The image we work on

MATLAB code to shift an entire image horizontally by taking the image's DTFT, then phase shifting in the frequency domain, and then taking the inverse DTFT. RGB is separately computed (unfortunately): shift11.m

The image before shifting

The image before shifting

This shows that the shifting algorithm works. The extra blue space to the right of the images is a result of zero padding the image matrix to give room for the shift.

We were prevented from returning the entire original image in shift18.m because we couldn't put the RGB matrix back together, not because our shifting was wrong.

This MATLAB code shifts blocks within a simpler image using the same method as above. It can be used on an image such as above, but visually, this is easier to see using a color matrix. shift18.m

The image before shifting

Here we implement a horizontal shift on one row of blocks. For a major part the shift is quite clear. There is some distortion of color in some of the blocks. This could be the result of the overlapping of neighbouring blocks.

Limitations

We were not very successful in making use of the 2D DTFT and therefore worked with the 1D transform first transforming and shifting horizontally, then vertically and then tranforming back to the time domain.

One of the limitations of applying the code to the real image lies in the fact that when decoded with MPEG there is a difference element encoded in the signal that we are forced to ignore as we focus our studies to motion vectors alone.