Paternain, D.; Fernandez, J.; Bustince, H.; Mesiar, R.; Beliakov, G. Construction of image reduction operators using averaging aggregation functions. (English) Zbl 1360.68881 Fuzzy Sets Syst. 261, 87-111 (2015). Summary: In this work we present an image reduction algorithm based on averaging aggregation functions. We axiomatically define the concepts of image reduction operator and local reduction operator. We study the construction of the latter by means of averaging functions and we propose an image reduction algorithm (image reduction operator). We analyze the properties of several averaging functions and their effect on the image reduction algorithm. Finally, we present experimental results where we apply our algorithm in two different applications, analyzing the best operators for each concrete application. Cited in 9 Documents MSC: 68U10 Computing methodologies for image processing Keywords:image reduction; reduction operators; local reduction operators; aggregation functions; averaging functions PDFBibTeX XMLCite \textit{D. Paternain} et al., Fuzzy Sets Syst. 261, 87--111 (2015; Zbl 1360.68881) Full Text: DOI References: [1] Barrenechea, E.; Bustince, H.; De Baets, B.; Lopez-Molina, C., Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images, IEEE Trans. Fuzzy Syst., 19, 819-830 (2011) [2] Beliakov, G.; Pradera, A.; Calvo, T., Aggregation functions: a guide for practitioners, Stud. Fuzziness Soft Comput., 221 (2007) · Zbl 1123.68124 [3] Beliakov, G.; Bustince, H.; Fernandez, J., The median and its extensions, Fuzzy Sets Syst., 175, 36-47 (2001) · Zbl 1217.62012 [4] Beliakov, G.; Bustince, H.; Paternain, D., Image reduction using means on discrete product lattices, IEEE Trans. Image Process., 21, 1070-1083 (2012) · Zbl 1372.94021 [5] Bustince, H.; Montero, J.; Barrenechea, E.; Pagola, M., Semiautoduality in a restricted family of aggregation operators, Fuzzy Sets Syst., 158, 1360-1377 (2007) · Zbl 1123.68125 [6] Bustince, H.; Pagola, M.; Barrenechea, E., Construction of fuzzy indices from fuzzy DI-subsethood measures: application to the global comparison of images, Inf. Sci., 177, 906-929 (2007) · Zbl 1112.94033 [7] Bustince, H.; Barrenechea, E.; Pagola, M.; Fernandez, J., Interval-valued fuzzy sets constructed from matrices: application to edge detection, Fuzzy Sets Syst., 160, 1819-1840 (2009) · Zbl 1182.68191 [8] Bustince, H.; Montero, J.; Mesiar, R., Migrativity of aggregation functions, Fuzzy Sets Syst., 160, 766-777 (2009) · Zbl 1186.68459 [9] Bustince, H.; Calvo, T.; De Baets, B.; Fodor, J.; Mesiar, R.; Montero, J.; Paternain, D.; Pradera, A., A class of aggregation functions encompassing two-dimensional OWA operators, Inf. Sci., 180, 1977-1989 (2010) · Zbl 1205.68419 [10] (Calvo, T.; Mayor, G.; Mesiar, R., Aggregation Operators. New Trends and Applications (2002), Physica Verlag: Physica Verlag Heidelberg, New York) · Zbl 0983.00020 [11] Calvo, T.; Beliakov, G., Aggregation functions based on penalties, Fuzzy Sets Syst., 161, 1420-1436 (2010) · Zbl 1207.68384 [12] Di Martino, F.; Sessa, S., Compression and decompression of images with discrete fuzzy transform, Inf. Sci., 177, 2349-2362 (2007) · Zbl 1116.68039 [13] Di Martino, F.; Loia, V.; Perfilieva, I.; Sessa, S., An image coding/decoding method based on direct and inverse fuzzy transforms, Int. J. Approx. Reason., 48, 110-131 (2008) · Zbl 1184.68582 [14] Di Martino, F.; Loia, V.; Sessa, S., A segmentation method for image compressed by fuzzy transform, Fuzzy Sets Syst., 161, 19-31 (2010) [15] Fodor, J.; Roubens, M., Fuzzy Preference Modelling and Multicriteria Decision Support (1994), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0827.90002 [16] Grabisch, M.; Marichal, J.-L.; Mesiar, R.; Pap, E., Aggregation Functions (2009), Cambridge University Press: Cambridge University Press Cambridge [17] Jurio, A.; Pagola, M.; Mesiar, R.; Beliakov, G.; Bustince, H., Image magnification using interval information, IEEE Trans. Image Process., 20, 3112-3123 (2011) · Zbl 1372.94126 [18] Karabassis, E.; Spetsakis, M. E., An analysis of image interpolation, differentiation, and reduction using local polynomial fits, Graph. Models Image Process., 57, 183-196 (1995) [19] Gonzales, R. C.; Woods, R. E., Digital Image Processing (2008), Pearson [20] Keys, R. G., Cubic convolution interpolation for digital image processing, IEEE Trans. Acoust. Speech Signal Process., 29, 1153-1160 (1981) · Zbl 0524.65006 [21] Klement, E.; Mesiar, R.; Pap, E., Triangular Norms (2000), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht · Zbl 0972.03002 [22] Lehmann, T. M.; Gonner, C.; Spitzer, K., Survey: interpolation methods in medical image processing, IEEE Trans. Med. Imaging, 18, 1049-1075 (1999) [23] Loia, V.; Sessa, S., Fuzzy relation equations for coding/decoding processes of images and videos, Inf. Sci., 171, 145-172 (2005) · Zbl 1078.68815 [24] Mukherjee, J.; Mitra, S. K., Image resizing in the compressed domain using subband DCT, IEEE Trans. Circuits Syst. Video Technol., 12, 620-627 (2002) [25] Muoz, A.; Blu, T.; Unser, M., Least-squares image resizing using finite differences, IEEE Trans. Image Process., 10, 1365-1378 (2001) · Zbl 1037.68783 [26] Park, S.; Park, M.; Kang, M., Super-resolution image reconstruction: a technical overview, IEEE Signal Process. Mag., 20, 21-36 (2003) [27] Perfilieva, I., Fuzzy transforms: theory and applications, Fuzzy Sets Syst., 157, 993-1023 (2006) · Zbl 1092.41022 [28] Perfilieva, I., Fuzzy transform and their applications to image compression, Lecture Notes in Artificial Intelligence, 3849, 19-31 (2006) · Zbl 1168.68383 [29] Perfilieva, I.; De Baets, B., Fuzzy transform of monotone functions with application to image compression, Inf. Sci., 180, 3304-3315 (2010) · Zbl 1194.94037 [30] Thavanaz, P.; Blu, T.; Unser, M., Interpolation revisited, IEEE Trans. Med. Imaging, 19, 739-758 (2000) [31] Trillas, E., Sobre funciones de negación en la teoría de conjuntos difusos, Stochastica. (Barro, S.; Bugarin, A.; Sobrino, A., Advances in Fuzzy Logic (1998), Universidad de Santiago de Compostela), III, 1, 31-43 (1979), (in Spanish). English translation reprinted [32] Unser, M.; Aldroubi, A.; Eden, M., Enlargement or reduction of digital images with minimum loss of information, IEEE Trans. Image Process., 4, 247-258 (1995) [33] Yager, R. R., Ordered weighted averaging aggregation operators in multicriteria decision making, IEEE Trans. Syst. Man Cybern., 18, 183-190 (1988) · Zbl 0637.90057 [34] Yager, R. R., Centered OWA operators, Soft Comput., 11, 631-639 (2007) · Zbl 1113.68106 [35] Wang, Z.; Bovik, A. C.; Sheikh, H. R.; Simoncelli, E. P., Image quality assessment: from error visibility to structural similarity, IEEE Trans. Image Process., 13, 600-612 (2004) [36] Xiang, S.; Nie, F.; Zhang, C., Learning a Mahalanobis distance metric for data clustering and classification, Pattern Recognit., 41, 3600-3612 (2008) · Zbl 1162.68642 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.