Browsing by Author "Melzi, Simone"

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    Adjoint Bijective ZoomOut: Efficient Upsampling for Learned Linearly-invariant Embedding
    (The Eurographics Association, 2023) Viganò, Giulio; Melzi, Simone; Banterle, Francesco; Caggianese, Giuseppe; Capece, Nicola; Erra, Ugo; Lupinetti, Katia; Manfredi, Gilda
    In this paper, we present a novel method for refining correspondences between 3D point clouds. Our method is compatible with the functional map framework, so it relies on the spectral representation of the correspondence. Although, differently from other similar approaches, this algorithm is specifically for a particular functional setting, being the only refinement method compatible with a recent data-driven approach, more suitable for point cloud matching. Our algorithm arises from a different way of converting functional operators into point-to-point correspondence, which we prove to promote bijectivity between maps, exploiting a theoretical result. Iterating this procedure and performing spectral upsampling in the same way as other similar methods, ours increases the accuracy of the correspondence, leading to more bijective correspondences. We tested our method over different datasets. It outperforms the previous methods in terms of map accuracy in all the tests considered.
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    Discrete Optimization for Shape Matching
    (The Eurographics Association and John Wiley & Sons Ltd., 2021) Ren, Jing; Melzi, Simone; Wonka, Peter; Ovsjanikov, Maks; Digne, Julie and Crane, Keenan
    We propose a novel discrete solver for optimizing functional map-based energies, including descriptor preservation and promoting structural properties such as area-preservation, bijectivity and Laplacian commutativity among others. Unlike the commonly-used continuous optimization methods, our approach enforces the functional map to be associated with a pointwise correspondence as a hard constraint, which provides a stronger link between optimized properties of functional and point-topoint maps. Under this hard constraint, our solver obtains functional maps with lower energy values compared to the standard continuous strategies. Perhaps more importantly, the recovered pointwise maps from our discrete solver preserve the optimized for functional properties and are thus of higher overall quality. We demonstrate the advantages of our discrete solver on a range of energies and shape categories, compared to existing techniques for promoting pointwise maps within the functional map framework. Finally, with this solver in hand, we introduce a novel Effective Functional Map Refinement (EFMR) method which achieves the state-of-the-art accuracy on the SHREC'19 benchmark.
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    A functional skeleton transfer
    (ACM, 2021) Musoni, Pietro; Marin, Riccardo; Melzi, Simone; Castellani, Umberto; Narain, Rahul and Neff, Michael and Zordan, Victor
    The animation community has spent significant effort trying to ease rigging procedures. This is necessitated because the increasing availability of 3D data makes manual rigging infeasible. However, object animations involve understanding elaborate geometry and dynamics, and such knowledge is hard to infuse even with modern data-driven techniques. Automatic rigging methods do not provide adequate control and cannot generalize in the presence of unseen artifacts. As an alternative, one can design a system for one shape and then transfer it to other objects. In previous work, this has been implemented by solving the dense point-to-point correspondence problem. Such an approach requires a significant amount of supervision, often placing hundreds of landmarks by hand. This paper proposes a functional approach for skeleton transfer that uses limited information and does not require a complete match between the geometries. To do so, we suggest a novel representation for the skeleton properties, namely the functional regressor, which is compact and invariant to different discretizations and poses. We consider our functional regressor a new operator to adopt in intrinsic geometry pipelines for encoding the pose information, paving the way for several new applications. We numerically stress our method on a large set of different shapes and object classes, providing qualitative and numerical evaluations of precision and computational efficiency. Finally, we show a preliminar transfer of the complete rigging scheme, introducing a promising direction for future explorations.
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    GIM3D: A 3D Dataset for Garment Segmentation
    (The Eurographics Association, 2022) Musoni, Pietro; Melzi, Simone; Castellani, Umberto; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    The 3D cloth segmentation task is particularly challenging due to the extreme variation of shapes, even among the same category of clothes. Several data-driven methods try to cope with this problem but they have to face the lack of available data capable to generalize to the variety of real-world data. For this reason, we present GIM3D (Garments In Motion 3D), a synthetic dataset of clothed 3D human characters in different poses. The over 4000 3D models in this dataset are produced by a physical simulation of clothes with different fabrics, sizes, and tightness, using animated human avatars having a large variety of shapes. Our dataset is composed of single meshes created to simulate 3D scans, with labels for the separate clothes and the visible body parts. We also provide an evaluation of the use of GIM3D as a training set on garment segmentation tasks using state-of-the-art data-driven methods for both meshes and point clouds.
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    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.
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    Local Geometry Processing for Deformations of Non-Rigid 3D Shapes
    (2018-06-19) Melzi, Simone
    Geometry processing and in particular spectral geometry processing deal with many different deformations that complicate shape analysis problems for non-rigid 3D objects. Furthermore, point-wise description of surfaces has increased relevance for several applications such as shape correspondences and matching, shape representation, shape modelling and many others. In this thesis we propose four local approaches to face the problems generated by the deformations of real objects and improving the point-wise characterization of surfaces. Differently from global approaches that work simultaneously on the entire shape we focus on the properties of each point and its local neighbour. Global analysis of shapes is not negative in itself. However, having to deal with local variations, distortions and deformations, it is often challenging to relate two real objects globally. For this reason, in the last decades, several instruments have been introduced for the local analysis of images, graphs, shapes and surfaces. Starting from this idea of localized analysis, we propose both theoretical insights and application tools within the local geometry processing domain. In more detail, we extend the windowed Fourier transform from the standard Euclidean signal processing to different versions specifically designed for spectral geometry processing. Moreover, from the spectral geometry processing perspective, we define a new family of localized basis for the functional space defined on surfaces that improve the spatial localization for standard applications in this field. Finally, we introduce the discrete time evolution process as a framework that characterizes a point through its pairwise relationship with the other points on the surface in an increasing scale of locality. The main contribute of this thesis is a set of tools for local geometry processing and local spectral geometry processing that could be used in standard useful applications. The overall observation of our analysis is that localization around points could factually improve the geometry processing in many different applications.
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    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.
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    PC-GAU: PCA Basis of Scattered Gaussians for Shape Matching via Functional Maps
    (The Eurographics Association, 2022) Colombo, Michele; Boracchi, Giacomo; Melzi, Simone; Cabiddu, Daniela; Schneider, Teseo; Allegra, Dario; Catalano, Chiara Eva; Cherchi, Gianmarco; Scateni, Riccardo
    Shape matching is a central problem in geometry processing applications, ranging from texture transfer to statistical shape analysis. The functional maps framework provides a compact representation of correspondences between discrete surfaces, which is then converted into point-wise maps required by real-world applications. The vast majority of methods based on functional maps involve the eigenfunctions of the Laplace-Beltrami Operator (LB) as the functional basis. A primary drawback of the LB basis is that its energy does not uniformly cover the surface. This fact gives rise to regions where the estimated correspondences are inaccurate, typically at tiny parts and protrusions. For this reason, state-of-the-art procedures to convert the functional maps (represented in the LB basis) into point-wise correspondences are often error-prone. We propose PCGAU, a new functional basis whose energy spreads on the whole shape more evenly than LB. As such, PC-GAU can replace the LB basis in existing shape matching pipelines. PC-GAU consists of the principal vectors obtained by applying Principal Component Analysis (PCA) to a dictionary of sparse Gaussian functions scattered on the surfaces. Through experimental evaluation of established benchmarks, we show that our basis produces more accurate point-wise maps —- compared to LB - when employed in the same shape-matching pipeline.
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    POP: Full Parametric model Estimation for Occluded People
    (The Eurographics Association, 2019) Marin, Riccardo; Melzi, Simone; Mitra, Niloy J.; Castellani, Umberto; Biasotti, Silvia and Lavoué, Guillaume and Veltkamp, Remco
    In the last decades, we have witnessed advances in both hardware and associated algorithms resulting in unprecedented access to volumes of 2D and, more recently, 3D data capturing human movement. We are no longer satisfied with recovering human pose as an image-space 2D skeleton, but seek to obtain a full 3D human body representation. The main challenges in acquiring 3D human shape from such raw measurements are identifying which parts of the data relate to body measurements and recovering from partial observations, often arising out of severe occlusion. For example, a person occluded by a piece of furniture, or being self-occluded in a profile view. In this paper, we propose POP, a novel and efficient paradigm for estimation and completion of human shape to produce a full parametric 3D model directly from single RGBD images, even under severe occlusion. At the heart of our method is a novel human body pose retrieval formulation that explicitly models and handles occlusion. The retrieved result is then refined by a robust optimization to yield a full representation of the human shape. We demonstrate our method on a range of challenging real world scenarios and produce high-quality results not possible by competing alternatives. The method opens up exciting AR/VR application possibilities by working on 'in-the-wild' measurements of human motion.
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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.