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Fuzzy sets in image processing

The growing interest of fuzzy sets for image processing and pattern recognition is due to their ability to represent imprecise, uncertain or ambiguous regions or structures in images. These ~peets are always present in images and are not treated with classical approaches in a satisfactory way. Examples of imprecision or uncertainty can be found at all levels, from the observed phenomenon itself to image processing results. Let us consider medical imaging for instance. A tumor is often difficult to delineate precisely because of the smooth transition between healthy and pathological tissues. This is an example of imprecision due to the nature of the observed phenomenon, which is reflected by the images, whatever the choice of the imaging technique. Imprecision at the sensor level is due for instance to the resolution. A pixel conveys all information contained in an elementary volume, leading to imprecision in the location of this information. A consequence is the well known partial volume effect which causes smooth transitions between tissues 'which have an interface not orthogonal to the slicing plane. Then, the numerical reconstruction algorithms also add imprecision and/or uncertainty in the images (Gibbs effect for instance). At last, image processing operators may provide results corrupted by imprecision. For instance, some edge detectors provide contours which are slightly displaced w.r.t. their true position.