cal_main.c

tsai经典标定程序 MATLAB语言

/*******************************************************************************\
*                                                                               *
* This file contains routines for calibrating Tsai's 11 parameter camera model. *
* The camera model is based on the pin hole model of 3D-2D perspective          *
* projection with 1st order radial lens distortion.  The model consists of      *
* 5 internal (also called intrinsic or interior) camera parameters:             *
*                                                                               *
*       f       - effective focal length of the pin hole camera                 *
*       kappa1  - 1st order radial lens distortion coefficient                  *
*       Cx, Cy  - coordinates of center of radial lens distortion               *
*		  (also used as the piercing point of the camera coordinate	*
*		   frame's Z axis with the camera's sensor plane)               *
*       sx      - uncertainty factor for scale of horizontal scanline           *
*                                                                               *
* and 6 external (also called extrinsic or exterior) camera parameters:         *
*                                                                               *
*       Rx, Ry, Rz, Tx, Ty, Tz  - rotational and translational components of    *
*                                 the transform between the world's coordinate  *
*                                 frame and the camera's coordinate frame.      *
*                                                                               *
* Data for model calibration consists of the (x,y,z) world coordinates of a     *
* feature point (in mm) and the corresponding coordinates (Xf,Yf) (in pixels)   *
* of the feature point in the image.  Two types of calibration are available:   *
*                                                                               *
*       coplanar     - all of the calibration points lie in a single plane      *
*       non-coplanar - the calibration points do not lie in a single plane      *
*                                                                               *
* This file contains routines for two levels of calibration.  The first level   *
* of calibration is a direct implementation of Tsai's algorithm in which only   *
* the f, Tz and kappa1 parameters are optimized for.  The routines are:         *
*                                                                               *
*       coplanar_calibration ()                                                 *
*       noncoplanar_calibration ()                                              *
*                                                                               *
* The second level of calibration optimizes for everything.  This level is      *
* very slow but provides the most accurate calibration.  The routines are:      *
*                                                                               *
*       coplanar_calibration_with_full_optimization ()                          *
*       noncoplanar_calibration_with_full_optimization ()                       *
*                                                                               *
* Routines are also provided for initializing camera parameter variables        *
* for five of our camera/frame grabber systems.  These routines are:            *
*                                                                               *
*       initialize_photometrics_parms ()                                        *
*       initialize_general_imaging_mos5300_matrox_parms ()                      *
*       initialize_panasonic_gp_mf702_matrox_parms ()                           *
*       initialize_sony_xc75_matrox_parms ()                                    *
*       initialize_sony_xc77_matrox_parms ()                                    *
*       initialize_sony_xc57_androx_parms ()                                    *
*                                                                               *
*                                                                               *
* External routines                                                             *
* -----------------                                                             *
*                                                                               *
* Nonlinear optimization for these camera calibration routines is performed     *
* by the MINPACK lmdif subroutine.  lmdif uses a modified Levenberg-Marquardt   *
* with a jacobian calculated by a forward-difference approximation.             *
* The MINPACK FORTRAN routines were translated into C generated using f2c.      *
*                                                                               *
* Matrix operations (inversions, multiplications, etc.) are also provided by    *
* external routines.                                                            *
*                                                                               *
*                                                                               *
* Extra notes                                                                   *
* -----------                                                                   *
*                                                                               *
* An explanation of the basic algorithms and description of the variables       *
* can be found in several publications, including:                              *
*                                                                               *
* "An Efficient and Accurate Camera Calibration Technique for 3D Machine        *
*  Vision", Roger Y. Tsai, Proceedings of IEEE Conference on Computer Vision    *
*  and Pattern Recognition, Miami Beach, FL, 1986, pages 364-374.               *
*                                                                               *
*  and                                                                          *
*                                                                               *
* "A versatile Camera Calibration Technique for High-Accuracy 3D Machine        *
*  Vision Metrology Using Off-the-Shelf TV Cameras and Lenses", Roger Y. Tsai,  *
*  IEEE Journal of Robotics and Automation, Vol. RA-3, No. 4, August 1987,      *
*  pages 323-344.                                                               *
*                                                                               *
*                                                                               *
* Notation                                                                      *
* --------                                                                      *
*                                                                               *
* The camera's X axis runs along increasing column coordinates in the           *
* image/frame.  The Y axis runs along increasing row coordinates.               *
*                                                                               *
* pix == image/frame grabber picture element                                    *
* sel == camera sensor element                                                  *
*                                                                               *
* Internal routines starting with "cc_" are for coplanar calibration.           *
* Internal routines starting with "ncc_" are for noncoplanar calibration.       *
*                                                                               *
*                                                                               *
* History                                                                       *
* -------                                                                       *
*                                                                               *
* 20-May-95  Reg Willson ([e-mail]) at 3M St. Paul, MN                 *
*       Return the error to lmdif rather than the squared error.                *
*         lmdif calculates the squared error internally during optimization.    *
*         Before this change calibration was essentially optimizing error^4.    *
*       Put transform and evaluation routines into separate files.              *
*                                                                               *
* 02-Apr-95  Reg Willson ([e-mail]) at 3M St. Paul, MN                 *
*       Rewrite memory allocation to avoid memory alignment problems            *
*       on some machines.                                                       *
*       Strip out IMSL code.  MINPACK seems to work fine.                       *
*       Filename changes for DOS port.                                          *
*                                                                               *
* 04-Jun-94  Reg Willson ([e-mail]) at 3M St. Paul, MN                 *
*       Replaced ncc_compute_Xdp_and_Ydp with ncc_compute_Xd_Yd_and_r_squared.  *
*         (effectively propagates the 22-Mar-94 to the non-coplanar routines)   *
*       Added alternate macro definitions for less common math functions.       *
*                                                                               *
* 25-Mar-94  Torfi Thorhallsson ([e-mail]) at the University of Iceland*
*       Added a new version of the routines:                                    *
*            cc_compute_exact_f_and_Tz ()                                       *
*            cc_five_parm_optimization_with_late_distortion_removal ()          *
*            cc_five_parm_optimization_with_early_distortion_removal ()         *
*            cc_nic_optimization ()                                             *
*            cc_full_optimization ()                                            *
*            ncc_compute_exact_f_and_Tz ()                                      *
*            ncc_nic_optimization ()                                            *
*            ncc_full_optimization ()                                           *
*                                                                               *
*       The new routines use the *public domain* MINPACK library for            *
*       optimization instead of the commercial IMSL library.                    *
*       To select the new routines, compile this file with the flag -DMINPACK   *
*                                                                               *
* 22-Mar-94  Torfi Thorhallsson ([e-mail]) at the University of Iceland*
*       Fixed a bug in cc_nic_optimization_error and cc_full_optimization_error.*
*       A division by cp.sx was missing.                                        *
*                                                                               *
* 15-Feb-94  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*       Included Frederic Devernay's (<[e-mail]>)	*
*	significantly improved routine for converting from undistorted to	*
*	distorted sensor coordinates.  Rather than iteratively solving a	*
*	system of two non-linear equations to perform the conversion, the 	*
*	new routine algebraically solves a cubic polynomial in Rd (using	*
*	the Cardan method).							*
*                                                                               *
* 14-Feb-94  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*	Fixed a coding bug in ncc_compute_R and ncc_compute_better_R.           *
*       The r4, r5, and r6 terms should not be divided by cp.sx.                *
*       Bug reported by: Volker Rodehorst <[e-mail]>                  *
*                                                                               *
* 04-Jul-93  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*	Added new routines to evaluate the accuracy of camera calibration.      *
*                                                                               *
*       Added check for coordinate handedness problem in calibration data.      *
*                                                                               *
* 01-May-93  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*	For efficiency the non-linear optimizations are now all based on	*
*	the minimization of squared error in undistorted image coordinates      *
*	instead of the squared error in distorted image coordinates.		*
*										*
*	New routine for inverse perspective projection.				*
*										*
* 14-Feb-93  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*       Bug fixes and speed ups.                                                *
*                                                                               *
* 07-Feb-93  Reg Willson ([e-mail]) at Carnegie-Mellon University         *
*       Original implementation.                                                *
*                                                                               *
\*******************************************************************************/

#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <errno.h>
#include "matrix/matrix.h"
#include "cal_main.h"
#include "minpack/f2c.h"


/* Variables used by the subroutines for I/O (perhaps not the best way of doing this) */
struct camera_parameters cp;
struct calibration_data cd;
struct calibration_constants cc;

/* Local working storage */
double    Xd[MAX_POINTS],
          Yd[MAX_POINTS],
          r_squared[MAX_POINTS],
          U[7];


char   camera_type[256] = "unknown";


/************************************************************************/
.
void      initialize_photometrics_parms ()
{
    strcpy (camera_type, "Photometrics Star I");

    cp.Ncx = 576;		/* [sel]        */
    cp.Nfx = 576;		/* [pix]        */
    cp.dx = 0.023;		/* [mm/sel]     */
    cp.dy = 0.023;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;		/* [mm/pix]     */
    cp.Cx = 576 / 2;		/* [pix]        */
    cp.Cy = 384 / 2;		/* [pix]        */
    cp.sx = 1.0;		/* []		 */

    /* something a bit more realistic */
    cp.Cx = 258.0;
    cp.Cy = 204.0;
}


/************************************************************************/
void      initialize_general_imaging_mos5300_matrox_parms ()
{
    strcpy (camera_type, "General Imaging MOS5300 + Matrox");

    cp.Ncx = 649;		/* [sel]        */
    cp.Nfx = 512;		/* [pix]        */
    cp.dx = 0.015;		/* [mm/sel]     */
    cp.dy = 0.015;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;		/* [mm/pix]     */
    cp.Cx = 512 / 2;		/* [pix]        */
    cp.Cy = 480 / 2;		/* [pix]        */
    cp.sx = 1.0;		/* []		 */
}


/************************************************************************/
void      initialize_panasonic_gp_mf702_matrox_parms ()
{
    strcpy (camera_type, "Panasonic GP-MF702 + Matrox");

    cp.Ncx = 649;		/* [sel]        */
    cp.Nfx = 512;		/* [pix]        */
    cp.dx = 0.015;		/* [mm/sel]     */
    cp.dy = 0.015;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;		/* [mm/pix]     */

    cp.Cx = 268;		/* [pix]        */
    cp.Cy = 248;		/* [pix]        */

    cp.sx = 1.078647;		/* []           */
}


/************************************************************************/
void      initialize_sony_xc75_matrox_parms ()
{
    strcpy (camera_type, "Sony XC75 + Matrox");

    cp.Ncx = 768;		/* [sel]        */
    cp.Nfx = 512;		/* [pix]        */
    cp.dx = 0.0084;		/* [mm/sel]     */
    cp.dy = 0.0098;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;		/* [mm/pix]     */
    cp.Cx = 512 / 2;		/* [pix]        */
    cp.Cy = 480 / 2;		/* [pix]        */
    cp.sx = 1.0;		/* []           */
}


/************************************************************************/
void      initialize_sony_xc77_matrox_parms ()
{
    strcpy (camera_type, "Sony XC77 + Matrox");

    cp.Ncx = 768;		/* [sel]        */
    cp.Nfx = 512;		/* [pix]        */
    cp.dx = 0.011;		/* [mm/sel]     */
    cp.dy = 0.013;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;		/* [mm/pix]     */
    cp.Cx = 512 / 2;		/* [pix]        */
    cp.Cy = 480 / 2;		/* [pix]        */
    cp.sx = 1.0;		/* []           */
}


/************************************************************************/
void      initialize_sony_xc57_androx_parms ()
{
    strcpy (camera_type, "Sony XC57 + Androx");

    cp.Ncx = 510;               /* [sel]        */
    cp.Nfx = 512;               /* [pix]        */
    cp.dx = 0.017;              /* [mm/sel]     */
    cp.dy = 0.013;              /* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;   /* [mm/pix]     */
    cp.dpy = cp.dy;             /* [mm/pix]     */
    cp.Cx = 512 / 2;            /* [pix]        */
    cp.Cy = 480 / 2;            /* [pix]        */
    cp.sx = 1.107914;           /* []           */
}


/************************************************************************/
/* John Krumm, 9 November 1993                                          */
/* This assumes that every other row, starting with the second row from */
/* the top, has been removed.  The Xap Shot CCD only has 250 lines, and */
/* it inserts new rows in between the real rows to make a full size     */
/* picture.  Its algorithm for making these new rows isn't very good,   */
/* so it's best just to throw them away.                                */
/* The camera's specs give the CCD size as 6.4(V)x4.8(H) mm.            */
/* A call to the manufacturer found that the CCD has 250 rows           */
/* and 782 columns.  It is underscanned to 242 rows and 739 columns.    */
/************************************************************************/
void      initialize_xapshot_matrox_parms ()
{
    strcpy (camera_type, "Canon Xap Shot");

    cp.Ncx = 739;			/* [sel]        */
    cp.Nfx = 512;			/* [pix]        */
    cp.dx = 6.4 / 782.0;		/* [mm/sel]     */
    cp.dy = 4.8 / 250.0;		/* [mm/sel]     */
    cp.dpx = cp.dx * cp.Ncx / cp.Nfx;	/* [mm/pix]     */
    cp.dpy = cp.dy;			/* [mm/pix]     */
    cp.Cx = 512 / 2;			/* [pix]        */
    cp.Cy = 240 / 2;			/* [pix]        */
    cp.sx = 1.027753;	/* from noncoplanar calibration *//* []           */
}


/***********************************************************************\
* This routine solves for the roll, pitch and yaw angles (in radians)	*
* for a given orthonormal rotation matrix (from Richard P. Paul,        *
* Robot Manipulators: Mathematics, Programming and Control, p70).       *
* Note 1, should the rotation matrix not be orthonormal these will not  *
* be the "best fit" roll, pitch and yaw angles.                         *
* Note 2, there are actually two possible solutions for the matrix.     *
* The second solution can be found by adding 180 degrees to Rz before   *
* Ry and Rx are calculated.                                             *
\***********************************************************************/
void      solve_RPY_transform ()
{
    double    sg,
              cg;

    cc.Rz = atan2 (cc.r4, cc.r1);

    SINCOS (cc.Rz, sg, cg);

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

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


/***********************************************************************\
* This routine simply takes the roll, pitch and yaw angles and fills in	*
* the rotation matrix elements r1-r9.					*
\***********************************************************************/
void      apply_RPY_transform ()
{
    double    sa,
              ca,
              sb,
              cb,
              sg,
              cg;

    SINCOS (cc.Rx, sa, ca);
    SINCOS (cc.Ry, sb, cb);
    SINCOS (cc.Rz, sg, cg);

    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;
}


/***********************************************************************\
* Routines for coplanar camera calibration	 			*
\***********************************************************************/
void      cc_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      cc_compute_U ()
{
    int       i;

    dmat      M,
              a,
              b;

    M = newdmat (0, (cd.point_count - 1), 0, 4, &errno);
    if (errno) {
	fprintf (stderr, "cc compute U: unable to allocate matrix M\n");
        exit (-1);
    }

    a = newdmat (0, 4, 0, 0, &errno);
    if (errno) {
	fprintf (stderr, "cc compute U: unable to allocate vector a\n");
	exit (-1);
    }

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