Browsing by Author "Patané, Giuseppe"

Now showing 1 - 3 of 3
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    Accurate and Efficient Computation of Laplacian Spectral Distances and Kernels
    (© 2017 The Eurographics Association and John Wiley & Sons Ltd., 2017) Patané, Giuseppe; Chen, Min and Zhang, Hao (Richard)
    This paper introduces the Laplacian spectral distances, as a function that resembles the usual distance map, but exhibits properties (e.g. smoothness, locality, invariance to shape transformations) that make them useful to processing and analysing geometric data. Spectral distances are easily defined through a filtering of the Laplacian eigenpairs and reduce to the heat diffusion, wave, biharmonic and commute‐time distances for specific filters. In particular, the smoothness of the spectral distances and the encoding of local and global shape properties depend on the convergence of the filtered eigenvalues to zero. Instead of applying a truncated spectral approximation or prolongation operators, we propose a computation of Laplacian distances and kernels through the solution of sparse linear systems. Our approach is free of user‐defined parameters, overcomes the evaluation of the Laplacian spectrum and guarantees a higher approximation accuracy than previous work.
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    A Graphical Framework to Study the Correlation between Geometric Design and Simulation
    (The Eurographics Association, 2022) Cabiddu, Daniela; Patané, Giuseppe; Spagnuolo, Michela; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    Partial differential equations can be solved on general polygonal and polyhedral meshes, through Polytopal Element Methods (PEMs). Unfortunately, the relation between geometry and analysis is still unknown and subject to ongoing research to identify weaker shape-regularity criteria under which PEMs can reliably work. We propose a graphical framework to support the analysis of the relation between the geometric properties of polygonal meshes and the numerical performances of PEM solvers. Our framework, namely PEMesh, allows the design of polygonal meshes that increasingly stress some geometric properties, by exploiting any external PEM solver, and supports the study of the correlation between the performances of such a solver and the geometric properties of the input mesh. Furthermore, it is highly modular, customisable, easy to use, and provides the possibility to export analysis results both as numerical values and graphical plots. The framework has a potential practical impact on ongoing and future research activities related to PEM methods, polygonal mesh generation and processing.
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    Mapping Grey-Levels on 3D Segmented Anatomical districts
    (The Eurographics Association, 2019) Paccini, Martina; Patané, Giuseppe; Spagnuolo, Michela; Agus, Marco and Corsini, Massimiliano and Pintus, Ruggero
    The study aims to perform a simple but effective integration of geometric information of segmented 3D bones' surface and density information provided by volume MRI (Magnetic Resonance Imaging). Such a representation method could support diagnosis process, biomedical simulation, computed assisted surgery and prosthesis fitting. The input consists of a volume MRI of a carpal district and the corresponding 3D surface model. The algorithm superimposes image and surface, and, once found the image voxel correspondent to each surface point, maps the grey level of the voxels identified on the segmented surface. The output is a surface mesh on which the texture, induced by the MRI, has been mapped. The approach is effective, general and applicable to different anatomical districts. Further elaboration of the results can be used to perform landmark identification or segmentation correction.