Image:

The technical name for a picture when it is stored in a computer. For a more detailed explanation, see below.

Pixel:

Every image is made up of a grid of dots of various colours. Each dot is called a pixel.

Compression:

Any image requires a certain amount of space to describe. The simplest description method is to record the exact colour of every single pixel. However, this needs a lot of space. The act of compression is to find a way of describing the image using less space.
Sometimes this will restore the image exactly as it was (lossless compression) and sometimes the quality of the image will be slightly degraded (lossy compression). Usually, this degradation of quality will not be noticeable to the human eye, since the original image contains far more information than our eye can differentiate anyway.

Self similar:

An image is self-similar if smaller copies of the whole image, or a part of it, may be found embedded within the image. In essence, IFS images are a subset of fractals.

Images and pixels

Pictures (e.g. photographs) are created by real physical processes. In the case of a photograph, this process is a chemical change in a piece of film caused when light falls onto it.

Images are pictures that are stored digitally in a computer. An image may be generated directly by a computer using a program such as a raytracer or paint package. A photograph that is stored on a computer is also technically now an image, simply by dint of being converted into a digital format and being stored in a computer.

A photograph or other pixture may be made up of randomly shaped areas of colour. There may be no precisely quantizable place where any colour change occurs, and even at a very fine level there may be a seemingly infinite number of places that can have a different colour, no matter how subtle the change.

However, an image is made up of a finite number of pixels. These are laid out in a precise pattern with constant spacing and each has a discrete colour from an enumerable set of possibilities. Images have a resolution which simply describes how many pixels there are horizontally and vertically. Each image also has a colour depth which describes how large the set of colours is that a pixel's colour may come from.

An example of a photograph that has been converted into an image is shown below.

For the curious, this image uses baseline Huffman JPEG compression.

An example of a computer-generated image is shown below.

For the curious, this image uses progressive Huffman JPEG compression.

The following image is an example of what an image would look like under a microscope, or when a computer stretches an image to make it look larger. As you can see, there is a grid pixels with a regular spacing. Each pixel should be a constant colour. There are technical reasons why this isn't quite the case. To find out more, mail me!

The zoomed area from the frog picture has a resolution of 36x32 pixels. I.E. it is 36 pixels across and 32 pixels down.

For the curious, this image is a compressed interlaced GIF 89a with transparency information.