} \f$, evaluated at the point p3D (read below the full explanation)

                        We define \f$ h = (h_x ~ h_y) \f$ as the projected point in pixels (origin at the top-left corner),
                        and \f$ y=( y_x ~ y_y ~ y_z ) \f$ as the 3D point in space, in coordinates relative to the camera (+Z pointing forwards).

                        Then this method computes the 2x3 Jacobian:

                        \f[
                        \frac{\partial h}{\partial y} =  \frac{\partial h}{\partial u} \frac{\partial u}{\partial y}
                        \f]

                        With:

                        \f[
                        \frac{\partial u}{\partial y} =
                        \left( \begin{array}{ccc}
                         \frac{f_x}{y_z} &  0 & - y \frac{f_x}{y_z^2} \\
                         0 & \frac{f_y}{y_z} & - y \frac{f_y}{y_z^2} \\
                        \end{array} \right)
                        \f]

                        where \f$ f_x, f_y \f$ is the focal length in units of pixel sizes in x and y, respectively.
                        And, if we define:

                        \f[
                         f = 1+ 2  k_1  (u_x^2+u_y^2)
                        \f]

                        then:

                        \f[
                        \frac{\partial h}{\partial u} =
                        \left( \begin{array}{cc}
                         \frac{ 1+2 k_1 u_y^2 }{f^{3/2}}  &  -\frac{2 u_x u_y k_1 }{f^{3/2}} \\
                         -\frac{2 u_x u_y k_1 }{f^{3/2}}  & \frac{ 1+2 k_1 u_x^2 }{f^{3/2}}
                        \end{array} \right)
                        \f]

                        \note JLBC: Added in March, 2009. Should be equivalent to Davison's WideCamera::ProjectionJacobian
                        \sa project_3D_point
                        */
                        void jacobian_project_with_distortion(const mrpt::math::TPoint3D &p3D, math::CMatrixDouble & dh_dy ) const;


                        /** Jacobian of the unprojection of a pixel (with distortion) back into a 3D point, as done in unproject_3D_point \f$ \frac{\partial y}{\partial h} \f$, evaluated at the pixel p
                        \note JLBC: Added in March, 2009. Should be equivalent to Davison's WideCamera::UnprojectionJacobian
                        \sa unproject_3D_point
                        */
                        void jacobian_unproject_with_distortion(const mrpt::vision::TPixelCoordf &p, math::CMatrixDouble & dy_dh ) const;

                        template<typename T> struct CameraTempVariables {
                                T x_,y_;
                                T x_2,y_2;
                                T R;
                                T K;
                                T x__,y__;
                        };
                        template<typename T,typename POINT> void getTemporaryVariablesForTransform(const POINT &p,CameraTempVariables<T> &v) const      {
                                v.x_=p[1]/p[0];
                                v.y_=p[2]/p[0];
                                v.x_2=square(v.x_);
                                v.y_2=square(v.y_);
                                v.R=v.x_2+v.y_2;
                                v.K=1+v.R*(cam.k1()+v.R*(cam.k2()+v.R*cam.k3()));
                                T xy=v.x_*v.y_,p1=cam.p1(),p2=cam.p2();
                                v.x__=v.x_*v.K+2*p1*xy+p2*(3*v.x_2+v.y_2);
                                v.y__=v.y_*v.K+p1*(v.x_2+3*v.y_2)+2*p2*xy;
                        }

                        template<typename T,typename POINT,typename PIXEL> inline void getFullProjection(const POINT &pIn,PIXEL &pOut) const    {
                                CameraTempVariables<T> tmp;
                                getTemporaryVariablesForTransform(pIn,tmp);
                                getFullProjectionT(tmp,pOut);
                        }

                        template<typename T,typename PIXEL> inline void getFullProjectionT(const CameraTempVariables<T> &tmp,PIXEL &pOut) const {
                                pOut[0]=cam.fx()*tmp.x__+cam.cx();
                                pOut[1]=cam.fy()*tmp.y__+cam.cy();
                        }

                        template<typename T,typename POINT,typename MATRIX> inline void getFullJacobian(const POINT &pIn,MATRIX &mOut) const    {
                                CameraTempVariables<T> tmp;
                                getTemporaryVariablesForTransform(pIn,tmp);
                                getFullJacobianT(pIn,tmp,mOut);
                        }

                        template<typename T,typename POINT,typename MATRIX> void getFullJacobianT(const POINT &pIn,const CameraTempVariables<T> &tmp,MATRIX &mOut) const        {
                                T x_=1/pIn[0];
                                T x_2=square(x_);
                                //First two jacobians...
                                CMatrixFixedNumeric<T,3,3> J21;
                                T tmpK=2*(cam.k1()+tmp.R*(2*cam.k2()+3*tmp.R*cam.k3()));
                                T tmpKx=tmpK*tmp.x_;
                                T tmpKy=tmpK*tmp.y_;
                                T yx2=-pIn[1]*x_2;
                                T zx2=-pIn[2]*x_2;
                                J21.set_unsafe(0,0,yx2);
                                J21.set_unsafe(0,1,x_);
                                J21.set_unsafe(0,2,0);
                                J21.set_unsafe(1,0,zx2);
                                J21.set_unsafe(1,1,0);
                                J21.set_unsafe(1,2,x_);
                                J21.set_unsafe(2,0,tmpKx*yx2+tmpKy*zx2);
                                J21.set_unsafe(2,1,tmpKx*x_);
                                J21.set_unsafe(2,2,tmpKy*x_);
                                //Last two jacobians...
                                T pxpy=2*(cam.p1()*tmp.x_+cam.p2()*tmp.y_);
                                T p1y=cam.p1()*tmp.y_;
                                T p2x=cam.p2()*tmp.x_;
                                CMatrixFixedNumeric<T,2,3> J43;
                                T fx=cam.fx(),fy=cam.fy();
                                J43.set_unsafe(0,0,fx*(tmp.K+2*p1y+6*p2x));
                                J43.set_unsafe(0,1,fx*pxpy);
                                J43.set_unsafe(0,2,fx*tmp.x_);
                                J43.set_unsafe(1,0,fy*pxpy);
                                J43.set_unsafe(1,1,fy*(tmp.K+6*p1y+2*p2x));
                                J43.set_unsafe(1,2,fy*tmp.y_);
                                mOut.multiply(J43,J21);
                                //cout<<"J21:\n"<<J21<<"\nJ43:\n"<<J43<<"\nmOut:\n"<<mOut;
                        }
                private:
                        //These functions are little tricks to avoid multiple initialization.
                        //They are intended to initialize the common parts of the jacobians just once,
                        //and not in each iteration.
                        //They are mostly useless outside the scope of this function.
                        CMatrixFixedNumeric<double,2,2> firstInverseJacobian() const    {
                                CMatrixFixedNumeric<double,2,2> res;
                                res.set_unsafe(0,1,0);
                                res.set_unsafe(1,0,0);
                                return res;
                        }
                        CMatrixFixedNumeric<double,4,2> secondInverseJacobian() const   {
                                CMatrixFixedNumeric<double,4,2> res;
                                res.set_unsafe(0,0,1);
                                res.set_unsafe(0,1,0);
                                res.set_unsafe(1,0,0);
                                res.set_unsafe(1,1,1);
                                return res;
                        }
                        CMatrixFixedNumeric<double,3,4> thirdInverseJacobian() const    {
                                CMatrixFixedNumeric<double,3,4> res;
                                res.set_unsafe(0,1,0);
                                res.set_unsafe(0,2,0);
                                res.set_unsafe(1,0,0);
                                res.set_unsafe(1,2,0);
                                res.set_unsafe(2,0,0);
                                res.set_unsafe(2,1,0);
                                res.set_unsafe(2,2,1);
                                res.set_unsafe(2,3,0);
                                return res;
                        }
                public:
                        template<typename POINTIN,typename POINTOUT,typename MAT22> void getFullInverseModelWithJacobian(const POINTIN &pIn,POINTOUT &pOut,MAT22 &jOut) const   {
                                //Temporary variables (well, there are some more, but these are the basics)
                                //WARNING!: this shortcut to avoid repeated initialization makes the method somewhat
                                //faster, but makes it incapable of being used in more than one thread
                                //simultaneously!
                                static CMatrixFixedNumeric<double,2,2> J1(firstInverseJacobian());
                                static CMatrixFixedNumeric<double,4,2> J2(secondInverseJacobian());
                                static CMatrixFixedNumeric<double,3,4> J3(thirdInverseJacobian());
                                static CMatrixFixedNumeric<double,2,3> J4;      //This is not initialized in a special way, although declaring it
                                CArray<double,4> tmp1;
                                CArray<double,2> tmp2;  //This would be a CArray<double,3>, but to avoid copying, we let "R2" lie in tmp1.
                                //Camera Parameters
                                double cx=cam.cx(),cy=cam.cy(),ifx=1/cam.fx(),ify=1/cam.fy();
                                double K1=cam.k1(),K2=cam.k2(),p1=cam.p1(),p2=cam.p2(),K3=cam.k3();
                                //First step: intrinsic matrix.
                                tmp1[0]=(pIn[0]-cx)*ifx;
                                tmp1[1]=(pIn[1]-cy)*ify;
                                J1.set_unsafe(0,0,ifx);
                                J1.set_unsafe(1,1,ify);
                                //Second step: adding temporary variables, related to the distortion.
                                tmp1[2]=square(tmp1[0])+square(tmp1[1]);
                                double sK1=square(K1);
                                double K12=sK1-K2;
                                double K123=-K1*sK1+2*K1*K2-K3; //-K1³+2K1K2-K3
                                //tmp1[3]=1-K1*tmp1[2]+K12*square(tmp1[2]);
                                tmp1[3]=1+tmp1[2]*(-K1+tmp1[2]*(K12+tmp1[2]*K123));
                                J2.set_unsafe(2,0,2*tmp1[0]);
                                J2.set_unsafe(2,1,2*tmp1[1]);
                                double jTemp=-2*K1+4*tmp1[2]*K12+6*square(tmp1[2])*K123;
                                J2.set_unsafe(3,0,tmp1[0]*jTemp);
                                J2.set_unsafe(3,1,tmp1[1]*jTemp);
                                //Third step: radial distortion. Really simple, since most work has been done in the previous step.
                                tmp2[0]=tmp1[0]*tmp1[3];
                                tmp2[1]=tmp1[1]*tmp1[3];
                                J3.set_unsafe(0,0,tmp1[3]);
                                J3.set_unsafe(0,3,tmp1[0]);
                                J3.set_unsafe(1,1,tmp1[3]);
                                J3.set_unsafe(1,3,tmp1[1]);
                                //Fourth step: tangential distorion. A little more complicated, but not much more.
                                double prod=tmp2[0]*tmp2[1];
                                //References to tmp1[2] are not errors! That element is "R2".
                                pOut[0]=tmp2[0]-p1*prod-p2*(tmp1[2]+2*square(tmp2[0]));
                                pOut[1]=tmp2[1]-p1*(tmp1[2]+2*square(tmp2[1]))-p2*prod;
                                J4.set_unsafe(0,0,1-p1*tmp2[1]-4*p2*tmp2[0]);
                                J4.set_unsafe(0,1,-p1*tmp2[0]);
                                J4.set_unsafe(0,2,-p2);
                                J4.set_unsafe(1,0,-p2*tmp2[1]);
                                J4.set_unsafe(1,1,1-4*p1*tmp2[1]-p2*tmp2[0]);
                                J4.set_unsafe(1,2,-p1);
                                //As fast as possible, and without more temporaries, let the jacobian be J4*J3*J2*J1;
                                jOut.multiply_ABC(J4,J3,J2);    //Note that using the other order is not possible due to matrix sizes (jOut may, and most probably will, be fixed).
                                jOut.multiply(jOut,J1);
                        }

                }; // end class

        } // end namespace
} // end namespace
#endif //__CCamModel_H