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Natasa Sladoje: Application of the fuzzy set theory in image processing |
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The advantages of representing objects in images as fuzzy spatial
sets are numerous and have lead to increased interest for fuzzy
approaches in image processing. Fuzziness is an intrinsic property of
images. It is additionally introduced in digital image processing by
discretization, and as a natural outcome of most imaging devices.
The fuzzy membership of a point reflects the level to which that
point fullfils certain criteria to belong to the object; the
membership of a pixel is often determined to be proportional to the
part of the pixel area covered by the observed object. Preservation
of fuzziness implies preservation of important information about
objects and images. Therefore, fuzziness should, in general, be kept
and utilized as long as possible when analyzing the image data.
The intention is to, first, give a brief introduction to the fuzzy set theory, and then, to discuss some of its applications to image analysis. Fuzzy segmentation methods and fuzzy shape analysis techniques are in focus. Several ways to incorporate fuzzy methods in segmentation process, and also ways to represent objects in images as fuzzy sets, are discussed. Methods to generalize well-known concepts, like perimeter and area of a set, or distance between elements of a set, from crisp to fuzzy sets, are explained. It is shown that, by using fuzzy approaches, an improved precision of some shape description can be achieved. In addition, some defuzzification approaches, that are used to reduce fuzzy sets to their crisp representatives, are presented, and their properties discussed. 
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