Mathematician Gemma Piella has developed a new technique for processing images. For this she used a mathematical operation that makes use of so-called wavelets. Just like a sinus, the upward and downward deviation of each of these small waves is the same. However, the wavelets only exist over a short distance and all of the peaks and troughs have different heights and widths. These characteristics ensure that a single operation can simultaneously render both large and small objects visible. This enables you to see both the entire wood and the individual trees at the same time.
A scene can only be fully understood if it can be seen at many different levels. For example, if you see a wood from a distance, your first impression is just a green surface. If you come closer by, you can see the trees. If you zoom in even further still, you can even see the leaves and the bark. Therefore, which information you extract from the picture depends upon the level at which you see it. So-called multiresolution techniques such as those used by Piella, render all details, at every level in the image visible at the same time.
The researcher modified existing wavelet techniques. Suppose that an image contains smooth areas which are separated by pieces of regularly crooked lines. Standard wavelets are good at isolating the start and end points of the crooked lines but not in recognising the trajectory of the line. Piella ensured that the wavelets made use of the geometrical information in the signal to be processed. As a result of this even the smallest details became clearly visible in images with a low resolution.
The mathematician also used her innovative technique to combine different images of the same object into a single detailed image. This is important, for example, in medicine, where imaging techniques are used to visualise different aspects of the human body. For example, combining a CT scan and an MRI scan of the brain makes both the brain tissue and the bones visible.
For further information please contact Dr Gemma Piella (Signals and Images, CWI and now working at the Telecommunications Engineering School, Polytechnical University of Catalonia, Spain), tel. 34-93-401-7758, e-mail: gemma.piella@cwi.nl or her assistant supervisor Dr H.J.M.A. Heijmans, tel. 31-20-592-4057, e-mail: Henk.Heijmans@cwi.nl. The doctoral thesis was defended on 30 October 2003 at the Universiteit van Amsterdam. Dr Piella's supervisor was Prof. P. W. Hemker.
The research was funded by the Technology Foundation STW.