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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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    Mesh Comparison Using Regular Grids
    (The Eurographics Association, 2024) Kaye, Patrizia; Ivrissimtzis, Ioannis; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    A symmetric grid-based approach to mesh comparison is proposed, providing intuitive visual results alongside an objective measure of the local differences between meshes. The difference function is defined on the nodes of a regular 3D lattice, making it suitable as input for a variety of analysis algorithms. The visual results are compared and comparable to the Metro tool.
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    Disambiguating Flat Spots in Digital Elevation Models
    (The Eurographics Association, 2024) Rocca, Luigi; Puppo, Enrico; Caputo, Ariel; Garro, Valeria; Giachetti, Andrea; Castellani, Umberto; Dulecha, Tinsae Gebrechristos
    We consider Digital Elevation Models (DEMs) encoded as regular grids of discrete elevation data samples. When the terrain's slope is low relative to the dataset's vertical resolution, the DEM may contain flat spots: connected areas where all points share the same elevation. Flat spots can hinder certain analyses, such as topological characterization or drainage network computations. We discuss the application of Morse-Smale theory to grids and the disambiguation of flat spots. Specifically, we show how to characterize the topology of flat spots and symbolically perturb their elevation data to make the DEM compatible with Morse-Smale theory while preserving its topological properties. Our approach applies equivalently to three different surface models derived from the DEM grid: the step model, the bilinear model, and a piecewise-linear model based on the quincunx lattice.