In MATLAB, a grey$-$scale image is stored a a matrix of numbers, all between $0($black$)$ and $255($white$).$ Since there are $256$ possible values, $8$ bits are needed or each pixel, in contrast to a normal integer, which is $64$ bits.To save memory, grey$-$scale images are stored with a special data type, uint$8($unsigned $8-$bit integer$).$ In computer terminology, $8$ bits $=1$ byte.

Even at one byte per pixel, a large image can consume a lot of memory. For example, a $1000$x$1000-$pixel image takes $1$ million bytes $($which is a little less than $1$ megabyte, since by convention $1$ Mbyte $=2^20$ bytes$).$

One technique for reducing the size of an image is quantization $-$ reducing the number of allowable levels from $256$ to something smaller. Surprisingly, most images can be quantized by a large factor without losing much information. In this problem, you will quantize a grey$-$scale image to only $4$ levels, so that it could $($in principle$)$ be stored as $2$ bits per pixel.

The template will read in an image file. Your job is to loop over all rows and columns of the image matrix, N$,$ and set each pixel to $0,1,2,$ or $3$ as follows:

original pixel value new pixel value

$0-640$

$65-1281$

$129-1922$

$193-2553$

Use imshow to display the original and modified images so that you can see the effect of the quantization.

Provided Script:

$\%$Load in the color image and convert it to grey$-$scale

M $=$ imread$(\text{'}$images$\_$L$8\_2.$jpg$\text{'})$;

N $=$ uint$8($mean$($M$,3))$;

imshow$($N$)\%$look at the original image

$\%\%$YOUR CODE GOES HERE

$\%$THIS WILL DISPLAY THE QUANTIZED IMAGE $--$ DO EVERYTHING ABOVE THIS LINE

figure

Levels $=$ uint$8([32,96,160,224])\%$display each pixel as the mid$-$point of its range

imshow$($Levels$($N$+1))$