arXiv subjects

Emanuele Rodolà

Publications and source records attributed to Emanuele Rodolà.

At least 109 records · Page 6Linked to original sources

arXiv2021

Shape registration in the time of transformers

In this paper, we propose a transformer-based procedure for the efficient registration of non-rigid 3D point clouds. The proposed approach is data-driven and adopts for the first time the transformer architecture in the registration task. Our method is general and applies to different settings. Given a fixed template with some desired properties (e.g. skinning weights or other animation cues), we can register raw acquired data to it, thereby transferring all the template properties to the input geometry. Alternatively, given a pair of shapes, our method can register the first onto the second (or vice-versa), obtaining a high-quality dense correspondence between the two. In both contexts, the quality of our results enables us to target real applications such as texture transfer and shape interpolation. Furthermore, we also show that including an estimation of the underlying density of the surface eases the learning process. By exploiting the potential of this architecture, we can train our model requiring only a sparse set of ground truth correspondences ($10\sim20\%$ of the total points). The proposed model and the analysis that we perform pave the way for future exploration of transformer-based architectures for registration and matching applications. Qualitative and quantitative evaluations demonstrate that our pipeline outperforms state-of-the-art methods for deformable and unordered 3D data registration on different datasets and scenarios.

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arXiv2021

Cluster-driven Graph Federated Learning over Multiple Domains

Federated Learning (FL) deals with learning a central model (i.e. the server) in privacy-constrained scenarios, where data are stored on multiple devices (i.e. the clients). The central model has no direct access to the data, but only to the updates of the parameters computed locally by each client. This raises a problem, known as statistical heterogeneity, because the clients may have different data distributions (i.e. domains). This is only partly alleviated by clustering the clients. Clustering may reduce heterogeneity by identifying the domains, but it deprives each cluster model of the data and supervision of others. Here we propose a novel Cluster-driven Graph Federated Learning (FedCG). In FedCG, clustering serves to address statistical heterogeneity, while Graph Convolutional Networks (GCNs) enable sharing knowledge across them. FedCG: i) identifies the domains via an FL-compliant clustering and instantiates domain-specific modules (residual branches) for each domain; ii) connects the domain-specific modules through a GCN at training to learn the interactions among domains and share knowledge; and iii) learns to cluster unsupervised via teacher-student classifier-training iterations and to address novel unseen test domains via their domain soft-assignment scores. Thanks to the unique interplay of GCN over clusters, FedCG achieves the state-of-the-art on multiple FL benchmarks.

cs.LG↗

arXiv2021

Universal Spectral Adversarial Attacks for Deformable Shapes

Machine learning models are known to be vulnerable to adversarial attacks, namely perturbations of the data that lead to wrong predictions despite being imperceptible. However, the existence of "universal" attacks (i.e., unique perturbations that transfer across different data points) has only been demonstrated for images to date. Part of the reason lies in the lack of a common domain, for geometric data such as graphs, meshes, and point clouds, where a universal perturbation can be defined. In this paper, we offer a change in perspective and demonstrate the existence of universal attacks for geometric data (shapes). We introduce a computational procedure that operates entirely in the spectral domain, where the attacks take the form of small perturbations to short eigenvalue sequences; the resulting geometry is then synthesized via shape-from-spectrum recovery. Our attacks are universal, in that they transfer across different shapes, different representations (meshes and point clouds), and generalize to previously unseen data.

cs.LG↗

arXiv2020

Non-Rigid Puzzles

Shape correspondence is a fundamental problem in computer graphics and vision, with applications in various problems including animation, texture mapping, robotic vision, medical imaging, archaeology and many more. In settings where the shapes are allowed to undergo non-rigid deformations and only partial views are available, the problem becomes very challenging. To this end, we present a non-rigid multi-part shape matching algorithm. We assume to be given a reference shape and its multiple parts undergoing a non-rigid deformation. Each of these query parts can be additionally contaminated by clutter, may overlap with other parts, and there might be missing parts or redundant ones. Our method simultaneously solves for the segmentation of the reference model, and for a dense correspondence to (subsets of) the parts. Experimental results on synthetic as well as real scans demonstrate the effectiveness of our method in dealing with this challenging matching scenario.

cs.CV↗

arXiv2020

Instant recovery of shape from spectrum via latent space connections

We introduce the first learning-based method for recovering shapes from Laplacian spectra. Given an auto-encoder, our model takes the form of a cycle-consistent module to map latent vectors to sequences of eigenvalues. This module provides an efficient and effective linkage between spectrum and geometry of a given shape. Our data-driven approach replaces the need for ad-hoc regularizers required by prior methods, while providing more accurate results at a fraction of the computational cost. Our learning model applies without modifications across different dimensions (2D and 3D shapes alike), representations (meshes, contours and point clouds), as well as across different shape classes, and admits arbitrary resolution of the input spectrum without affecting complexity. The increased flexibility allows us to provide a proxy to differentiable eigendecomposition and to address notoriously difficult tasks in 3D vision and geometry processing within a unified framework, including shape generation from spectrum, mesh super-resolution, shape exploration, style transfer, spectrum estimation from point clouds, segmentation transfer and point-to-point matching.

cs.CV↗

arXiv2020

High-Resolution Augmentation for Automatic Template-Based Matching of Human Models

We propose a new approach for 3D shape matching of deformable human shapes. Our approach is based on the joint adoption of three different tools: an intrinsic spectral matching pipeline, a morphable model, and an extrinsic details refinement. By operating in conjunction, these tools allow us to greatly improve the quality of the matching while at the same time resolving the key issues exhibited by each tool individually. In this paper we present an innovative High-Resolution Augmentation (HRA) strategy that enables highly accurate correspondence even in the presence of significant mesh resolution mismatch between the input shapes. This augmentation provides an effective workaround for the resolution limitations imposed by the adopted morphable model. The HRA in its global and localized versions represents a novel refinement strategy for surface subdivision methods. We demonstrate the accuracy of the proposed pipeline on multiple challenging benchmarks, and showcase its effectiveness in surface registration and texture transfer.

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arXiv2020

Nonlinear Spectral Geometry Processing via the TV Transform

We introduce a novel computational framework for digital geometry processing, based upon the derivation of a nonlinear operator associated to the total variation functional. Such operator admits a generalized notion of spectral decomposition, yielding a sparse multiscale representation akin to Laplacian-based methods, while at the same time avoiding undesirable over-smoothing effects typical of such techniques. Our approach entails accurate, detail-preserving decomposition and manipulation of 3D shape geometry while taking an especially intuitive form: non-local semantic details are well separated into different bands, which can then be filtered and re-synthesized with a straightforward linear step. Our computational framework is flexible, can be applied to a variety of signals, and is easily adapted to different geometry representations, including triangle meshes and point clouds. We showcase our method throughout multiple applications in graphics, ranging from surface and signal denoising to detail transfer and cubic stylization.

cs.GR↗

arXiv2020

LIMP: Learning Latent Shape Representations with Metric Preservation Priors

In this paper, we advocate the adoption of metric preservation as a powerful prior for learning latent representations of deformable 3D shapes. Key to our construction is the introduction of a geometric distortion criterion, defined directly on the decoded shapes, translating the preservation of the metric on the decoding to the formation of linear paths in the underlying latent space. Our rationale lies in the observation that training samples alone are often insufficient to endow generative models with high fidelity, motivating the need for large training datasets. In contrast, metric preservation provides a rigorous way to control the amount of geometric distortion incurring in the construction of the latent space, leading in turn to synthetic samples of higher quality. We further demonstrate, for the first time, the adoption of differentiable intrinsic distances in the backpropagation of a geodesic loss. Our geometric priors are particularly relevant in the presence of scarce training data, where learning any meaningful latent structure can be especially challenging. The effectiveness and potential of our generative model is showcased in applications of style transfer, content generation, and shape completion.

cs.LG↗

arXiv2020

The Whole Is Greater Than the Sum of Its Nonrigid Parts

According to Aristotle, a philosopher in Ancient Greece, "the whole is greater than the sum of its parts". This observation was adopted to explain human perception by the Gestalt psychology school of thought in the twentieth century. Here, we claim that observing part of an object which was previously acquired as a whole, one could deal with both partial matching and shape completion in a holistic manner. More specifically, given the geometry of a full, articulated object in a given pose, as well as a partial scan of the same object in a different pose, we address the problem of matching the part to the whole while simultaneously reconstructing the new pose from its partial observation. Our approach is data-driven, and takes the form of a Siamese autoencoder without the requirement of a consistent vertex labeling at inference time; as such, it can be used on unorganized point clouds as well as on triangle meshes. We demonstrate the practical effectiveness of our model in the applications of single-view deformable shape completion and dense shape correspondence, both on synthetic and real-world geometric data, where we outperform prior work on these tasks by a large margin.

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arXiv2019

ZoomOut: Spectral Upsampling for Efficient Shape Correspondence

We present a simple and efficient method for refining maps or correspondences by iterative upsampling in the spectral domain that can be implemented in a few lines of code. Our main observation is that high quality maps can be obtained even if the input correspondences are noisy or are encoded by a small number of coefficients in a spectral basis. We show how this approach can be used in conjunction with existing initialization techniques across a range of application scenarios, including symmetry detection, map refinement across complete shapes, non-rigid partial shape matching and function transfer. In each application we demonstrate an improvement with respect to both the quality of the results and the computational speed compared to the best competing methods, with up to two orders of magnitude speed-up in some applications. We also demonstrate that our method is both robust to noisy input and is scalable with respect to shape complexity. Finally, we present a theoretical justification for our approach, shedding light on structural properties of functional maps.

cs.GR↗

arXiv2019

Correspondence-Free Region Localization for Partial Shape Similarity via Hamiltonian Spectrum Alignment

We consider the problem of localizing relevant subsets of non-rigid geometric shapes given only a partial 3D query as the input. Such problems arise in several challenging tasks in 3D vision and graphics, including partial shape similarity, retrieval, and non-rigid correspondence. We phrase the problem as one of alignment between short sequences of eigenvalues of basic differential operators, which are constructed upon a scalar function defined on the 3D surfaces. Our method therefore seeks for a scalar function that entails this alignment. Differently from existing approaches, we do not require solving for a correspondence between the query and the target, therefore greatly simplifying the optimization process; our core technique is also descriptor-free, as it is driven by the geometry of the two objects as encoded in their operator spectra. We further show that our spectral alignment algorithm provides a remarkably simple alternative to the recent shape-from-spectrum reconstruction approaches. For both applications, we demonstrate improvement over the state-of-the-art either in terms of accuracy or computational cost.

cs.CG↗

arXiv2019

Isospectralization, or how to hear shape, style, and correspondence

The question whether one can recover the shape of a geometric object from its Laplacian spectrum ('hear the shape of the drum') is a classical problem in spectral geometry with a broad range of implications and applications. While theoretically the answer to this question is negative (there exist examples of iso-spectral but non-isometric manifolds), little is known about the practical possibility of using the spectrum for shape reconstruction and optimization. In this paper, we introduce a numerical procedure called isospectralization, consisting of deforming one shape to make its Laplacian spectrum match that of another. We implement the isospectralization procedure using modern differentiable programming techniques and exemplify its applications in some of the classical and notoriously hard problems in geometry processing, computer vision, and graphics such as shape reconstruction, pose and style transfer, and dense deformable correspondence.

cs.CG↗

arXiv2019

Functional Maps Representation on Product Manifolds

We consider the tasks of representing, analyzing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace--Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices.

cs.GR↗

arXiv2018

Self-supervised Learning of Dense Shape Correspondence

We introduce the first completely unsupervised correspondence learning approach for deformable 3D shapes. Key to our model is the understanding that natural deformations (such as changes in pose) approximately preserve the metric structure of the surface, yielding a natural criterion to drive the learning process toward distortion-minimizing predictions. On this basis, we overcome the need for annotated data and replace it by a purely geometric criterion. The resulting learning model is class-agnostic, and is able to leverage any type of deformable geometric data for the training phase. In contrast to existing supervised approaches which specialize on the class seen at training time, we demonstrate stronger generalization as well as applicability to a variety of challenging settings. We showcase our method on a wide selection of correspondence benchmarks, where we outperform other methods in terms of accuracy, generalization, and efficiency.

cs.CV↗

arXiv2018

FARM: Functional Automatic Registration Method for 3D Human Bodies

We introduce a new method for non-rigid registration of 3D human shapes. Our proposed pipeline builds upon a given parametric model of the human, and makes use of the functional map representation for encoding and inferring shape maps throughout the registration process. This combination endows our method with robustness to a large variety of nuisances observed in practical settings, including non-isometric transformations, downsampling, topological noise, and occlusions; further, the pipeline can be applied invariably across different shape representations (e.g. meshes and point clouds), and in the presence of (even dramatic) missing parts such as those arising in real-world depth sensing applications. We showcase our method on a selection of challenging tasks, demonstrating results in line with, or even surpassing, state-of-the-art methods in the respective areas.

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arXiv2017

Localized Manifold Harmonics for Spectral Shape Analysis

The use of Laplacian eigenfunctions is ubiquitous in a wide range of computer graphics and geometry processing applications. In particular, Laplacian eigenbases allow generalizing the classical Fourier analysis to manifolds. A key drawback of such bases is their inherently global nature, as the Laplacian eigenfunctions carry geometric and topological structure of the entire manifold. In this paper, we introduce a new framework for local spectral shape analysis. We show how to efficiently construct localized orthogonal bases by solving an optimization problem that in turn can be posed as the eigendecomposition of a new operator obtained by a modification of the standard Laplacian. We study the theoretical and computational aspects of the proposed framework and showcase our new construction on the classical problems of shape approximation and correspondence. We obtain significant improvement compared to classical Laplacian eigenbases as well as other alternatives for constructing localized bases.

cs.GR↗

arXiv2017

Efficient Deformable Shape Correspondence via Kernel Matching

We present a method to match three dimensional shapes under non-isometric deformations, topology changes and partiality. We formulate the problem as matching between a set of pair-wise and point-wise descriptors, imposing a continuity prior on the mapping, and propose a projected descent optimization procedure inspired by difference of convex functions (DC) programming. Surprisingly, in spite of the highly non-convex nature of the resulting quadratic assignment problem, our method converges to a semantically meaningful and continuous mapping in most of our experiments, and scales well. We provide preliminary theoretical analysis and several interpretations of the method.

cs.CV↗

arXiv2017

Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.

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