Open Access
Neuro-inspired edge feature fusion using Choquet integrals
(Elsevier, 2021) Marco Detchart, Cedric; Lucca, Giancarlo; López Molina, Carlos; Miguel Turullols, Laura de; Pereira Dimuro, Graçaliz; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
It is known that the human visual system performs a hierarchical information process in which early vision cues (or primitives) are fused in the visual cortex to compose complex shapes and descriptors. While different aspects of the process have been extensively studied, such as lens adaptation or feature detection, some other aspects, such as feature fusion, have been mostly left aside. In this work, we elaborate on the fusion of early vision primitives using generalizations of the Choquet integral, and novel aggregation operators that have been extensively studied in recent years. We propose to use generalizations of the Choquet integral to sensibly fuse elementary edge cues, in an attempt to model the behaviour of neurons in the early visual cortex. Our proposal leads to a fully-framed edge detection algorithm whose performance is put to the test in state-of-the-art edge detection datasets.
Open Access
On generalized overlap and grouping indices in n-dimensional contexts
(Springer, 2025-05-08) Asmus, Tiago da Cruz; Dimuro, Graçaliz Pereira; Lucca, Giancarlo; Marco Detchart, Cedric; Santos, Helida; Camargo, Heloisa A.; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC; Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa
Overlap and grouping indices are functions measuring, respectively, the fuzzy intersection and fuzzy union of two fuzzy sets. They have been applied successfully in several fields, such as in interpolative fuzzy systems, fuzzy rule-based classification systems and comparison of fuzzy inference rules. Overlap and grouping indices can be built employing overlap and grouping functions, respectively, which are possibly non-associative aggregation functions with features that provide good results when applied to practical bivariate problems. Many studies have generalized the concepts of overlap and grouping functions to be applied in n-dimensional problems. However, the concepts of overlap/grouping indices have not been generalized in similar pattern. Since the associative property may not hold, their application in n-dimensional domains, for comparing more than two fuzzy sets at a time, is not immediate, which limit their application in such contexts. The objective of this paper is to introduce the concepts of n-dimensional and general overlap/grouping indices, with special attention to the development of their construction methods based on generalized overlap/grouping functions. As an application example, we introduce the concept of n-dimensional Jaccard index, with a construction method based on n-dimensional overlap/grouping indices, providing an n-dimensional fuzzy set similarity score.
Open Access
Fuzzy integrals for edge detection
(Springer, 2023) Marco Detchart, Cedric; Lucca, Giancarlo; Pereira Dimuro, Graçaliz; Da Cruz Asmus, Tiago; López Molina, Carlos; Borges, Eduardo N.; Rincón Arango, Jaime Andrés; Julian, Vicente; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
In this work, we compare different families of fuzzy integrals in the context of feature aggregation for edge detection. We analyze the behaviour of the Sugeno and Choquet integral and some of its generalizations. In addition, we study the influence of the fuzzy measure over the extracted image features. For testing purposes, we follow the Bezdek Breakdown Structure for edge detection and compare the different fuzzy integrals with some classical feature aggregation methods in the literature. The results of these experiments are analyzed and discussed in detail, providing insights into the strengths and weaknesses of each approach. The overall conclusion is that the configuration of the fuzzy measure does have a paramount effect on the results by the Sugeno integral, but also that satisfactory results can be obtained by sensibly tuning such parameter. The obtained results provide valuable guidance in choosing the appropriate family of fuzzy integrals and settings for specific applications. Overall, the proposed method shows promising results for edge detection and could be applied to other image-processing tasks.
Open Access
Systematic review of aggregation functions applied to image edge detection
(MDPI, 2023) Amorim, Miqueias; Pereira Dimuro, Graçaliz; Borges, Eduardo N.; Dalmazo, Bruno L.; Marco Detchart, Cedric; Lucca, Giancarlo; Bustince Sola, Humberto; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika
Edge detection is a crucial process in numerous stages of computer vision. This field of study has recently gained momentum due to its importance in various applications. The uncertainty, among other characteristics of images, makes it difficult to accurately determine the edge of objects. Furthermore, even the definition of an edge is vague as an edge can be considered as the maximum boundary between two regions with different properties. Given the advancement of research in image discontinuity detection, especially using aggregation and pre-aggregation functions, and the lack of systematic literature reviews on this topic, this paper aims to gather and synthesize the current state of the art of this topic. To achieve this, this paper presents a systematic review of the literature, which selected 24 papers filtered from 428 articles found in computer databases in the last seven years. It was possible to synthesize important related information, which was grouped into three approaches: (i) based on both multiple descriptor extraction and data aggregation, (ii) based on both the aggregation of distance functions and fuzzy C-means, and (iii) based on fuzzy theory, namely type-2 fuzzy and neutrosophic sets. As a conclusion, this review provides interesting gaps that can be explored in future work.
Open Access
Data stream clustering: introducing recursively extendable aggregation functions for incremental cluster fusion processes
(IEEE, 2025-03-07) Urío Larrea, Asier; Camargo, Heloisa A.; Lucca, Giancarlo; Asmus, Tiago da Cruz; Marco Detchart, Cedric; Schick, L.; López Molina, Carlos; Andreu-Pérez, Javier; Bustince Sola, Humberto; Dimuro, Graçaliz Pereira; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute of Smart Cities - ISC
In data stream (DS) learning, the system has to extract knowledge from data generated continuously, usually at high speed and in large volumes, making it impossible to store the entire set of data to be processed in batch mode. Hence, machine learning models must be built incrementally by processing the incoming examples, as data arrive, while updating the model to be compatible with the current data. In fuzzy DS clustering, the model can either absorb incoming data into existing clusters or initiate a new cluster. As the volume of data increases, there is a possibility that the clusters will overlap to the point where it is convenient to merge two or more clusters into one. Then, a cluster comparison measure (CM) should be applied, to decide whether such clusters should be combined, also in an incremental manner. This defines an incremental fusion process based on aggregation functions that can aggregate the incoming inputs without storing all the previous inputs. The objective of this article is to solve the fuzzy DS clustering problem of incrementally comparing fuzzy clusters on a formal basis. First, we formalize and operationalize incremental fusion processes of fuzzy clusters by introducing recursively extendable (RE) aggregation functions, studying construction methods and different classes of such functions. Second, we propose two approaches to compare clusters: 1) similarity and 2) overlapping between clusters, based on RE aggregation functions. Finally, we analyze the effect of those incremental CMs on the online and offline phases of the well-known fuzzy clustering algorithm d-FuzzStream, showing that our new approach outperforms the original algorithm and presents better or comparable performance to other state-of-the-art DS clustering algorithms found in the literature.