Guada, CarelyGómez González, DanielRodríguez González, Juan TinguaroYáñez Gestoso, Francisco JavierMontero De Juan, Francisco JavierKacprzyk, JanuszSzmidt, EulaliaZadrożny, SlawomirAtanassov, K. T.Krawczak, Maciej2023-06-182023-06-182017Kacprzyk, J., Szmidt, E., Zadrożny, S., Atanassov, K.T., Krawczak, M. eds: Advances in Fuzzy Logic and Technology 2017. Springer International Publishing, Cham (2018)978-331966829110.1007/978-3-319-66824-6 18https://hdl.handle.net/20.500.14352/19470In this paper we discuss about graph approach in image segmentation. In first place, some main image processing techniques are classified based upon the output these methods provide. Then, a fuzzy image segmentation definition is presented because in the literature review was found that it was not clearly defined. This definition of fuzzy image segmentation is then related to a hierarchical image segmentation procedure, so this concept is also formally defined in this work. As every output of an image processing algorithm has to be evaluated, then a method to evaluate a hierarchical segmentation output is proposed in order to later propose a method to evaluate a fuzzy image segmentation output. Computational experiences point to some advantages of the proposed hierarchical image segmentation procedure over other algorithms.engbook parthttps//doi.org/10.1007/978-3-319-66824-6 18https://link.springer.com/chapter/10.1007/978-3-319-66824-6_18restricted access510.6Graph approachHierarchical segmentationEdge detectionBenchmarkingFuzzy setsLógica simbólica y matemática (Matemáticas)1102.14 Lógica Simbólica