Mr. Shadi Saleh,

The documentation of OpenCV may help you: 

http://docs.opencv.org/2.4/doc/tutorials/calib3d/camera_calibration/camera_calibration.html

http://docs.opencv.org/2.4/doc/tutorials/calib3d/camera_calibration/camera_calibration.html

thankx  Teruo Matos Maruyama and Sarah Hachemi Benziane 

yes using a regular grid of circles as calibration pattern is more accurate ,but My question:

 how I can determine rows=? X columns=? of the calibration sheet(calibration pattern size), and also the distance = ? between each row an column(distance bewteen circle & its size), and the position=? for the calibration sheet, in order to obtain the accurate calibration for the camera mounted on the car

I'm not sure about the specifics for wide lens cameras, although I believe you might be able to find some references on this.

In general terms, I don't believe the distance between circles is relevant, as long as the distance is known (since you use this as input information) and the pattern is printed with precision (altough this issue with precision might be overcome).

When dealing with rows and columns, I believe the importance is actually on the number of points in the pattern, which determines the number of correspondences used when solving the calibration parameters. So you can use any regular grid and if you wish to increase the number of correspondences you can use multiple frames.

You wrote "using a regular grid of circles as calibration pattern is more accurate" but the answer here (http://dsp.stackexchange.com/questions/24734/camera-calibration-why-chessboards) suggests that checkerboard patterns may yield more accurate (subpixel) calibration results and be more robust.

There is also a paper (http://www.cipa.dcu.ie/papers/Prl_bias_preprint_2007.pdf) from John Mallon and Paul F. Whelan comparing biasing aspects.

But if you have some text showing that the grid of circles may be more accurate, that would be a useful bit of information.

thanks alot Hakan Hekimgil

for example those papers 

http://www.mdpi.com/1424-8220/14/9/17471/htm 

and 

http://www.public.navy.mil/spawar/Pacific/Robotics/Documents/Publications/2014/SPIE_2014_Harguess.pdf

We  can use following patterns for calibration process 

-  Classical Black-White chess board  

-  Symmetrical Circle Pattern  

-  Asymmetrical Circle Pattern

-,,,, 

in order to reduce the distortion and for more accuracy  is better to use circles as calibration pattern.  

my confusing is that, which are the standards  that , should be used to define the size of the calibration pattern sheet and its  position on the ground or ,,,,,?

also it is not sufficient for calibration process to place the patterns as the boundary of the capture frames .

Regarding accuracy both checkerboard and circular patterns can be used with subpixel methods and be accurate.

Circular patterns can be potentially more accurate (up to 0.1 or 0.01 pixel in some controlled cases) but only if there is proper subpixel determination of the center of mass or center of the circles (detected as ellipses). That's why they are used in industrial photogrammetry mostly. However the math involved is also more complex regarding corrections, and is sensitive to a proper choice of circle sizes, which it is not always easy to apply fully.  In practice subpixel determination of edges in a checkerboard pattern is also possible and you can get a great improvement there with simple math.

However this are really fine issues to dig into the subpixel accuracy. It is normally way more important to choose the right camera model and an adequate pattern for the application. In my experience image coverage is typically more overlooked and the most important aspect than anything else and calibration errors there are in the range of several pixels.

For instance if the pattern is designed to be shown fully in the images it will not allow easily to match points close to the edge of the images in oblique shots. You will be extrapolating the model there more often than not with a lot of empty space.

A pattern which is large enough to cover all or most of the image in every shot is ahuge advantage, but it will require to have some identifiable points in the middle such as:

http://cdn.iopscience.com/images/0957-0233/24/10/105106/Full/mst475049f5_online.jpg

http://www.k2.t.u-tokyo.ac.jp/mvf/FractalCalibrationPattern/index-e.html

It is easy to achieve low residuals with lower coverage but that does not mean directly better calibration. This really depends on the scenario and use case.

Regarding spacing of circles or edges, this a practical question. A 20x20 grid should be enough in most cases since the camera models are typically simple. However highly distorted lenses may require higher density. Denser grids are normally better with high resolution images, but it is a trade-off with computation time and detection capabilities (smaller features are normally harder to find).

Regarding the size of the dots, this is and advantage and disadvantage with respect to checkerboard. You need to decide, of course smaller than the spacing to avoid overlap. Larger allow for finer subpixel accuracy determination of center of mass, but require more complex corrections (projections are no longer ellipses and aberrations become very relevant). Smaller are simpler and less biased, but sometimes harder to find and detect.

There is no easy general answer. Everything is based on practical decisions depending on the specific case and don't forget that automatic and fast detection and matching are often an important issue, not just accuracy.

Here are some ”best practices“ regarding camera calibratio:

https://calib.io/blogs/knowledge-base/calibration-best-practices

As Antonio Martos said, accuracy depends on proper subpixel detection which is often not implemented for maximum accuracy. For instance, in OpenCV (v. 3.X), there is subpixel saddle point detection, albeit not accounting for perspective and distortion. The circles detection is usually even more crude (simple blob-detector).