WARNING: It is forbidden to use array operations that perform complete $2$ D array processing in

one command during our course!

For any $512512$ gray$-$scale digital image in our Images database $($example images are: cameraman, house,

jetplane, lake, livingroom, walkbridge$),$ do the following:

Write a MATLAB program to change $($downsample$)$ the spatial resolution to $256256,128128,$ and $3232$

pixels. Save these three images as $512512$ images. To do this, you will replicate pixels $($upsample$)$ to reach

the desired size; i$.$e$.,$ perform nearest$-$neighbor interpolation. Do not change the gray$-$scale resolution.

Note that you must write MATLAB code that explicitly scans through the $2$D array of an image in the $x$

and $y$ directions, per the example main.m file. Also, to read in a tif$-$format, such as "walkbridge.tif", you

will need the following commands:

$f=$ imread$(\text{'}$walkbridge$.$tif'$)$; $($Read the image into $"$ f $")$

$f=f($:$,$:$,1)$; $($Get the first "layer" of the tif image$)$

Create an interpolated $512512$ image from your $3232$ image of part $1($before you upsampled it to

$512512!)$ using either bilinear, bicubic, or inverse$-$distance interpolation, as discussed in G&W Sect. $2\mathrm{.}4$

and the Project Material document "Proj$1-$Interpolation.pdf$."$

Write a program to change the gray$-$level quantization of the original $512512$ image by reducing the number

of bits per pixel from $8$ to $7,6,5,4,3,2$ and $1$ bits$/$pixel$.$ Save these $7$ new images. Be sure that the gray

levels used in the new images span the $8-$bit range! For example, for the new $6$ bits$/$pixel image, the image

pixels should use the $64$ gray levels $0,4,8,12,$dots$252.$