Activity 13: Correcting Geometric Distortion

Objectives: To demonstrate the process of correcting geometric distortions present in images.

Tools: Scilab with SIP.

Procedure: In order to simplify the computation, we use a grid of horizontal and vertical lines with barrel distortion present like the one we have below:

Using an idealized matrix of points, that is in the proper perpendicular vertex loci which is derived either using software or manually through the interface, we establish our reference grid. This is represented as a set of points occurring on the intersections of the lines.

Now using the least distorted part of the test grid image, we compute c1 through c8 using the following matrices:

Using linear algebra, the details of which we will omit as they are redundant, we get an expression for the coordinates of all the points of the image translated into the undistorted or proper frame:

This gives us the coordinates of the vertices in the correct frame. We use 2 interpolation methods to generate the points in between. We first use the bilinear interpolation which yields a grid like:

And then using the nearest neighbor interpolation we get:

As is consistent with theory, the bilinear method yields better results in terms of reconstructions.

Evaluation: For the properly reconstructed grid, a grade of 10 is justified.

Acknowledgements: As usual I thank Earl Panganiban and Gilbert Gubatan for their assistance.