cal_main.c

标准tsai摄像机标定源代码。（两步标定）

	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];
	M.el[i][3] = -Xd[i] * cd.xw[i];
	M.el[i][4] = -Xd[i] * cd.yw[i];
	b.el[i][0] = Xd[i];
    }

    if (solve_system (M, a, b)) {
	fprintf (stderr, "cc compute U: unable to solve system  Ma=b\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];

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


void      cc_compute_Tx_and_Ty ()
{
    int       i,
              far_point;

    double    Tx,
              Ty,
              Ty_squared,
              x,
              y,
              Sr,
              r1p,
              r2p,
              r4p,
              r5p,
              r1,
              r2,
              r4,
              r5,
              distance,
              far_distance;

    r1p = U[0];
    r2p = U[1];
    r4p = U[3];
    r5p = U[4];

    /* first find the square of the magnitude of Ty */
    if ((fabs (r1p) < EPSILON) && (fabs (r2p) < EPSILON))
	Ty_squared = 1 / (SQR (r4p) + SQR (r5p));
    else if ((fabs (r4p) < EPSILON) && (fabs (r5p) < EPSILON))
	Ty_squared = 1 / (SQR (r1p) + SQR (r2p));
    else if ((fabs (r1p) < EPSILON) && (fabs (r4p) < EPSILON))
	Ty_squared = 1 / (SQR (r2p) + SQR (r5p));
    else if ((fabs (r2p) < EPSILON) && (fabs (r5p) < EPSILON))
	Ty_squared = 1 / (SQR (r1p) + SQR (r4p));
    else {
	Sr = SQR (r1p) + SQR (r2p) + SQR (r4p) + SQR (r5p);
	Ty_squared = (Sr - sqrt (SQR (Sr) - 4 * SQR (r1p * r5p - r4p * r2p))) /
	 (2 * SQR (r1p * r5p - r4p * r2p));
    }

    /* 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;
    Tx = U[2] * Ty;
    r4 = U[3] * Ty;
    r5 = U[4] * Ty;
    x = r1 * cd.xw[far_point] + r2 * cd.yw[far_point] + Tx;
    y = r4 * cd.xw[far_point] + r5 * cd.yw[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[2] * Ty;
    cc.Ty = Ty;
}


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

    r1 = U[0] * cc.Ty;
    r2 = U[1] * cc.Ty;
    r3 = sqrt (1 - SQR (r1) - SQR (r2));

    r4 = U[3] * cc.Ty;
    r5 = U[4] * cc.Ty;
    r6 = sqrt (1 - SQR (r4) - SQR (r5));
    if (!SIGNBIT (r1 * r4 + r2 * r5))
	r6 = -r6;

    /* 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      cc_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, "cc compute apx: unable to allocate matrix M\n");
	exit (-1);
    }

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

    b = newdmat (0, (cd.point_count - 1), 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "cc 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.Ty;
	M.el[i][1] = -Yd[i];
	b.el[i][0] = (cc.r7 * cd.xw[i] + cc.r8 * cd.yw[i]) * Yd[i];
    }

    if (solve_system (M, a, b)) {
	fprintf (stderr, "cc 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      cc_compute_exact_f_and_Tz_error (m_ptr, n_ptr, params, err)
    integer  *m_ptr;		/* pointer to number of points to fit */
    integer  *n_ptr;		/* pointer to number of parameters */
    doublereal *params;		/* vector of parameters */
    doublereal *err;		/* vector of error from data */
{
    int       i;

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

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

    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 = cc.r1 * cd.xw[i] + cc.r2 * cd.yw[i] + cc.Tx;
	yc = cc.r4 * cd.xw[i] + cc.r5 * cd.yw[i] + cc.Ty;
	zc = cc.r7 * cd.xw[i] + cc.r8 * cd.yw[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 * (SQR (Xd[i]) + SQR (Yd[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);
    }
}


void      cc_compute_exact_f_and_Tz ()
{
#define NPARAMS 3

    int       i;

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

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

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

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

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

    /* use the current calibration constants as an initial guess */
    x[0] = cc.f;
    x[1] = cc.Tz;
    x[2] = cc.kappa1;

    /* 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_compute_exact_f_and_Tz_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 constants */
    cc.f = x[0];
    cc.Tz = x[1];
    cc.kappa1 = x[2];

    /* 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
}


/************************************************************************/
void      cc_three_parm_optimization ()
{
    int       i;

    for (i = 0; i < cd.point_count; i++)
	if (cd.zw[i]) {
	    fprintf (stderr, "error - coplanar calibration tried with data outside of Z plane\n\n");
	    exit (-1);
	}

    cc_compute_Xd_Yd_and_r_squared ();

    cc_compute_U ();

    cc_compute_Tx_and_Ty ();

    cc_compute_R ();

    cc_compute_approximate_f_and_Tz ();

    if (cc.f < 0) {
        /* try the other solution for the orthonormal matrix */
	cc.r3 = -cc.r3;
	cc.r6 = -cc.r6;
	cc.r7 = -cc.r7;
	cc.r8 = -cc.r8;
	solve_RPY_transform ();

	cc_compute_approximate_f_and_Tz ();

	if (cc.f < 0) {
	    fprintf (stderr, "error - possible handedness problem with data\n");
	    exit (-1);
	}
    }

    cc_compute_exact_f_and_Tz ();
}


/************************************************************************/
void      cc_remove_sensor_plane_distortion_from_Xd_and_Yd ()
{
    int       i;
    double    Xu,
              Yu;

    for (i = 0; i < cd.point_count; i++) {
	distorted_to_undistorted_sensor_coord (Xd[i], Yd[i], &Xu, &Yu);
	Xd[i] = Xu;
	Yd[i] = Yu;
	r_squared[i] = SQR (Xu) + SQR (Yu);
    }
}


/************************************************************************/
void      cc_five_parm_optimization_with_late_distortion_removal_error (m_ptr, n_ptr, params, err)
    integer  *m_ptr;		/* pointer to number of points to fit */
    integer  *n_ptr;		/* pointer to number of parameters */
    doublereal *params;		/* vector of parameters */
    doublereal *err;		/* vector of error from data */
{
    int       i;

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

    /* in this routine radial lens distortion is only taken into account */
    /* after the rotation and translation constants have been determined */

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

    cp.Cx = params[3];
    cp.Cy = params[4];

    cc_compute_Xd_Yd_and_r_squared ();

    cc_compute_U ();

    cc_compute_Tx_and_Ty ();

    cc_compute_R ();

    cc_compute_approximate_f_and_Tz ();