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16 December 1992 New prospect in image clustering from the fuzzy set theory
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Image clustering aims at obtaining a partition of the image in such a way that each partition sub-set can be taken as an object; most of the time this procedure is iterative. Following a string of binary decisions, errors are generated which can be avoided using fuzzy partitioning. The key point which remains is to choose for each image pixel a coefficient of assignment to the fuzzy sub-set. This makes it necessary to carefully define a fuzzy equivalence relationship but we consider that the existing definitions are not consistent if not contradictory. So we propose a new definition of the fuzzy set equivalence relationship. In this communication we first give some evidence of the importance of changing the definitions of the reflexivity and the transitivity of the relation. Then we show the consistency of the proposed new definition. A simple example is presented to define a fuzzy partition and fuzzy included partitions; this leads to an application in the specific case of image processing. A comparison is proposed between the results obtained with a classical hierarchical region growing method and with fuzzy set logic.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Patrick Faurous "New prospect in image clustering from the fuzzy set theory", Proc. SPIE 1766, Neural and Stochastic Methods in Image and Signal Processing, (16 December 1992);

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