Browsing by Author "Mancinelli, Claudio"

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    Nearly Smooth Differential Operators on Surface Meshes
    (The Eurographics Association, 2022) Mancinelli, Claudio; Puppo, Enrico; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    Estimating the differential properties of a signal sampled on a surface is of paramount importance in many fields of applied sciences. In the common practice, the surface is discretized with a polygonal mesh, the signal is sampled at its vertices and extended linearly over the triangles. This means that the polyhedral metric is assumed over the surface; the first derivatives of the signal become discontinuous across edges; and the second derivatives vanish. We present a new method based on surface fitting, which efficiently estimates the metric tensor, and the first and second order Riemannian differential operators at any point on the surface. All our differential operators are smooth within each triangle and continuous across the edges, providing a much better estimate of differential quantities on the - yet unknown - underlying smooth manifold.
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    Spectral-based Segmentation for Functional Shape-matching
    (The Eurographics Association, 2023) Mancinelli, Claudio; Melzi, Simone; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, Gilda
    In Computer Graphics and Computer Vision, shape co-segmentation and shape-matching are fundamental tasks with diverse applications, from statistical shape analysis to human-robot interaction. These problems respectively target establishing segmentto- segment and point-to-point correspondences between shapes, which are crucial task for numerous practical scenarios. Notably, co-segmentation can aid in point-wise correspondence estimation in shape-matching pipelines like the functional maps framework. Our paper introduces an innovative shape segmentation pipeline which provides coherent segmentation for shapes within the same class. Through comprehensive evaluation on a diverse test set comprising shapes from various datasets and classes, we demonstrate the coherence of our segmentation approach. Moreover, our method significantly improves accuracy in shape matching scenarios, as evidenced by comparisons with the original functional maps approach. Importantly, these enhancements come with minimal computational overhead. Our work not only introduces a novel coherent segmentation method and a valuable tool for improving correspondence accuracy within functional maps, but also contributes to the theoretical foundations of this impactful field, inspiring further research.
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    Straightedge and Compass Constructions on Surfaces
    (The Eurographics Association, 2021) Mancinelli, Claudio; Puppo, Enrico; Frosini, Patrizio and Giorgi, Daniela and Melzi, Simone and RodolĂ , Emanuele
    We discuss how classical straightedge and compass constructions can be ported to manifold surfaces under the geodesic metric. After defining the equivalent tools in the manifold domain, we analyze the most common constructions and show what happens when trying to port them to surfaces. Most such constructions fail, because the geometric properties on which they rely no longer hold under the geodesic metric. We devise some alternative constructions that guarantee at least some of the properties of their Euclidean counterpart; while we show that it is usually impossible to guarantee all properties together. Some constructions remain still unsolved, unless additional tools are used, which violate the constraints of the straightedge and compass framework since they take explicit distance measures. We integrate our constructions in the context of a prototype system that supports the interactive drawing of vector primitives on a surface represented with a high-resolution mesh.