Department of Mathematics

Images and Signals

Digital images are "mosaics" where the pieces (called pixels) are so small that they cannot be seen individually by the naked eye. These mosaic tiles are represented in the computer as numbers, which, with the help of mathematical methods, can tell us much more than the eye can. This field is called digital image processing.

For greyscale images, we have only one number (the greyscale value), while for colour images one has in each picture element three numbers (i.e. a vector) with a value for the red, green and blue components respectively. Colour images are therefore also referred to as RGB-images. Consequently, images can be thought of as large tables or matrices of numbers. This enables one to process the image digitally using mathematical methods, and thus, the field is called digital image processing.

Examples of digital image processing are clipping, zooming, noise removal, edge sharpening, contrast enhancement, blurring and deblurring, as well as the more advanced methods of contour detection, object recognition in still images or tracking of objects in dynamic image acquisition (video), and content analysis ("computer vision" or "image understanding").

Computer programs for processing images (such as Photoshop) are based on mathematical methods that perform various transformations on the image, but for more advanced content analysis Photoshop comes up short.

In various sectors in industry, government, defence and medicine, digital image processing is used to an increasing extent, and the mathematics employed is also often more complex and abstract. Examples of applications are plentiful, we mention only a few here: analysis of images taken from satellites, telescopes or microscopes; recognition of objects or symbols on number plates or scanned text documents; analysis of images taken from MRI, ultrasound, CT and PET scanners to achieve faster and more reliable medical diagnoses; process monitoring and reservoir modelling in the oil industry; the estimation of biomass (e.g. the quantity of fish) from sonar data; recognition of redeemable value in recyclable packaging (e.g. Tomra); detection of "suspicious" behaviour in video footage; occurrence of oil spills or degree of snow melting in the context of monitoring; recognition of fingerprints, retinal patterns or DNA profiles (biometrics) in the context of identification; video games and movies.

We have a good collaboration with MedViz, a new interdisciplinary initiative in medical visualisation and image processing, and with the Visualization Group in the Department of Informatics.

For more information, follow the relevant links on the right-hand side.