Browsing by Author "Fugacci, Ulderico"

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    Efficient Homology‐Preserving Simplification of High‐Dimensional Simplicial Shapes
    (© 2020 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2020) Fellegara, Riccardo; Iuricich, Federico; De Floriani, Leila; Fugacci, Ulderico; Benes, Bedrich and Hauser, Helwig
    Simplicial complexes are widely used to discretize shapes. In low dimensions, a 3D shape is represented by discretizing its boundary surface, encoded as a triangle mesh, or by discretizing the enclosed volume, encoded as a tetrahedral mesh. High‐dimensional simplicial complexes have recently found their application in topological data analysis. Topological data analysis aims at studying a point cloud P, possibly embedded in a high‐dimensional metric space, by investigating the topological characteristics of the simplicial complexes built on P. Analysing such complexes is not feasible due to their size and dimensions. To this aim, the idea of simplifying a complex while preserving its topological features has been proposed in the literature. Here, we consider the problem of efficiently simplifying simplicial complexes in arbitrary dimensions. We provide a new definition for the edge contraction operator, based on a top‐based data structure, with the objective of preserving structural aspects of a simplicial shape (i.e., its homology), and a new algorithm for verifying the link condition on a top‐based representation. We implement the simplification algorithm obtained by coupling the new edge contraction and the link condition on a specific top‐based data structure, that we use to demonstrate the scalability of our approach.
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    Eurographics Workshop on 3D Object Retrieval - Short Papers: Frontmatter
    (The Eurographics Association, 2023) Fugacci, Ulderico; Lavoué, Guillaume; Veltkamp, Remco C.; Fugacci, Ulderico; Lavoué, Guillaume; Veltkamp, Remco C.
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    Persistent Homology vs. Learning Methods: A Comparative Study in Limited Data Scenarios
    (The Eurographics Association, 2024) Via, Andrea Di; Via, Roberto Di; Fugacci, Ulderico; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    This exploratory study compares persistent homology methods with traditional machine learning and deep learning techniques for label-efficient classification. We propose pure topological approaches, including persistence thresholding and Bottleneck distance classification, and explore hybrid methods combining persistent homology with machine learning. These are evaluated against conventional machine learning algorithms and deep neural networks on two binary classification tasks: surface crack detection and malaria cell identification. We assess performance across various number of samples per class, ranging from 1 to 500. Our study highlights the efficacy of persistent homology-based methods in low-data scenarios. Using the Bottleneck distance approach, we achieve 95.95% accuracy in crack detection and 93.11% in malaria diagnosis with only one labeled sample per class. These results outperform the best performance from machine learning models, which achieves 69.40% and 39.75% accuracy, respectively, and deep learning models, which attains up to 95.96% in crack detection and 62.72% in malaria diagnosis. This demonstrates the superior performance of topological methods in classification tasks with few labeled data. Hybrid approaches demonstrate enhanced performance as the number of labeled samples increases, effectively leveraging topological features to boost classification accuracy. This study highlights the robustness of topological methods in extracting meaningful features from limited data, offering promising directions for efficient, label-conserving classification strategies. The results underscore the worth of persistent homology, both as a standalone tool and in combination with machine learning, particularly in domains where labeled data scarcity challenges traditional deep learning approaches.