Activity 8: Camera Calibration

The formula for deriving the necessary parameters in camera calibration is given by the solution of Eq. 1.

Equation 1

From the values of the coefficients derived from this equation, a formula for acquiring the value of the image coordinates given its associated real-world coordinates can be derived given by Eq. 2 and Eq. 3.

Equation 2

Equation 3

In this activity which tackles the method of camera calibration [1], we used a checkerboard at right angle placed above another checkerboard as illustrated in Fig. 1.

Figure 1:  Checkerboard used for the camera calibration.

From this setup, we take sample pictures using a camera to be calibrated.  We chose an image and we selected certain points in the image plane to be used in the calibration denoted by the white dots in Fig. 2.  These points will be inputted to the camera calibration formula so that the calibrating parameters will be known.

Figure 2: 

The camera calibration formula requires the coordinates of the reference points both in the image coordinates and the real-world coordinates.  The resulting parameters should allow the person to know the value of the image coordinates of the region of interest given the real-world position ,and vice-versa.

We performed the camera calibration and we yield values for the coefficients as shown in Table 1.

Table 1:  Computed coefficients using the camera calibration formula.

We used these coefficients as parameters in Eqs. 2 and 3 to predict the image coordinates of known points in the image marked by red colored dots in Fig. 2.  This was done to ensure the correctness of the derived coefficients.

Table 2

 

Table 2 summarizes the results of the predictions which verifies the accuracy of the derived coefficients from the camera calibration formula.  The errors in the prediction never exceeded 1%.


Code:

Sources:
    [1] Dr. Maricor Soriano - Applied Physics 187 - Activity 8 Manual