Activity 13: Correcting Geometric Distortions

Distortion is an example of monochromatic aberrations. Distortion arises because different areas of the lens have different focal length and different magnifications. There are two types of distortion positive or pincushion distortion and negative or barrel distortion. Ideally, a thin lens will have no distortion. [1]

Figure 1. Left: Barrel distortion. Right:Pincushion distortion. If there is no distortion, the above images will be regularly spaced grids.

For this activity, we are tasked to correct a distorted image by first assuming that the distorted image is just a linear transform of the ideal image and vice versa.

Figure 2. Coordinate transformation.

The transformation functions are assumed to be bilinear functions of the form

where x and y in the LHS are the pixel coordinates in the distorted image and the x and y in the RHS are for the ideal image. After finding the coordinate transform, we look for the grayvalue at the ideal image pixel locations using a bilinear interpolation.

For my distorted images, I used the ones below (Click for a larger view.)

Figure 3. Distorted images.

The results are the following. (Click for a larger view.)

Figure 4. Corrected images.

Then results show that the method is sufficient to correct distortion of small images.

For this activity, I'll give myself a 10 for satisfactory result. Note that the reconstructed image does not require anymore a second bilinear interpolation because no null pixels are found.

Reference
[1] E. Hecht (2002). Optics 4th edition. Addison Wesley , CA.