A Method for Image Reduction Based on a Generalization of Ordered Weighted Averaging Functions

In this paper we propose a special type of aggregation function which generalizes the notion of Ordered Weighted Averaging Function OWA. The resulting functions are called Dynamic Ordered Weighted Averaging Functions — DYOWAs. This generalization will be developed in such way that the weight vectors are variables depending on the input vector. Particularly, this operators generalize the aggregation functions: Minimum, Maximum, Arithmetic Mean, Median etc, which are extensively used in image processing. In this field of research two problems are considered: The determination of methods to reduce images and the ∗Preprint submitted to IEEE Transactions on Fuzzy Systems. †Federal University of Semi-Arid UFERSA, Pau dos Ferros, RN, Brazil, 59.900-000, [email protected] ‡DIMAp, [email protected] §DIMAp, [email protected] ¶DIMAp, [email protected] ‖Dimap, [email protected] ∗∗DIMAP: Department of Informatics and Applied Mathematics, Federal University of Rio Grande do Norte — UFRN, Natal, RN, Brazil, 59.072-970 1 ar X iv :1 60 1. 03 78 5v 1 [ cs .A I] 1 5 Ja n 20 16 construction of techniques which provide noise reduction. The operators described here are able to be used in both cases. In terms of image reduction we apply the methodology provided in [1]. We use the noise reduction operators obtained here to treat the images obtained in the first part of the paper, thus obtaining images with better quality.