Calibration Procedure

For the calibration procedure, we used a series of checker boards as the test pattern. For the camera calibration, we used a checker board printed on a piece of paper and placed it in front of the camera. For the projector calibration, we had the projector project a checker board onto a flat surface.

To do the calibration, we selected the corners of the black boxes on the images. We then used a least squares method to recursively find the camera and projector parameters. Below is a list of parameters for the camera and projector.

Focal length - The focal length of the camera
Center	     - The center of the camera image
Distortion   - The distortion caused by the camera lense.
Position     - The postion of the camera relative to the projector.

The calibration is required so we can get an acurate reconstruction of the object. We need the distortion parameters in our calculations to take into account the distortion effects of the camera lense. The postions of the camera is very important because it allows us to map the points from the camera to the object and projector and vice versa.

The calibration can be seperate into 2 stages: Camera and Projector calibration:

Camera Calibration:

Here we are looking for the camera intrinsic parameters and position relative to the object. Below is pattern we used for the camera calibration.

We performed the minimizations over the focal length, postion (T), rotation (omega), and distortion.

The camera calibration results are shown below.


	T = [-6.5553
	     -13.5758
	      181.1232 ]

	om = [-0.4394
	       0.5546
	       0.1668 ]

	fc = [ 2794.8
	       2586.0 ]

	kc = -0.3523

	cc = [ 320
	       240 ]

Projector Calibration:

Here we are looking for the position of the projector with respect to the object. Below is the pattern we have the projector project for the projector calibration.

The minimization was performed over the rotation and translation (omega and T), focal length, and distortion.

The projector calibration results are shown below.


	T = [-21.8351
	      0.8678
	      209.1172 ]

	om = [-0.7453
	      -0.0838
	      -0.0100 ]

	fp = [ 2014.7
	       2126.1 ]

	kp = 0.9181

	cp = [ 320
	       240 ]

Final Results:

The final postion is computed using the projector and camera rotation and translation parameters. The equations are given below.

	R = Rp * Rc'
	T = Tp - Rp * Rc' * Tc
	om = rodrigues(R)

The final parameters are shown below.

	T = [ 94.2450
	     -28.9124
	      72.4737 ]

	om = [-0.2824
	      -0.6567
	       0.0552 ]

To make sure that these parameters are correct, I took the norm of T and om to see if the values "made sense." The norm of om turns out to be 41.0818 degrees and the norm of T is 122.3539. These sounded reasonable given the setup of the system.