v3d_distortion.h

A version of a sparse bundle adjustment implementation with adjustable intrinsics and distortion par

// -*- C++ -*-
/*
Copyright (c) 2008 University of North Carolina at Chapel Hill

This file is part of SSBA (Simple Sparse Bundle Adjustment).

SSBA is free software: you can redistribute it and/or modify it under the
terms of the GNU Lesser General Public License as published by the Free
Software Foundation, either version 3 of the License, or (at your option) any
later version.

SSBA 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 Lesser General Public License for more
details.

You should have received a copy of the GNU Lesser General Public License along
with SSBA. If not, see <http://www.gnu.org/licenses/>.
*/

#ifndef V3D_DISTORTION_H
#define V3D_DISTORTION_H

#include "Math/v3d_linear.h"
#include "Math/v3d_linear_utils.h"

namespace V3D
{

   struct StdDistortionFunction
   {
         double k1, k2, p1, p2;

         StdDistortionFunction()
            : k1(0), k2(0), p1(0), p2(0)
         { }

         Vector2d operator()(Vector2d const& xu) const
         {
            double const r2 = xu[0]*xu[0] + xu[1]*xu[1];
            double const r4 = r2*r2;
            double const kr = 1 + k1*r2 + k2*r4;

            Vector2d xd;
            xd[0] = kr * xu[0] + 2*p1*xu[0]*xu[1] + p2*(r2 + 2*xu[0]*xu[0]);
            xd[1] = kr * xu[1] + 2*p2*xu[0]*xu[1] + p1*(r2 + 2*xu[1]*xu[1]);
            return xd;
         }

         Matrix2x2d derivativeWrtRadialParameters(Vector2d const& xu) const
         {
            double const r2 = xu[0]*xu[0] + xu[1]*xu[1];
            double const r4 = r2*r2;
            double const kr = 1 + k1*r2 + k2*r4;

            Matrix2x2d deriv;

            deriv[0][0] = xu[0] * r2; // d xd/d k1
            deriv[0][1] = xu[0] * r4; // d xd/d k2
            deriv[1][0] = xu[1] * r2; // d yd/d k1
            deriv[1][1] = xu[1] * r4; // d yd/d k2
            return deriv;
         }

         Matrix2x2d derivativeWrtTangentialParameters(Vector2d const& xu) const
         {
            double const r2 = xu[0]*xu[0] + xu[1]*xu[1];
            double const r4 = r2*r2;
            double const kr = 1 + k1*r2 + k2*r4;

            Matrix2x2d deriv;
            deriv[0][0] = 2*xu[0]*xu[1];      // d xd/d p1
            deriv[0][1] = r2 + 2*xu[0]*xu[0]; // d xd/d p2
            deriv[1][0] = r2 + 2*xu[1]*xu[1]; // d yd/d p1
            deriv[1][1] = deriv[0][0];        // d yd/d p2
            return deriv;
         }

         Matrix2x2d derivativeWrtUndistortedPoint(Vector2d const& xu) const
         {
            double const r2 = xu[0]*xu[0] + xu[1]*xu[1];
            double const r4 = r2*r2;
            double const kr = 1 + k1*r2 + k2*r4;
            double const dkr = 2*k1 + 4*k2*r2;

            Matrix2x2d deriv;
            deriv[0][0] = kr + xu[0] * xu[0] * dkr + 2*p1*xu[1] + 6*p2*xu[0]; // d xd/d xu
            deriv[0][1] =      xu[0] * xu[1] * dkr + 2*p1*xu[0] + 2*p2*xu[1]; // d xd/d yu
            deriv[1][0] = deriv[0][1];                                        // d yd/d xu
            deriv[1][1] = kr + xu[1] * xu[1] * dkr + 6*p1*xu[1] + 2*p2*xu[0]; // d yd/d yu
            return deriv;
         }
   }; // end struct StdDistortionFunction

} // end namespace V3D

#endif