Assignment 2

Theoretical Part

Practical Part

I expected that there would both methods would reconstruct the image perfectly because the polynomials calculated for a given pixel are an exact fit for the 9 data points in the 3x3 block of pixels around the center pixel.  Neither method in the assignment required evaluating the polynomial at anything but pixel centers of the 3x3 regions.  This intuition turned out to be correct.

Here are the Matlab functions I developed for this assignment.

Tiled Reconstructrion:

This figure shows the original image on the left with the reconstructed image on the right:

The absolute value of the difference is shown below (and is uniformly zero):

Full Reconstruction:

This figure shows the original image on the left with the reconstructed image on the right:

As expected there was no difference in the images.  Here is absolute value of the image differences: