NEW calibration toolbox : no prior knowledge is needed on the camera or mirror parameters and we keep the flexibility of only having to select four points for each calibration grid (we do not have to select each corner individually).

The functions containing the projection model (and Jacobians) are available separately in Matlab and as a C++ class with the associated mex functions. The class is initialised with a file generated during the calibration process. It enables the projection of 3D points but also the lifting of image points to their projective rays.

This new "Omnidirectional Calibration Toolbox" is a complete rewrite of the previous version. It uses some functions from the "Caltech Calibration Toolbox" by Jean-Yves Bouguet.

This page gives an example of a calibration session. These images are available for trying out the toolbox. You can find a calibration grid/pattern here. The projection model used is available here.

The toolbox has been successfully used to calibrate hyperbolic, parabolic, folded mirror, spherical and wide-angle sensors.

IMPORTANT : the calibration parameters are calculated with Matlab coordinates (which start at 1) and not with the C/C++ convention (starting at 0).

I would like to thank the ACFR (Australian Center for Field Robotics) for making available some hyperbolic images, and in particular Alex Brooks.

The projection model used is described here. It is a combination of the unified projection model from Geyer and Barreto and a radial distortion function. This model makes it possible take into account the distortion introduced by telecentric lenses (for parabolic mirrors) and gives a greater flexibility (spherical mirrors can be calibrated).

The calibration will estimate :

• the extrinsic parameters corresponding to the rotation (quaternion : Qw) and translation (Tw) between the grid and the mirror
• the parameters describing the mirror shape (xi)
• the distortion induced by the lens (eg. telecentric) (kc)
• the intrinsic parameters of the generalised camera : skew (alpha_c), generalised focal lengths (gamma1,gamma2) and principal points (cc)
  

>>omni_calib_gui

Go to the directory containing the images.
If you would like to know straight away the use of the different buttons, go to this section.

Mirror type

1 or [] : parabola (xi=1)
2 : catadioptric (hyperbola,ellipse,sphere)
3 : dioptric (fisheye)
Choice :
Camera type : parabolic.

>>
.                      Omni_Fixed_Values.m    cameraAvecOmni_00.tif  cameraAvecOmni_02.tif  cameraAvecOmni_04.tif  cameraAvecOmni_06.tif 
..                     Omni_Fixed_Values.mat  cameraAvecOmni_01.tif  cameraAvecOmni_03.tif  cameraAvecOmni_05.tif 

Basename camera calibration images (without number nor suffix): cameraAvecOmni_
Image format: ([]='r'='ras', 'b'='bmp', 't'='tif', 'p'='pgm', 'j'='jpg', 'm'='ppm') t
Loading image 1...2...3...4...5...6...7...
done

Please click on the mirror center and then on the mirror inner border.
Calculating edges... done.
Rejecting inner points... done.
Doing a simplified RANSAC to obtain circle parameters... done.
Was the extraction successful ? ([]=yes, other=no) :

We are now going to estimate the generalised focal (gammac) from line images.
Which image shall we use ? ([] = 1) : 2
Please select at least 4 ALIGNED edge points on a NON-RADIAL line on the grid.
Click with the right button when finished.
done.

Pressing on "Calibration" will start the minimisation :

>>
Aspect ratio optimized (est_aspect_ratio = 1) -> both components of fc are estimated (DEFAULT).
Principal point optimized (center_optim=1) - (DEFAULT). To reject principal point, set center_optim=0
Skew not optimized (est_alpha=0) - (DEFAULT)

Main calibration optimization procedure - Number of images : 7
Gradient descent iterations : WARNING: removing singular matrix warning and managing it internally.
1...2...(r) 3...4...5...6...7...8...9...10...11...12...(r) 13...14...15...16...17...18...19...20...21...22...(r) 23...24...25...26...27...28...29...30...31...32...(r) 33...34...35...36...37...38...39...40...41..
42...(r) 43...44...45...46...47...48...49...50...51...52...(r) 53...54...55...56...57...58...59...Matrix badly conditioned, stopping...
done
Estimation of uncertainties...done


Calibration results after optimization (with uncertainties):

Focal Length:          fc = [17.92581   17.91205 ] ± [ 0.18220   0.21302 ]
Principal point:       cc = [ 980.75605   544.84446 ] ± [ 4.41434   4.64072 ]
Skew:             alpha_c = [ 0.00000 ] ± [ 0.00283  ]   => angle of pixel axes = 90.00000 ± 0.16228 degrees
Distortion:            kc = [ -0.00008   0.00000   0.00000   -0.00000  0.00000 ] ± [ 0.00001   0.00000   0.00003   0.00002  0.00000 ]
Pixel error+-std :          err = [ 0.17324   0.29971 ]+-[ 0.13750   0.24850 ]
Note: The numerical errors are approximately three times the standard deviations (for reference).

Recommendation: The skew coefficient alpha_c is found to be equal to zero (within its uncertainty).
                You may want to reject it from the optimization by setting est_alpha=0 and run Calibration

Recommendation: Some distortion coefficients are found equal to zero (within their uncertainties).
                To reject them from the optimization set est_dist=[1;1;0;0;0] and run Calibration

(r) Indicates that the extrinsic parameters are being re-estimated independently.
"Pixel error" is the mean absolute error.

1. "Plot Pix/Rad errors" that gives you the error in the image versus the distance of the points from the image center :
   
   
   
   
   
2. "Analyse error" this will give you the reprojection error, each color is associated to an image. This will help you identify the points that have been incorrectly extracted.
   You can then reextract corners using "Recomp. corners".
   
   
   
   
3. "Draw 3D" shows the grids in 3D :
   
   
   
   
   

• "Mirror type" to input the values of the mirror diameter and parameters
  
• "Load images" to load the images used for the calibration
  
• "Estimate camera intri." to obtain initial values for the calibration using the mirror border
  
• "Extract grid corners" helps extract the grid corners for the calibration
  
• "Draw Grid Estimate" projects in yellow the grid points according to the calculated values, in red are the extracted points
  
• "Calibration" launches the minimisation using the distance in the image
  
• "Rm Calibration" removes the calibration parameters
• "Analyse error" reprojects the error, this can be used to find images where the points have not been properly extracted
  
• "Recomp. corners" recomputes the point extraction after reprojecting the grid points (this can be used when "Analyse Error" shows that some grid points have been incorrectly extracted)
  
• "Draw 3D" draws a 3D view of the camera and grids
• "Plot Pix/Rad errors" plots the error in pixels versus the distance of the points to the image center
  
• "Add/Suppress images" makes it possible to add or remove images
  
• "Show calib results" show the calibration values and errors
  
• "Save" saves the extrinsic and intrinsic parameters, the grid points, ...
  
• "Load" loads the values obtained during the calibration
  
• "Exit" quits the program
  

The files that are not part of the "Caltech Calibration Toolbox" by Jean-Yves Bouguet are issued under the GPL license Version 2.

If you have any suggestions, bug corrections please write to : Christopher.Mei@sophia.inria.fr

Old toolbox, no longer maintained.