DSpace Repository :: Browsing by Author "Rodolà, Emanuele"

Browsing by Author "Rodolà, Emanuele"

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Deep Learning for Computer Graphics and Geometry Processing
(The Eurographics Association, 2019) Bronstein, Michael; Guibas, Leonidas; Kokkinos, Iasonas; Litany, Or; Mitra, Niloy; Monti, Federico; Rodolà, Emanuele; Jakob, Wenzel and Puppo, Enrico
In computer graphics and geometry processing, many traditional problems are now becoming increasingly handled by data-driven methods. In an increasing variety of problem settings, deep networks are state-of-the-art, beating dedicated hand-crafted methods by significant margins. This tutorial gives an organized overview of core theory, practice, and graphics-related applications of deep learning.
Generating Adversarial Surfaces via Band-Limited Perturbations
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Mariani, Giorgio; Cosmo, Luca; Bronstein, Alex M.; Rodolà, Emanuele; Jacobson, Alec and Huang, Qixing
Adversarial attacks have demonstrated remarkable efficacy in altering the output of a learning model by applying a minimal perturbation to the input data. While increasing attention has been placed on the image domain, however, the study of adversarial perturbations for geometric data has been notably lagging behind. In this paper, we show that effective adversarial attacks can be concocted for surfaces embedded in 3D, under weak smoothness assumptions on the perceptibility of the attack. We address the case of deformable 3D shapes in particular, and introduce a general model that is not tailored to any specific surface representation, nor does it assume access to a parametric description of the 3D object. In this context, we consider targeted and untargeted variants of the attack, demonstrating compelling results in either case. We further show how discovering adversarial examples, and then using them for adversarial training, leads to an increase in both robustness and accuracy. Our findings are confirmed empirically over multiple datasets spanning different semantic classes and deformations.
Inverse Computational Spectral Geometry
(The Eurographics Association, 2021) Rodolà, Emanuele; Melzi, Simone; Cosmo, Luca; Bronstein, Michael; Ovsjanikov, Maks; O'Sullivan, Carol and Schmalstieg, Dieter
In the last decades, geometry processing has attracted a growing interest thanks to the wide availability of new devices and software that make 3D digital data available and manipulable to everyone. Typical issues that are faced by geometry processing algorithms include the variety of discrete representations for 3D data (point clouds, polygonal or tet-meshes and voxels), or the type of deformation this data may undergo. Powerful approaches to address these issues come from looking at the spectral decomposition of canonical differential operators, such as the Laplacian, which provides a rich, informative, robust, and invariant representation of the 3D objects. Reasoning about spectral quantities is at the core of spectral geometry, which has enabled unprecedented performance in many tasks of computer graphics (e.g., shape matching with functional maps, shape retrieval, compression, and texture transfer), as well as contributing in opening new directions of research. The focus of this tutorial is on inverse computational spectral geometry. We will offer a different perspective on spectral geometric techniques, supported by recent successful methods in the graphics and 3D vision communities, as well as older, but notoriously overlooked results. Here, the interest shifts from studying the “forward” path typical of spectral geometry pipelines (e.g., computing Laplacian eigenvalues and eigenvectors of a given shape) to studying the inverse path (e.g., recovering a shape from given Laplacian eigenvalues, like in the classical “hearing the shape of the drum” problem). As is emblematic of inverse problems, the ill-posed nature of the reverse direction requires additional effort, but the benefits can be quite considerable as showcased on several challenging tasks in graphics and geometry processing. The purpose of the tutorial is to overview the foundations and the current state of the art on inverse computational spectral geometry, to highlight the main benefits of inverse spectral pipelines, as well as their current limitations and future developments in the context of computer graphics. The tutorial is aimed at a wide audience with a basic understanding of geometry processing, and will be accessible and interesting to students, researchers and practitioners from both the academia and the industry.
Inverse Computational Spectral Geometry
(The Eurographics Association, 2022) Rodolà, Emanuele; Cosmo, Luca; Ovsjanikov, Maks; Rampini, Arianna; Melzi, Simone; Bronstein, Michael; Marin, Riccardo; Hahmann, Stefanie; Patow, Gustavo A.
In the last decades, geometry processing has attracted a growing interest thanks to the wide availability of new devices and software that make 3D digital data available and manipulable to everyone. Typical issues faced by geometry processing algorithms include the variety of discrete representations for 3D data (point clouds, polygonal or tet-meshes and voxels), or the type of deformation this data may undergo. Powerful approaches to address these issues come from looking at the spectral decomposition of canonical differential operators, such as the Laplacian, which provides a rich, informative, robust, and invariant representation of the 3D objects. The focus of this tutorial is on computational spectral geometry. We will offer a different perspective on spectral geometric techniques, supported by recent successful methods in the graphics and 3D vision communities and older but notoriously overlooked results. We will discuss both the “forward” path typical of spectral geometry pipelines (e.g. computing Laplacian eigenvalues and eigenvectors of a given shape) with its widespread applicative relevance, and the inverse path (e.g. recovering a shape from given Laplacian eigenvalues, like in the classical “hearing the shape of the drum” problem) with its ill-posed nature and the benefits showcased on several challenging tasks in graphics and geometry processing.
Learning Spectral Unions of Partial Deformable 3D Shapes
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Moschella, Luca; Melzi, Simone; Cosmo, Luca; Maggioli, Filippo; Litany, Or; Ovsjanikov, Maks; Guibas, Leonidas; Rodolà, Emanuele; Chaine, Raphaëlle; Kim, Min H.
Spectral geometric methods have brought revolutionary changes to the field of geometry processing. Of particular interest is the study of the Laplacian spectrum as a compact, isometry and permutation-invariant representation of a shape. Some recent works show how the intrinsic geometry of a full shape can be recovered from its spectrum, but there are approaches that consider the more challenging problem of recovering the geometry from the spectral information of partial shapes. In this paper, we propose a possible way to fill this gap. We introduce a learning-based method to estimate the Laplacian spectrum of the union of partial non-rigid 3D shapes, without actually computing the 3D geometry of the union or any correspondence between those partial shapes. We do so by operating purely in the spectral domain and by defining the union operation between short sequences of eigenvalues. We show that the approximated union spectrum can be used as-is to reconstruct the complete geometry [MRC*19], perform region localization on a template [RTO*19] and retrieve shapes from a database, generalizing ShapeDNA [RWP06] to work with partialities. Working with eigenvalues allows us to deal with unknown correspondence, different sampling, and different discretizations (point clouds and meshes alike), making this operation especially robust and general. Our approach is data-driven and can generalize to isometric and non-isometric deformations of the surface, as long as these stay within the same semantic class (e.g., human bodies or horses), as well as to partiality artifacts not seen at training time.
Localized Shape Modelling with Global Coherence: An Inverse Spectral Approach
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Pegoraro, Marco; Melzi, Simone; Castellani, Umberto; Marin, Riccardo; Rodolà, Emanuele; Campen, Marcel; Spagnuolo, Michela
Many natural shapes have most of their characterizing features concentrated over a few regions in space. For example, humans and animals have distinctive head shapes, while inorganic objects like chairs and airplanes are made of well-localized functional parts with specific geometric features. Often, these features are strongly correlated - a modification of facial traits in a quadruped should induce changes to the body structure. However, in shape modelling applications, these types of edits are among the hardest ones; they require high precision, but also a global awareness of the entire shape. Even in the deep learning era, obtaining manipulable representations that satisfy such requirements is an open problem posing significant constraints. In this work, we address this problem by defining a data-driven model upon a family of linear operators (variants of the mesh Laplacian), whose spectra capture global and local geometric properties of the shape at hand. Modifications to these spectra are translated to semantically valid deformations of the corresponding surface. By explicitly decoupling the global from the local surface features, our pipeline allows to perform local edits while simultaneously maintaining a global stylistic coherence. We empirically demonstrate how our learning-based model generalizes to shape representations not seen at training time, and we systematically analyze different choices of local operators over diverse shape categories.
MoMaS: Mold Manifold Simulation for Real-time Procedural Texturing
(The Eurographics Association and John Wiley & Sons Ltd., 2022) Maggioli, Filippo; Marin, Riccardo; Melzi, Simone; Rodolà, Emanuele; Umetani, Nobuyuki; Wojtan, Chris; Vouga, Etienne
The slime mold algorithm has recently been under the spotlight thanks to its compelling properties studied across many disciplines like biology, computation theory, and artificial intelligence. However, existing implementations act only on planar surfaces, and no adaptation to arbitrary surfaces is available. Inspired by this gap, we propose a novel characterization of the mold algorithm to work on arbitrary curved surfaces. Our algorithm is easily parallelizable on GPUs and allows to model the evolution of millions of agents in real-time over surface meshes with several thousand triangles, while keeping the simplicity proper of the slime paradigm. We perform a comprehensive set of experiments, providing insights on stability, behavior, and sensibility to various design choices. We characterize a broad collection of behaviors with a limited set of controllable and interpretable parameters, enabling a novel family of heterogeneous and high-quality procedural textures. The appearance and complexity of these patterns are well-suited to diverse materials and scopes, and we add another layer of generalization by allowing different mold species to compete and interact in parallel.
Orthogonalized Fourier Polynomials for Signal Approximation and Transfer
(The Eurographics Association and John Wiley & Sons Ltd., 2021) Maggioli, Filippo; Melzi, Simone; Ovsjanikov, Maks; Bronstein, Michael M.; Rodolà, Emanuele; Mitra, Niloy and Viola, Ivan
We propose a novel approach for the approximation and transfer of signals across 3D shapes. The proposed solution is based on taking pointwise polynomials of the Fourier-like Laplacian eigenbasis, which provides a compact and expressive representation for general signals defined on the surface. Key to our approach is the construction of a new orthonormal basis upon the set of these linearly dependent polynomials. We analyze the properties of this representation, and further provide a complete analysis of the involved parameters. Our technique results in accurate approximation and transfer of various families of signals between near-isometric and non-isometric shapes, even under poor initialization. Our experiments, showcased on a selection of downstream tasks such as filtering and detail transfer, show that our method is more robust to discretization artifacts, deformation and noise as compared to alternative approaches.
A Parametric Analysis of Discrete Hamiltonian Functional Maps
(The Eurographics Association and John Wiley & Sons Ltd., 2020) Postolache, Emilian; Fumero, Marco; Cosmo, Luca; Rodolà, Emanuele; Jacobson, Alec and Huang, Qixing
In this paper we develop an in-depth theoretical investigation of the discrete Hamiltonian eigenbasis, which remains quite unexplored in the geometry processing community. This choice is supported by the fact that Dirichlet eigenfunctions can be equivalently computed by defining a Hamiltonian operator, whose potential energy and localization region can be controlled with ease. We vary with continuity the potential energy and study the relationship between the Dirichlet Laplacian and the Hamiltonian eigenbases with the functional map formalism. We develop a global analysis to capture the asymptotic behavior of the eigenpairs. We then focus on their local interactions, namely the veering patterns that arise between proximal eigenvalues. Armed with this knowledge, we are able to track the eigenfunctions in all possible configurations, shedding light on the nature of the functional maps. We exploit the Hamiltonian-Dirichlet connection in a partial shape matching problem, obtaining state of the art results, and provide directions where our theoretical findings could be applied in future research.
Smart Tools and Applications in computer Graphics: Frontmatter
(The Eurographics Association, 2021) Frosini, Patrizio; Giorgi, Daniela; Melzi, Simone; Rodolà, Emanuele; Frosini, Patrizio and Giorgi, Daniela and Melzi, Simone and Rodolà, Emanuele
Wavelet‐based Heat Kernel Derivatives: Towards Informative Localized Shape Analysis
(© 2021 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2021) Kirgo, Maxime; Melzi, Simone; Patanè, Giuseppe; Rodolà, Emanuele; Ovsjanikov, Maks; Benes, Bedrich and Hauser, Helwig
In this paper, we propose a new construction for the Mexican hat wavelets on shapes with applications to partial shape matching. Our approach takes its main inspiration from the well‐established methodology of diffusion wavelets. This novel construction allows us to rapidly compute a multi‐scale family of Mexican hat wavelet functions, by approximating the derivative of the heat kernel. We demonstrate that this leads to a family of functions that inherit many attractive properties of the heat kernel (e.g. local support, ability to recover isometries from a single point, efficient computation). Due to its natural ability to encode high‐frequency details on a shape, the proposed method reconstructs and transfers ‐functions more accurately than the Laplace‐Beltrami eigenfunction basis and other related bases. Finally, we apply our method to the challenging problems of partial and large‐scale shape matching. An extensive comparison to the state‐of‐the‐art shows that it is comparable in performance, while both simpler and much faster than competing approaches.

Browsing by Author "Rodolà, Emanuele"

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