Approximation by Shepard type pseudo-linear operators and applications to Image Processing |
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| Authors: | Barnabás Bede Emil Daniel Schwab Hajime Nobuhara Imre J. Rudas |
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| Affiliation: | 1. Department of Mathematics, University of Texas–Pan American, Edinburg, TX 78541, USA;2. Department of Mathematical Sciences, The University of Texas at El Paso, 500 West University, El Paso, TX 79968, USA;3. Department of Intelligent Interaction Technologies, Graduate School of Systems and Information Engineering, University of Tsukuba Tenoudai 1-1-1, Tsukuba Science City, Ibaraki 305-8573, Japan;4. Department of Intelligent Engineering Systems, Budapest Tech Polytechnical Institution, Bécsi út 96/b H1034, Hungary |
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| Abstract: | Recently, it has been shown that sum and product are not the only operations that can be used in order to define concrete approximation operators. Several other operations provided by fuzzy sets theory can be used. In the present paper, pseudo-linear approximation operators are investigated from the practical point of view in Image Processing. We study max–min, max–product Shepard type approximation operators together with Shepard operators based on pseudo-operations generated by an increasing continuous generator. It is shown that in several cases these outperform classical approximation operators based on sum and product operations. |
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