Abstract
We present a comparison between two images A and B based on the greatest solution of a system of bilinear fuzzy relation equations A○x = B○x, where “○” is the max–min composition, being A and B known as fuzzy relations and x is unknown. Here A and B are images considered as fuzzy relations being their pixels normalized in [0, 1] with respect to the grey scale used. Due to symmetry of every equation involved, A (resp., B) could be the original image and B (resp., A) is an image modified of A (resp., B), for instance, either noised or watermarked. The comparison is made by using an index which is more robust than other two indices used in previous works: the first one is based on the greatest eigen fuzzy set (with respect to max–min composition) and smallest eigen fuzzy set (with respect to min–max composition) and the second one is based on the Lukasiewicz triangular norm. The comparison is made between the original image and the same image with noise introduced at several values σ of the standard deviation.
Similar content being viewed by others
References
Avants B, Tustison BJ, Song G, Cook PA, Klein A, Gee JC (2011) A reproducible evaluation of ANT’s similarity metric performance in brain image registration. Neuroimage 64:2033–2044. doi:10.1016/j.neuroimage.2010.09.025
Di Martino F, Nobuhara H, Sessa S (2008) Eigen fuzzy sets and image information retrieval. In: Pedrycz W, Skowron A, Kreinovich V (eds) Handbook of granular computing. John Wiley, Chichester, pp 863–872. doi:10.1002/9780470724163.ch40
Di Martino F, Loia V, Sessa S (2010) Fuzzy transforms for compression and decompression of color videos. Inf Sci 180:3914–3931. doi:10.1016/j.ins.2010.06.030
Fucheng T (1988) Fuzzy bilinear equations. Fuzzy Sets Syst 28:217–226. doi:10.1016/0165-0114(88)90202-3
Jaiswal A, Kumar N, Agrawal RK (2012) A hybrid of principal component analysis and partial least squares for face recognition across pose. In: Alvarez L, Mejail M, Gomez L, Jacobo J (eds) Progress in pattern recognition, image analysis, computer vision, and applications. CIARP 2012. Lecture notes in computer science, vol 7441. Springer, Berlin, Heidelberg, pp 67–73. doi:10.1007/978-3-642-33275-3_8
Klare B, Jain AK (2013) Heterogeneous face recognition using kernel prototyping similarities. IEEE Trans Pattern Anal Mach Intell 35:1410–1422. doi:10.1109/TPAMI.2012.229
Li JX (1992) A new algorithm for the greatest solution of fuzzy bilinear equations. Fuzzy Sets Syst 46:193–210. doi:10.1016/0165-0114(92)90132-N
Loia V, Sessa S (2005) Fuzzy relation equations for coding/decoding processes of images and videos. Inf Sci 171:145–172. doi:10.1016/j.ins.2004.04.003
Penney GP (1998) A comparison of similarity measures for use in 2D/3D medical image registration. IEEE Trans Med Imaging 17:586–595. doi:10.1109/42.730403
RehmanA, Gao Y, Wang J, Wang Z (2013) Image classification based on complex wavelet structural similarity. Signal Process Image Commun 28:984–992. doi:10.1016/j.image.2012.07.004
Sanchez E (1978) Resolution of eigen fuzzy sets equations. Fuzzy Sets Syst 1:69–74. doi:10.1016/0165-0114(78)90033-7
Sanchez E (1981) Eigen fuzzy sets and fuzzy relations. J Math Anal Appl 81:399–421. doi:10.1016/0022-247X(81)90073-1
Wolf L, Hassner T, Taigman Y (2010) Similarity scores based on background samples. In: Zha H, Taniguchi R, Maybank S (eds) Computer Vision–ACCV 2009. ACCV 2009. Lecture notes in computer science, vol 5995. Springer, Berlin, Heidelberg, pp 88–97. doi:10.1007/978-3-642-12304-7_9
Zhang L, Zhang D, Xuangin M, Zhang D (2011) A feature similarity index for image quality assessment. IEEE Trans Image Process 20:2378–2386. doi:10.1109/TIP.2011.2109730
Zhao M, Ohshima H, Tanaka K (2012) Panoramic image search by similarity and adjancency for similar landscape discovery. In: Wang XS, Cruz I, Delis A, Huang G (eds) Web information systems engineering-WISE 2012. WISE 2012. Lecture notes in computer science, vol 7651. Springer, Berlin, Heidelberg, pp 284–297. doi:10.1007/978-3-642-35063-4_21
Zhou W, Gupta S, Bovik AC, Markey MK (2009) Complex wavelet structural similarity: a new image similarity index. IEEE Trans Image Process 18:2385–2401. doi:10.1109/TIP.2009.2025923
Acknowledgements
We perform this research under the auspices of the INDAM-GCNS, Italy.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Di Martino, F., Sessa, S. Comparison between images via bilinear fuzzy relation equations. J Ambient Intell Human Comput 9, 1517–1525 (2018). https://doi.org/10.1007/s12652-017-0576-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12652-017-0576-3