cal_main.cpp

有关摄像头定标的C++代码

    x[1] = cc.Ry;
    x[2] = cc.Rz;
    x[3] = cc.Tx;
    x[4] = cc.Ty;
    x[5] = cc.Tz;
    x[6] = cc.kappa1;
    x[7] = cc.f;

    /* define optional scale factors for the parameters */
    if ( mode == 2 ) {
        for (i = 0; i < NPARAMS; i++)
            diag[i] = 1.0;             /* some user-defined values */
    }
 
    /* perform the optimization */
    lmdif_ (cc_nic_optimization_error,
            &m, &n, x, fvec, &ftol, &xtol, &gtol, &maxfev, &epsfcn,
            diag, &mode, &factor, &nprint, &info, &nfev, fjac, &ldfjac,
            ipvt, qtf, wa1, wa2, wa3, wa4);

    /* update the calibration and camera constants */
    cc.Rx = x[0];
    cc.Ry = x[1];
    cc.Rz = x[2];
    apply_RPY_transform ();

    cc.Tx = x[3];
    cc.Ty = x[4];
    cc.Tz = x[5];
    cc.kappa1 = x[6];
    cc.f = x[7];

    /* release allocated workspace */
    free (fvec);
    free (fjac);
    free (wa4);

#ifdef DEBUG
    /* print the number of function calls during iteration */
    fprintf(stderr,"info: %d nfev: %d\n\n",info,nfev);
#endif

#undef NPARAMS
}

//全参数优化；
/************************************************************************/
void      cc_full_optimization_error (long *m_ptr, long *n_ptr, double *params, double *err)
{
    int       i;

    double    xc,
              yc,
              zc,
              Xd_,
              Yd_,
              Xu_1,
              Yu_1,
              Xu_2,
              Yu_2,
              distortion_factor,
              Rx,
              Ry,
              Rz,
              Tx,
              Ty,
              Tz,
              kappa1,
              f,
              Cx,
              Cy,
              r1,
              r2,
              r4,
              r5,
              r7,
              r8,
              sa,
              sb,
              sg,
              ca,
              cb,
              cg;

    Rx = params[0];
    Ry = params[1];
    Rz = params[2];
    Tx = params[3];
    Ty = params[4];
    Tz = params[5];
    kappa1 = params[6];
    f = params[7];
    Cx = params[8];
    Cy = params[9];

    SINCOS (Rx, sa, ca);
    SINCOS (Ry, sb, cb);
    SINCOS (Rz, sg, cg);
    r1 = cb * cg;
    r2 = cg * sa * sb - ca * sg;
    r4 = cb * sg;
    r5 = sa * sb * sg + ca * cg;
    r7 = -sb;
    r8 = cb * sa;

    for (i = 0; i < cd.point_count; i++) {
	/* convert from world coordinates to camera coordinates */
	/* Note: zw is implicitly assumed to be zero for these (coplanar) calculations */
	xc = r1 * cd.xw[i] + r2 * cd.yw[i] + Tx;
	yc = r4 * cd.xw[i] + r5 * cd.yw[i] + Ty;
	zc = r7 * cd.xw[i] + r8 * cd.yw[i] + Tz;

	/* convert from camera coordinates to undistorted sensor plane coordinates */
	Xu_1 = f * xc / zc;
	Yu_1 = f * yc / zc;

	/* convert from 2D image coordinates to distorted sensor coordinates */
	Xd_ = cp.dpx * (cd.Xf[i] - Cx) / cp.sx; 
	Yd_ = cp.dpy * (cd.Yf[i] - Cy);

	/* convert from distorted sensor coordinates to undistorted sensor plane coordinates */
	distortion_factor = 1 + kappa1 * (SQR (Xd_) + SQR (Yd_));
	Xu_2 = Xd_ * distortion_factor;
	Yu_2 = Yd_ * distortion_factor;

        /* record the error in the undistorted sensor coordinates */
        err[i] = hypot (Xu_1 - Xu_2, Yu_1 - Yu_2);
    }
}


void      cc_full_optimization ()
{
#define NPARAMS 10

    int       i;

    /* Parameters needed by MINPACK's lmdif() */

    long     m = cd.point_count;
    long     n = NPARAMS;
    double  x[NPARAMS];
    double *fvec;
    double  ftol = REL_SENSOR_TOLERANCE_ftol;
    double  xtol = REL_PARAM_TOLERANCE_xtol;
    double  gtol = ORTHO_TOLERANCE_gtol;
    long     maxfev = MAXFEV;
    double  epsfcn = EPSFCN;
    double  diag[NPARAMS];
    long     mode = MODE;
    double  factor = FACTOR;
    long     nprint = 0;
    long     info;
    long     nfev;
    double *fjac;
    long     ldfjac = m;
    long     ipvt[NPARAMS];
    double  qtf[NPARAMS];
    double  wa1[NPARAMS];
    double  wa2[NPARAMS];
    double  wa3[NPARAMS];
    double *wa4;

    /* allocate some workspace */
    if (( fvec = (double *) calloc ((unsigned int) m, (unsigned int) sizeof(double))) == NULL ) {
       fprintf(stderr,"calloc: Cannot allocate workspace fvec\n");
       exit(-1);
    }

    if (( fjac = (double *) calloc ((unsigned int) m*n, (unsigned int) sizeof(double))) == NULL ) {
       fprintf(stderr,"calloc: Cannot allocate workspace fjac\n");
       exit(-1);
    }

    if (( wa4 = (double *) calloc ((unsigned int) m, (unsigned int) sizeof(double))) == NULL ) {
       fprintf(stderr,"calloc: Cannot allocate workspace wa4\n");
       exit(-1);
    }

    /* use the current calibration and camera constants as a starting point */
    x[0] = cc.Rx;
    x[1] = cc.Ry;
    x[2] = cc.Rz;
    x[3] = cc.Tx;
    x[4] = cc.Ty;
    x[5] = cc.Tz;
    x[6] = cc.kappa1;
    x[7] = cc.f;
    x[8] = cp.Cx;
    x[9] = cp.Cy;

    /* define optional scale factors for the parameters */
    if ( mode == 2 ) {
        for (i = 0; i < NPARAMS; i++)
            diag[i] = 1.0;             /* some user-defined values */
    }

    /* perform the optimization */
    lmdif_ (cc_full_optimization_error,
            &m, &n, x, fvec, &ftol, &xtol, &gtol, &maxfev, &epsfcn,
            diag, &mode, &factor, &nprint, &info, &nfev, fjac, &ldfjac,
            ipvt, qtf, wa1, wa2, wa3, wa4);

    /* update the calibration and camera constants */
    cc.Rx = x[0];
    cc.Ry = x[1];
    cc.Rz = x[2];
    apply_RPY_transform ();

    cc.Tx = x[3];
    cc.Ty = x[4];
    cc.Tz = x[5];
    cc.kappa1 = x[6];
    cc.f = x[7];
    cp.Cx = x[8];
    cp.Cy = x[9];

    /* release allocated workspace */
    free (fvec);
    free (fjac);
    free (wa4);

#ifdef DEBUG
    /* print the number of function calls during iteration */
    fprintf(stderr,"info: %d nfev: %d\n\n",info,nfev);
#endif

#undef NPARAMS
}

//以上为共面标定；以下为非共面标定；
/***********************************************************************\
* Routines for noncoplanar camera calibration	 			*
\***********************************************************************/
void      ncc_compute_Xd_Yd_and_r_squared ()
{
    int       i;

    double    Xd_,
              Yd_;

    for (i = 0; i < cd.point_count; i++) {
	Xd[i] = Xd_ = cp.dpx * (cd.Xf[i] - cp.Cx) / cp.sx;      /* [mm] */
	Yd[i] = Yd_ = cp.dpy * (cd.Yf[i] - cp.Cy);              /* [mm] */
	r_squared[i] = SQR (Xd_) + SQR (Yd_);                   /* [mm^2] */
    }
}


void      ncc_compute_U ()
{
    int       i;

    dmat      M,
              a,
              b;

    M = newdmat (0, (cd.point_count - 1), 0, 6, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute U: unable to allocate matrix M\n");
	exit (-1);
    }

    a = newdmat (0, 6, 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute U: unable to allocate vector a\n");
	exit (-1);
    }

    b = newdmat (0, (cd.point_count - 1), 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute U: unable to allocate vector b\n");
	exit (-1);
    }

    for (i = 0; i < cd.point_count; i++) {
	M.el[i][0] = Yd[i] * cd.xw[i];
	M.el[i][1] = Yd[i] * cd.yw[i];
	M.el[i][2] = Yd[i] * cd.zw[i];
	M.el[i][3] = Yd[i];
	M.el[i][4] = -Xd[i] * cd.xw[i];
	M.el[i][5] = -Xd[i] * cd.yw[i];
	M.el[i][6] = -Xd[i] * cd.zw[i];
	b.el[i][0] = Xd[i];
    }

    if (solve_system (M, a, b)) {
	fprintf (stderr, "ncc compute U: error - non-coplanar calibration tried with data which may possibly be coplanar\n\n");
	exit (-1);
    }

    U[0] = a.el[0][0];
    U[1] = a.el[1][0];
    U[2] = a.el[2][0];
    U[3] = a.el[3][0];
    U[4] = a.el[4][0];
    U[5] = a.el[5][0];
    U[6] = a.el[6][0];

    freemat (M);
    freemat (a);
    freemat (b);
}


void      ncc_compute_Tx_and_Ty ()
{
    int       i,
              far_point;

    double    Tx,
              Ty,
              Ty_squared,
              x,
              y,
              r1,
              r2,
              r3,
              r4,
              r5,
              r6,
              distance,
              far_distance;

    /* first find the square of the magnitude of Ty */
    Ty_squared = 1 / (SQR (U[4]) + SQR (U[5]) + SQR (U[6]));

    /* find a point that is far from the image center */
    far_distance = 0;
    far_point = 0;
    for (i = 0; i < cd.point_count; i++)
	if ((distance = r_squared[i]) > far_distance) {
	    far_point = i;
	    far_distance = distance;
	}

    /* now find the sign for Ty */
    /* start by assuming Ty > 0 */
    Ty = sqrt (Ty_squared);
    r1 = U[0] * Ty;
    r2 = U[1] * Ty;
    r3 = U[2] * Ty;
    Tx = U[3] * Ty;
    r4 = U[4] * Ty;
    r5 = U[5] * Ty;
    r6 = U[6] * Ty;
    x = r1 * cd.xw[far_point] + r2 * cd.yw[far_point] + r3 * cd.zw[far_point] + Tx;
    y = r4 * cd.xw[far_point] + r5 * cd.yw[far_point] + r6 * cd.zw[far_point] + Ty;

    /* flip Ty if we guessed wrong */
    if ((SIGNBIT (x) != SIGNBIT (Xd[far_point])) ||
	(SIGNBIT (y) != SIGNBIT (Yd[far_point])))
	Ty = -Ty;

    /* update the calibration constants */
    cc.Tx = U[3] * Ty;
    cc.Ty = Ty;
}


void      ncc_compute_sx ()
{
    cp.sx = sqrt (SQR (U[0]) + SQR (U[1]) + SQR (U[2])) * fabs (cc.Ty);
}


void      ncc_compute_R ()
{
    double    r1,
              r2,
              r3,
              r4,
              r5,
              r6,
              r7,
              r8,
              r9;

    r1 = U[0] * cc.Ty / cp.sx;
    r2 = U[1] * cc.Ty / cp.sx;
    r3 = U[2] * cc.Ty / cp.sx;

    r4 = U[4] * cc.Ty;
    r5 = U[5] * cc.Ty;
    r6 = U[6] * cc.Ty;

    /* use the outer product of the first two rows to get the last row */
    r7 = r2 * r6 - r3 * r5;
    r8 = r3 * r4 - r1 * r6;
    r9 = r1 * r5 - r2 * r4;

    /* update the calibration constants */
    cc.r1 = r1;
    cc.r2 = r2;
    cc.r3 = r3;
    cc.r4 = r4;
    cc.r5 = r5;
    cc.r6 = r6;
    cc.r7 = r7;
    cc.r8 = r8;
    cc.r9 = r9;

    /* fill in cc.Rx, cc.Ry and cc.Rz */
    solve_RPY_transform ();
}


void      ncc_compute_better_R ()
{
    double    r1,
              r2,
              r3,
              r4,
              r5,
              r6,
              r7,
              sa,
              ca,
              sb,
              cb,
              sg,
              cg;

    r1 = U[0] * cc.Ty / cp.sx;
    r2 = U[1] * cc.Ty / cp.sx;
    r3 = U[2] * cc.Ty / cp.sx;

    r4 = U[4] * cc.Ty;
    r5 = U[5] * cc.Ty;
    r6 = U[6] * cc.Ty;

    /* use the outer product of the first two rows to get the last row */
    r7 = r2 * r6 - r3 * r5;

    /* now find the RPY angles corresponding to the estimated rotation matrix */
    cc.Rz = atan2 (r4, r1);

    SINCOS (cc.Rz, sg, cg);

    cc.Ry = atan2 (-r7, r1 * cg + r4 * sg);

    cc.Rx = atan2 (r3 * sg - r6 * cg, r5 * cg - r2 * sg);

    SINCOS (cc.Rx, sa, ca);

    SINCOS (cc.Ry, sb, cb);

    /* now generate a more orthonormal rotation matrix from the RPY angles */
    cc.r1 = cb * cg;
    cc.r2 = cg * sa * sb - ca * sg;
    cc.r3 = sa * sg + ca * cg * sb;
    cc.r4 = cb * sg;
    cc.r5 = sa * sb * sg + ca * cg;
    cc.r6 = ca * sb * sg - cg * sa;
    cc.r7 = -sb;
    cc.r8 = cb * sa;
    cc.r9 = ca * cb;
}


void      ncc_compute_approximate_f_and_Tz ()
{
    int       i;

    dmat      M,
              a,
              b;

    M = newdmat (0, (cd.point_count - 1), 0, 1, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute apx: unable to allocate matrix M\n");
	exit (-1);
    }

    a = newdmat (0, 1, 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute apx: unable to allocate vector a\n");
	exit (-1);
    }

    b = newdmat (0, (cd.point_count - 1), 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "ncc compute apx: unable to allocate vector b\n");
	exit (-1);
    }

    for (i = 0; i < cd.point_count; i++) {
	M.el[i][0] = cc.r4 * cd.xw[i] + cc.r5 * cd.yw[i] + cc.r6 * cd.zw[i] + cc.Ty;
	M.el[i][1] = -Yd[i];
	b.el[i][0] = (cc.r7 * cd.xw[i] + cc.r8 * cd.yw[i] + cc.r9 * cd.zw[i]) * Yd[i];
    }

    if (solve_system (M, a, b)) {
	fprintf (stderr, "ncc compute apx: unable to solve system  Ma=b\n");
	exit (-1);
    }

    /* update the calibration constants */
    cc.f = a.el[0][0];
    cc.Tz = a.el[1][0];
    cc.kappa1 = 0.0;		/* this is the assumption that our calculation was made under */

    freemat (M);
    freemat (a);
    freemat (b);
}


/************************************************************************/
void      ncc_compute_exact_f_and_Tz_error (long *m_ptr, long *n_ptr, double *params, double *err)
{
    int       i;

    double    xc,
              yc,
              zc,
              Xu_1,
              Yu_1,
              Xu_2,
              Yu_2,
              distortion_factor,
              f,
              Tz,
              kappa1;

    f = params[0];
    Tz = params[1];
    kappa1 = params[2];

    for (i = 0; i < cd.point_count; i++) {
	/* convert from world coordinates to camera coordinates */
	xc = cc.r1 * cd.xw[i] + cc.r2 * cd.yw[i] + cc.r3 * cd.zw[i] + cc.Tx;
	yc = cc.r4 * cd.xw[i] + cc.r5 * cd.yw[i] + cc.r6 * cd.zw[i] + cc.Ty;
	zc = cc.r7 * cd.xw[i] + cc.r8 * cd.yw[i] + cc.r9 * cd.zw[i] + Tz;

	/* convert from camera coordinates to undistorted sensor coordinates */
	Xu_1 = f * xc / zc;
	Yu_1 = f * yc / zc;

	/* convert from distorted sensor coordinates to undistorted sensor coordinates */
	distortion_factor = 1 + kappa1 * r_squared[i];
	Xu_2 = Xd[i] * distortion_factor;
	Yu_2 = Yd[i] * distortion_factor;

        /* record the error in the undistorted sensor coordinates */
        err[i] = hypot (Xu_1 - Xu_2, Yu_1 - Yu_2);
    }
}