Learning OpenCV

Exercises

1. Use Figure 11-2 to derive the equations x = f_x · (X/Z) + c_x and y – f_y · (Y/Z) + c_y using similar triangles with a center-position offset.

2. Will errors in estimating the true center location (c_x, c_y) affect the estimation of other parameters such as focus?

   Hint: See the q = MQ equation.

3. Draw an image of a square:

   1. Under radial distortion.

   2. Under tangential distortion.

   3. Under both distortions.

4. Refer to Figure 11-13. For perspective views, explain the following.

   1. Where does the "line at infinity" come from?

   2. Why do parallel lines on the object plane converge to a point on the image plane?

   3. Assume that the object and image planes are perpendicular to one another. On the object plane, starting at a point p₁, move 10 units directly away from the image plane to p₂. What is the corresponding movement distance on the image plane?

5. Figure 11-3 shows the outward-bulging "barrel distortion" effect of radial distortion, which is especially evident in the left panel of Figure 11-12. Could some lenses generate an inward-bending effect? How would this be possible?

6. Using a cheap web camera or cell phone, create examples of radial and tangential distortion in images of concentric squares or chessboards.

7. Calibrate the camera in exercise 6. Display the pictures before and after undistortion.

8. Experiment with numerical stability and noise by collecting many images of chessboards and doing a "good" calibration on all of them. Then see how the calibration parameters change as you reduce the number of chessboard images. ...