DSpace Repository :: Browsing by Author "Melzi, Simone"

Browsing by Author "Melzi, Simone"

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Attention And Positional Encoding Are (Almost) All You Need For Shape Matching
(The Eurographics Association and John Wiley & Sons Ltd., 2023) Raganato, Alessandro; Pasi, Gabriella; Melzi, Simone; Memari, Pooran; Solomon, Justin
The fast development of novel approaches derived from the Transformers architecture has led to outstanding performance in different scenarios, from Natural Language Processing to Computer Vision. Recently, they achieved impressive results even in the challenging task of non-rigid shape matching. However, little is known about the capability of the Transformer-encoder architecture for the shape matching task, and its performances still remained largely unexplored. In this paper, we step back and investigate the contribution made by the Transformer-encoder architecture compared to its more recent alternatives, focusing on why and how it works on this specific task. Thanks to the versatility of our implementation, we can harness the bi-directional structure of the correspondence problem, making it more interpretable. Furthermore, we prove that positional encodings are essential for processing unordered point clouds. Through a comprehensive set of experiments, we find that attention and positional encoding are (almost) all you need for shape matching. The simple Transformer-encoder architecture, coupled with relative position encoding in the attention mechanism, is able to obtain strong improvements, reaching the current state-of-the-art.
CMH: Coordinates Manifold Harmonics for Functional Remeshing
(The Eurographics Association, 2019) Marin, Riccardo; Melzi, Simone; Musoni, Pietro; Bardon, Filippo; Tarini, Marco; Castellani, Umberto; Biasotti, Silvia and Lavoué, Guillaume and Veltkamp, Remco
In digital world reconstruction, 2-dimensional surface of real objects are often obtained as polygonal meshes after an acquisition procedure using 3D sensors. However, such representation requires several manual efforts from highly experts to correct the irregularity of tessellation and make it suitable for professional applications, such as those in the gaming or movie industry. Moreover, for modelling and animation purposes it is often required that the same connectivity is shared among two or more different shapes. In this paper we propose a new method that exploits a remeshing-by-matching approach where the observed noisy shape inherits a regular tessellation from a target shape which already satisfies the professional constraints. A fully automatic pipeline is introduced based on a variation of the functional mapping framework. In particular, a new set of basis functions, namely the Coordinates Manifold Harmonics (CMH), is properly designed for this tessellation transfer task. In our experiments an exhaustive quantitative and quality evaluation is reported for human body shapes in T-pose where the effectiveness of the proposed functional remeshing is clearly shown in comparison with other methods.
Complex Functional Maps: A Conformal Link Between Tangent Bundles
(© 2022 Eurographics ‐ The European Association for Computer Graphics and John Wiley & Sons Ltd, 2022) Donati, Nicolas; Corman, Etienne; Melzi, Simone; Ovsjanikov, Maks; Hauser, Helwig and Alliez, Pierre
In this paper, we introduce complex functional maps, which extend the functional map framework to conformal maps between tangent vector fields on surfaces. A key property of these maps is their . More specifically, we demonstrate that unlike regular functional maps that link of two manifolds, our complex functional maps establish a link between , thus permitting robust and efficient transfer of tangent vector fields. By first endowing and then exploiting the tangent bundle of each shape with a complex structure, the resulting operations become naturally orientation‐aware, thus favouring across shapes, without relying on descriptors or extra regularization. Finally, and perhaps more importantly, we demonstrate how these objects enable several practical applications within the functional map framework. We show that functional maps and their complex counterparts can be estimated jointly to promote orientation preservation, regularizing pipelines that previously suffered from orientation‐reversing symmetry errors.
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.
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.
Reposing and Retargeting Unrigged Characters with Intrinsic-extrinsic Transfer
(The Eurographics Association, 2021) Musoni, Pietro; Marin, Riccardo; Melzi, Simone; Castellani, Umberto; Frosini, Patrizio and Giorgi, Daniela and Melzi, Simone and Rodolà, Emanuele
In the 3D digital world, deformations and animations of shapes are fundamental topics for several applications. The entertainment industry, virtual and augmented reality, human-robot interactions are just some examples that pay attention to animation processes and related tools. In these contexts, researchers from several communities desire to govern deformations and animations of 3D geometries. This task is generally very complicated because it requires several skills covering different kinds of knowledge. For this reason, we propose a ready-to-use procedure to transfer a given animation from a source shape to a target shape that shares the same global structure. Our method proposes highly geometrical transferring, reposing, and retargeting, providing high-quality and efficient transfer, as shown in the qualitative evaluation that we report in the experimental section. The animation transfer we provide will potentially impact different scenarios, such as data augmentation for learning-based procedures or virtual avatar generation for orthopedic rehabilitation and social applications.
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 "Melzi, Simone"

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