Before we continue with the specifics of cropping and resizing, it is essential to understand the notion of aspect ratio. As you might imagine, it is the ratio of width over height. In mathematical notation:
A lot of the time, this is given. For example, video recorded by my camcorder has an aspect ratio of 4:3 (4 units across to 3 unit’s height), although the size is 720x576. Calculating the aspect ratio from the pixel resolution would give 5:4, which is not correct. This is because the pixels are not square in most analogue devices; the pixel aspect ratio is not 1:1 and it is not the case on computer screens. Because of this, you will need to know the aspect ratio beforehand or, guess it!
Often it is necessary to resize i.e. change the dimensions of a video, usually to increase the coding efficiency and therefore reduce the size of the output. Other reasons include conformance to video standards; if you plan to burn your video onto PAL VideoCD for example, you will...