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    S4A: Scalable Spectral Statistical Shape Analysis
    (The Eurographics Association, 2024) Maccarone, Francesca; Longari, Giorgio; Viganò, Giulio; Peruzzo, Denis; Maggioli, Filippo; Melzi, Simone; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    Statistical shape analysis is a crucial technique for studying deformations within collections of shapes, particularly in the field of Medical Imaging. However, the high density of meshes typically used to represent medical data poses a challenge for standard geometry processing tools due to their limited efficiency. While spectral approaches offer a promising solution by effectively handling high-frequency variations inherent in such data, their scalability is questioned by their need to solve eigendecompositions of large sparse matrices. In this paper, we introduce S4A, a novel and efficient method based on spectral geometry processing, that addresses these issues with a low computational cost. It operates in four stages: (i) establishing correspondences between each pair of shapes in the collection, (ii) defining a common latent space to encode deformations across the entire collection, (iii) computing statistical quantities to identify, highlight, and measure the most representative variations within the collection, and iv) performing information transfer from labeled data to large collections of shapes. Unlike previous methods, S4A provides a highly efficient solution across all stages of the process.We demonstrate the advantages of our approach by comparing its accuracy and computational efficiency to existing pipelines, and by showcasing the comprehensive statistical insights that can be derived from applying our method to a collection of medical data.
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    Localized Gaussians as Self-Attention Weights for Point Clouds Correspondence
    (The Eurographics Association, 2024) Riva, Alessandro; Raganato, Alessandro; Melzi, Simone; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    Current data-driven methodologies for point cloud matching demand extensive training time and computational resources, presenting significant challenges for model deployment and application. In the point cloud matching task, recent advancements with an encoder-only Transformer architecture have revealed the emergence of semantically meaningful patterns in the attention heads, particularly resembling Gaussian functions centered on each point of the input shape. In this work, we further investigate this phenomenon by integrating these patterns as fixed attention weights within the attention heads of the Transformer architecture. We evaluate two variants: one utilizing predetermined variance values for the Gaussians, and another where the variance values are treated as learnable parameters. Additionally we analyze the performances on noisy data and explore a possible way to improve robustness to noise. Our findings demonstrate that fixing the attention weights not only accelerates the training process but also enhances the stability of the optimization. Furthermore, we conducted an ablation study to identify the specific layers where the infused information is most impactful and to understand the reliance of the network on this information.
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    TACO: a Benchmark for Connectivity-invariance in Shape Correspondence
    (The Eurographics Association, 2024) Pedico, Simone; Melzi, Simone; Maggioli, Filippo; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    In real-world scenarios, a major limitation for shape-matching datasets is represented by having all the meshes of the same subject share their connectivity across different poses. Specifically, similar connectivities could provide a significant bias for shape matching algorithms, simplifying the matching process and potentially leading to correspondences based on the recurring triangle patterns rather than geometric correspondences between mesh parts. As a consequence, the resulting correspondence may be meaningless, and the evaluation of the algorithm may be misled. To overcome this limitation, we introduce TACO, a new dataset where meshes representing the same subject in different poses do not share the same connectivity, and we compute new ground truth correspondences between shapes. We extensively evaluate our dataset to ensure that ground truth isometries are properly preserved. We also use our dataset for validating state-of-the-art shape-matching algorithms, verifying a degradation in performance when the connectivity gets altered.