Determine all camera parameters of a binocular stereo system.

In general, binocular calibration means the exact determination of the parameters that model the 3D reconstruction of a 3D point from the corresponding images of this point in a binocular stereo system. This reconstruction is specified by the internal parameters CamParam1 of camera 1 and CamParam2 of camera 2 describing the underlying camera model, and the external parameters RelPose describing the relative pose of camera system 2 in relation to camera system 1.

Thus, known 3D model points (with coordinates NX, NY, NZ) are projected in the image planes of both cameras (camera 1 and camera 2) and the sum of the squared distances between these projections and the corresponding measured image points (with coordinates NRow1, NCol1 for camera 1 and NRow2, NCol2 for camera 2) is minimized. It should be noted that all these model points must be visible in both images. The projection uses the initial values StartCamParam1 and StartCamParam2 of the internal parameters of camera 1 and camera 2 which can be obtained from the camera data sheets. In addition, the initial guesses NStartPose1 and NStartPose2 of the poses of the 3D calibration model in relation to the camera coordinate systems (CCS) of camera 1 and camera 2 are needed as well. These 3D transformation poses can be determined by the find_marks_and_pose operator. Since this calibration algorithm simultaneously handles correspondences between measured image and known model points from different image pairs, poses (NStartPose1,NStartPose2), and measured points (NRow1,NCol1,NRow2, NCol2) must be passed concatenated in a corresponding order.

The input parameter EstimateParams is used to select the parameters to be estimated. Usually this parameter is set to 'all', i.e., all external camera parameters (translation and rotation) and all internal camera parameters are determined. Otherwise, EstimateParams contains a tuple of strings indicating the combination of parameters to estimate. For instance, if the interior camera parameters already have been determined (e.g., by previous calls to camera_calibration) it is often desired to only determine relative the pose of the two cameras to each other (RelPose). In this case, EstimateParams can be set to 'pose_rel'. This has the same effect as EstimateParams = ['pose1','pose2']. The internal parameters can be subsumed by the parameter values 'cam_param1' and 'cam_param2', as well. In addition, parameters can be excluded from estimation by using the prefix ~. For example, the values ['pose1', '~transx1'] have the same effect as ['alpha1','beta1','gamma1','transy1','transz1']. Whereas ['all','~focus1'] determines all internal and external parameters except the focus of camera 1, for instance. The prefix ~ can be used with all parameter values except 'all'.

The underlying camera model is explained in the description of the camera_calibration operator. It is specified by the parameters [focus1, kappa1, sx1, sy1, cx1, cy1, image_width1, image_height1] of camera 1 returned in CamParam1 and [focus2, kappa2, sx2, sy2, cx2, cy2, image_width2, image_height2] of camera 2 (CamParam2). The external parameters [alpha_rel, beta_rel, gamma_rel, transx_rel, transy_rel, transz_rel] are returned in RelPose and specify the 3D transformation of points of CCS 2 into CCS 1. Note that according to the description of poses at create_pose one parameter is appended to the pose tuple at the last position to define the representation type of this pose.

According to camera_calibration the 3D transformation poses of the calibration model to the respective CCS are returned in NFinalPose1 and NFinalPose2. These transformations are related to RelPose according to the following equation (neglecting differences due to the balancing effects of the multi image calibration):

 HomMat3D_NFinalPose2 = INV(HomMat3D_RelPose) * HomMat3D_NFinalPose1 ,

The computed average errors returned in Errors give an impression of the accuracy of the calibration. Using the determined camera parameters they denote the average of the euklidean distance of the projection of the mark centers of the model to their image.

// open image source
close_all_framegrabbers ()
open_framegrabber ('File', 1, 1, 0, 0, 0, 0, 'default', -1, 'default', -1,
                   'default', 'images_l.seq', 'default', 0, -1, FGHandle1)
open_framegrabber ('File', 1, 1, 0, 0, 0, 0, 'default', -1, 'default', -1,
                   'default', 'images_r.seq', 'default', 1, -1, FGHandle2)

// initialize the start parameters
create_caltab (0.03, 'caltab_30.descr', 'caltab_30.ps')
caltab_points ('caltab_30.descr', X, Y, Z)
StartCamParam1 := [0.0125, 0, 7.4e-6, 7.4e-6,Width/2.0,Height/2.0,Width,Height]
StartCamParam2 := StartCamParam1
Rows1 := []
Cols1 := []
StartPoses1 := []
Rows2 := []
Cols2 := []
StartPoses2 := []

// find calibration marks and startposes
for i := 0 to 11 by 1
  grab_image_async (Image1, FGHandle1, -1)
  grab_image_async (Image2, FGHandle2, -1)
  find_caltab (Image1, Caltab1, 'caltab_30.descr', 3, 120, 5)
  find_caltab (Image2, Caltab2, 'caltab_30.descr', 3, 120, 5)
  find_marks_and_pose (Image1, Caltab1, 'caltab_30.descr', StartCamParam1,
                       128, 10, 20, 0.7, 5, 100, RCoord1, CCoord1,
                       StartPose1)
  Rows1 := [Rows1,RCoord1]
  Cols1 := [Cols1,CCoord1]
  StartPoses1 := [StartPoses1,StartPose1]
  find_marks_and_pose (Image2, Caltab2, 'caltab_30.descr', StartCamParam2,
                       128, 10, 20, 0.7, 5, 100, RCoord2, CCoord2,
                       StartPose2)
  Rows2 := [Rows2,RCoord2]
  Cols2 := [Cols2,CCoord2]
  StartPoses2 := [StartPoses2,StartPose2]
endfor

// calibrate the stereo rig
binocular_calibration (X, Y, Z, Rows1, Cols1, Rows2, Cols2, StartCamParam1,
                       StartCamParam2, StartPoses1, StartPoses2, 'all',
                       CamParam1, CamParam2, NFinalPose1, NFinalPose2,
                       RelPose, Errors)
// archive the results
write_cam_par (CamParam1, 'cam_left-125.dat')
write_cam_par (CamParam2, 'cam_right-125.dat')
write_pose (RelPose, 'rel_pose.dat')

// ... rectify the stereo images
gen_binocular_rectification_map (Map1, Map2, CamParam1, CamParam2, RelPose, 
  'geometric', 'bilinear', CamParamRect1, CamParamRect2, Cam1PoseRect1, 
  Cam2PoseRect2, RelPoseRect)
map_image (Image1, Map1, ImageMapped1)
map_image (Image2, Map2, ImageMapped2)

binocular_calibration returns 2 (H_MSG_TRUE) if all parameter values are correct and the desired parameters have been determined by the minimization algorithm. If necessary, an exception handling is raised.

binocular_calibration is reentrant and processed without parallelization.

find_marks_and_pose, caltab_points, read_cam_par

write_pose, write_cam_par, pose_to_hom_mat3d, disp_caltab, gen_binocular_rectification_map

find_caltab, sim_caltab, read_cam_par, create_pose, convert_pose_type, read_pose, hom_mat3d_to_pose, create_caltab, binocular_disparity, binocular_distance

3D Metrology