Well, in order to apply mathematical operations to an image, we somehow have to interpret them as numbers. How? For simplicity, we'll assume that it's 1955 and there's only shades of grey to work with - no colour (so the scenery is rather dull ... like New Hampshire in winter).
Having assigned numbers to shades of gray, where's the image come in? It comes in this way: we consider an image to be an array (either square or rectangular) of numbers. Such an array of such numbers is called a matrix. For example, here's an array of four numbers, arranged in a square. Since this square has two rows and two columns, we call it a 2-by-2 matrix.
Each box is called a pixel. Now let me make a square that has the same area as the one above, but this time has a total of 16 pixels, 4 per row, 4 per column, and assign a random shade of gray to each of those. The individual pixels get smaller:
Why stop there? Again, let me make a square that has the same area as the one above, but this time has a total of 64 pixels, 8 per row, 8 per column, and assign a random shade of gray to each of those. As before, the individual pixels get smaller:
Let's introduce a little mathematical notation. An image is a function f(x,y) that gives the level of brightness, or intensity at a specific spatial location (x,y). A shortcoming of computers is that they only work with digital data. So, to work with an image, we need to sample the function lots of times. This is why we consider images to be matrices (and vice versa). When we do something like remove noise from an image, all we're doing is applying some mathematical operations to a matrix whose entries are the pixel intensities.
To give just a brief hint of things to come ... how might we even begin to think about compressing Kramer? Suppose the above image is too large to fit on a single floppy disk. How might we be able to shrink the image? To store it on the floppy disk? One way to tackle this problem is to divide the matrix into pieces, and treat each piece as a separate, smaller problem:
Abode Photoshop is a very powerful tool that allows one to do all sort of manipulations on images.
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