Abstract
Image processing represents an important challenge in different fields, especially in biomedical field. Mathematical Morphology uses concepts from set theory, geometry, algebra and topology to analyze the geometrical structure of an image. In addition, it is possible to consider methods where the starting point to analyze an image is a fuzzy relation. This paper studies three methods to image edge detection based on a construction method for interval-valued fuzzy relations which can be understood as a gradient from a morphological point of view. The performance of the proposal in detecting medical image edges is tested, showing the method performing better with regard to a least squared adjust.
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References
De Baets B, Kerre E, Gupta M (1995) The fundamentals of fuzzy mathematical morphology, Part 1: basic concepts. Int J Gen Syst 23:155–171
De Baets B, Kerre E, Gupta M (1995) The fundamentals of fuzzy mathematical morphology. Part 2: idempotence, convexity and decomposition. Int J Gen Syst 23:307–322
De Baets B (1997) Fuzzy morphology: a logical approach. In: Ayyub BM, Gupta MM (eds) Uncertainty analysis in engineering and sciences: fuzzy logic, statistics, and neural network approach. Kluwer Academic Publishers, Boston, pp 53–67
Barrrenechea E, Bustince H, De Baets B, Lopez-Molina C (2011) Construction of interval-valued fuzzy relations with application to the generation of fuzzy edge images. IEEE Trans Fuzzy Syst 19:819–830
Bloch I, Maitre H (1995) Fuzzy mathematical morphologies: a comparative study. Pattern Recogn 28:1341–1387
Bouchet A, Benalczar Palacios F, Brun M, Ballarin VL (2014) Performance analysis of fuzzy mathematical morphology operators on noisy MRI. Lat Am Appl Res 44(3):231–236
Buades A, Coll B, Morel JM (2005) A review of image denoising algorithms, with a new one. Multiscale Model Simul 4(2):490–530
Bustince H (2010) Interval-valued fuzzy sets in soft computing. Int J Comput Intell Syst 3(2):215–222
Frank MJ (1979) On the simultaneous associativity of \(F(x, y)\) and \(x+y+F(x, y)\). Aequationes Math 19:194–226
Di Gesu V, Maccarone MC, Tripiciano M (1993) Mathematical morphology based on fuzzy operators. In: Lowen R, Roubens M (eds) Fuzzy logic. Kluwer Academic Publishers, pp 477–486
Hermosilla T, Bermejo E, Balaguer A, Ruiz LA (2008) Non linear fourth order image interpolation for subpixel edge detection and localization. J Image Vis Comput 26:1240–1248
Heric D, Zazula D (2007) Combined edge detection using wavelet transform and signal registration. J Image Vis Comput 25:652–662
Kerre E, Nachtegael M (2000) Fuzzy techniques in image processing, vol 52. New York
Marr D, Hildreth E (1980) Theory of edge detection. In: Proceedings of the royal society of London, pp 187–217
Klir GJ, Wheeler B (1995) Fuzzy sets and fuzzy logic. Prentice Hall, New Jersey
Konishi S, Yuille AL, Coughlan JM, Zhu SC (2003) Statistical edge detection: learning and evaluating edge cues. IEEE Trans Pattern Anal Mach Intell 25(1):57–74
Martin D, Fowlkes C, Tal D, Malik J (2001) A database of human segmented natural images and its application to evaluating segmentation algorithms and measuring ecological statistics. In: Proceedings of the 8th International Conference on Computer Vision, vol 2, pp 416–423
Quirós P, Alonso P, Díaz I, Jurío A, Montes S (2015) An hybrid construction method based on weight functions to obtain interval-valued fuzzy relations. In: Mathematical methods in the applied sciencies (in press)
Rulaningtyas R, Ain K (2009) Edge detection for brain tumor pattern recognition, instrumentation, communications, information technology, and biomedical engineering (ICICI-BME), vol 3, pp 1–3
Sambuc R (1975) Fonctions \(\Phi \)-floues. Application l’Aide au Diagnostic en Patholologie Thyroidienne. Ph. D. Thesis, Univ. Marseille
Serra J (1988) Image analysis and mathematical morphology. Academic Press, London
Wang R, Gao L, Yang S, Liu Y (2005) An edge detection method by combining fuzzy logic and neural networks. Mach Learn cybern 7:4539–4543
Yager RR (1980) On a general class of fuzzy connectives. Fuzzy Sets Syst 4:235–242
Zadeh L (1971) Similarity relations and fuzzy orderings. Inf Sci 3:177–200
Acknowledgments
This work has been partially supported by MEC and FEDER Grant TEC2012-38142-C04-04 and by ERASMUS Mundus Project EUREKA SD 2013-2591.
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Bouchet, A., Quirós, P., Alonso, P., Díaz, I., Montes, S. (2015). Medical Edge Detection Combining Fuzzy Mathematical Morphology with Interval-Valued Relations. In: Herrero, Á., Sedano, J., Baruque, B., Quintián, H., Corchado, E. (eds) 10th International Conference on Soft Computing Models in Industrial and Environmental Applications. Advances in Intelligent Systems and Computing, vol 368. Springer, Cham. https://doi.org/10.1007/978-3-319-19719-7_20
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DOI: https://doi.org/10.1007/978-3-319-19719-7_20
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