Name
Abstract | ||
|---|---|---|
In this study, we formulate and solve a problem of image reconstruction using eigen fuzzy sets. Treating images as fuzzy relations, we propose two algorithms of generating eigen fuzzy sets that are used in the reconstruction process. The first one corresponds to a convex combination of eigen fuzzy set equations, i.e., fuzzy relational equations involving convex combination of max-min and min-max compositions. In the case of the first algorithm, various eigen fuzzy sets can be generated by changing the parameter controlling the convex combination of the corresponding equations. The second algorithm generates various eigen fuzzy sets with respect to the original fuzzy relation using a permutation matrix. A thorough comparison of the proposed algorithms and a conventional algorithm which reconstructs an image using the greatest and smallest eigen fuzzy sets is presented as well. In the experiments, 10,000 artificial images of size 5x5 pixels. The approximation error in the case of the first/second algorithm is decreased to 68.2%/97.9% of that of the conventional algorithm, respectively. Furthermore, through the experimentation using real images extracted from Standard Image DataBAse (SIDBA), it is confirmed that the approximation error of the first algorithm is decreased to 41.5% of that of the conventional one. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.ins.2005.11.008 | Inf. Sci. |
Keywords | Field | DocType |
original fuzzy relation,eigen fuzzy set,conventional algorithm,various eigen fuzzy set,eigen fuzzy set equation,fuzzy relational,approximation error,convex combination,image reconstruction,smallest eigen fuzzy set,fuzzy relation,permutation matrix,fuzzy set | Discrete mathematics,Defuzzification,Fuzzy classification,Fuzzy set operations,Convex combination,Fuzzy logic,Fuzzy set,Fuzzy associative matrix,Fuzzy number,Mathematics | Journal |
Volume | Issue | ISSN |
176 | 20 | 0020-0255 |
Citations | PageRank | References |
32 | 1.13 | 11 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Hajime Nobuhara | 1 | 192 | 34.02 |
| Barnabás Bede | 2 | 689 | 44.85 |
| Kaoru Hirota | 3 | 1634 | 195.49 |