Random Variables and Fields

Abstract

Digital image processing can be regarded as a subarea of digital signal processing. As such, all the methods for taking and analyzing measurements and their errors can also be applied to image processing. In particular, any measurement we take from images — e.g., the size or the position of an object or its mean gray value — can only be determined with a certain precision and is only useful if we can also estimate its uncertainty. This basic fact, which is well known to any scientist and engineer, was often neglected in the initial days of image processing. Using empirical and ill-founded techniques made reliable error estimates impossible. Fortunately, knowledge in image processing has advanced considerably. Nowadays, many sound image processing techniques are available that include reliable error estimates.