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With the increase of computational power for the available hardware, the demand for high-resolution data in computer graphics applications increases. Consequently, classical geometry processing techniques based on linear algebra solutions are starting to become obsolete. In this setting, we propose a novel approach for tackling mesh deformation tasks on high-resolution meshes. By reducing the input size with a fast remeshing technique and preserving a consistent representation of the original mesh with local reference frames, we provide a solution that is both scalable and robust. We extensively test our technique and compare it against state-of-the-art methods, proving that our approach can handle meshes with hundreds of thousands of vertices in tens of seconds while still achieving results comparable with the other solutions.

Current data-driven methodologies for point cloud matching demand extensive training time and computational resources, presenting significant challenges for model deployment and application. In the point cloud matching task, recent advancements with an encoder-only Transformer architecture have revealed the emergence of semantically meaningful patterns in the attention heads, particularly resembling Gaussian functions centered on each point of the input shape. In this work, we further investigate this phenomenon by integrating these patterns as fixed attention weights within the attention heads of the Transformer architecture. We evaluate two variants: one utilizing predetermined variance values for the Gaussians, and another where the variance values are treated as learnable parameters. Additionally we analyze the performances on noisy data and explore a possible way to improve robustness to noise. Our findings demonstrate that fixing the attention weights not only accelerates the training process but also enhances the stability of the optimization. Furthermore, we conducted an ablation study to identify the specific layers where the infused information is most impactful and to understand the reliance of the network on this information.

For the last decade, there has been a push to use multi-dimensional (latent) spaces to represent concepts; and yet how to manipulate these concepts or reason with them remains largely unclear. Some recent methods exploit multiple latent representations and their connection, making this research question even more entangled. Our goal is to understand how operations in the latent space affect the underlying concepts. To that end, we explore the task of concept blending through diffusion models. Diffusion models are based on a connection between a latent representation of textual prompts and a latent space that enables image reconstruction and generation. This task allows us to try different text-based combination strategies, and evaluate easily through a visual analysis. Our conclusion is that concept blending through space manipulation is possible, although the best strategy depends on the context of the blend.

In this work, we present the local patch mesh representation for neural signed distance fields. This technique allows to discretize local regions of the level sets of an input SDF by projecting and deforming flat patch meshes onto the level set surface, using exclusively the SDF information and its gradient. Our analysis reveals this method to be more accurate than the standard marching cubes algorithm for approximating the implicit surface. Then, we apply this representation in the setting of handle-guided deformation: we introduce two distinct pipelines, which make use of 3D neural fields to compute As-Rigid-As-Possible deformations of both high-resolution meshes and neural fields under a given set of constraints. We run a comprehensive evaluation of our method and various baselines for neural field and mesh deformation which show both pipelines achieve impressive efficiency and notable improvements in terms of quality of results and robustness. With our novel pipeline, we introduce a scalable approach to solve a well-established geometry processing problem on high-resolution meshes, and pave the way for extending other geometric tasks to the domain of implicit surfaces via local patch meshing., Comment: 12 pages, 16 figures

Synthetic data is gaining increasing relevance for training machine learning models. This is mainly motivated due to several factors such as the lack of real data and intra-class variability, time and errors produced in manual labeling, and in some cases privacy concerns, among others. This paper presents an overview of the 2nd edition of the Face Recognition Challenge in the Era of Synthetic Data (FRCSyn) organized at CVPR 2024. FRCSyn aims to investigate the use of synthetic data in face recognition to address current technological limitations, including data privacy concerns, demographic biases, generalization to novel scenarios, and performance constraints in challenging situations such as aging, pose variations, and occlusions. Unlike the 1st edition, in which synthetic data from DCFace and GANDiffFace methods was only allowed to train face recognition systems, in this 2nd edition we propose new sub-tasks that allow participants to explore novel face generative methods. The outcomes of the 2nd FRCSyn Challenge, along with the proposed experimental protocol and benchmarking contribute significantly to the application of synthetic data to face recognition., Comment: arXiv admin note: text overlap with arXiv:2311.10476

Reconstructing 2D curves from sample points has long been a critical challenge in computer graphics, finding essential applications in vector graphics. The design and editing of curves on surfaces has only recently begun to receive attention, primarily relying on human assistance, and where not, limited by very strict sampling conditions. In this work, we formally improve on the state-of-the-art requirements and introduce an innovative algorithm capable of reconstructing closed curves directly on surfaces from a given sparse set of sample points. We extend and adapt a state-of-the-art planar curve reconstruction method to the realm of surfaces while dealing with the challenges arising from working on non-Euclidean domains. We demonstrate the robustness of our method by reconstructing multiple curves on various surface meshes. We explore novel potential applications of our approach, allowing for automated reconstruction of curves on Riemannian manifolds.

Large-scale face recognition datasets are collected by crawling the Internet and without individuals' consent, raising legal, ethical, and privacy concerns. With the recent advances in generative models, recently several works proposed generating synthetic face recognition datasets to mitigate concerns in web-crawled face recognition datasets. This paper presents the summary of the Synthetic Data for Face Recognition (SDFR) Competition held in conjunction with the 18th IEEE International Conference on Automatic Face and Gesture Recognition (FG 2024) and established to investigate the use of synthetic data for training face recognition models. The SDFR competition was split into two tasks, allowing participants to train face recognition systems using new synthetic datasets and/or existing ones. In the first task, the face recognition backbone was fixed and the dataset size was limited, while the second task provided almost complete freedom on the model backbone, the dataset, and the training pipeline. The submitted models were trained on existing and also new synthetic datasets and used clever methods to improve training with synthetic data. The submissions were evaluated and ranked on a diverse set of seven benchmarking datasets. The paper gives an overview of the submitted face recognition models and reports achieved performance compared to baseline models trained on real and synthetic datasets. Furthermore, the evaluation of submissions is extended to bias assessment across different demography groups. Lastly, an outlook on the current state of the research in training face recognition models using synthetic data is presented, and existing problems as well as potential future directions are also discussed., Comment: The 18th IEEE International Conference on Automatic Face and Gesture Recognition (FG 2024)

This study investigates the possibility of mitigating the demographic biases that affect face recognition technologies through the use of synthetic data. Demographic biases have the potential to impact individuals from specific demographic groups, and can be identified by observing disparate performance of face recognition systems across demographic groups. They primarily arise from the unequal representations of demographic groups in the training data. In recent times, synthetic data have emerged as a solution to some problems that affect face recognition systems. In particular, during the generation process it is possible to specify the desired demographic and facial attributes of images, in order to control the demographic distribution of the synthesized dataset, and fairly represent the different demographic groups. We propose to fine-tune with synthetic data existing face recognition systems that present some demographic biases. We use synthetic datasets generated with GANDiffFace, a novel framework able to synthesize datasets for face recognition with controllable demographic distribution and realistic intra-class variations. We consider multiple datasets representing different demographic groups for training and evaluation. Also, we fine-tune different face recognition systems, and evaluate their demographic fairness with different metrics. Our results support the proposed approach and the use of synthetic data to mitigate demographic biases in face recognition., Comment: 8 pages, 3 figures

Despite the widespread adoption of face recognition technology around the world, and its remarkable performance on current benchmarks, there are still several challenges that must be covered in more detail. This paper offers an overview of the Face Recognition Challenge in the Era of Synthetic Data (FRCSyn) organized at WACV 2024. This is the first international challenge aiming to explore the use of synthetic data in face recognition to address existing limitations in the technology. Specifically, the FRCSyn Challenge targets concerns related to data privacy issues, demographic biases, generalization to unseen scenarios, and performance limitations in challenging scenarios, including significant age disparities between enrollment and testing, pose variations, and occlusions. The results achieved in the FRCSyn Challenge, together with the proposed benchmark, contribute significantly to the application of synthetic data to improve face recognition technology., Comment: 10 pages, 1 figure, WACV 2024 Workshops

In deep learning, auxiliary objectives are often used to facilitate learning in situations where data is scarce, or the principal task is extremely complex. This idea is primarily inspired by the improved generalization capability induced by solving multiple tasks simultaneously, which leads to a more robust shared representation. Nevertheless, finding optimal auxiliary tasks that give rise to the desired improvement is a crucial problem that often requires hand-crafted solutions or expensive meta-learning approaches. In this paper, we propose a novel framework, dubbed Detaux, whereby a weakly supervised disentanglement procedure is used to discover new unrelated classification tasks and the associated labels that can be exploited with the principal task in any Multi-Task Learning (MTL) model. The disentanglement procedure works at a representation level, isolating a subspace related to the principal task, plus an arbitrary number of orthogonal subspaces. In the most disentangled subspaces, through a clustering procedure, we generate the additional classification tasks, and the associated labels become their representatives. Subsequently, the original data, the labels associated with the principal task, and the newly discovered ones can be fed into any MTL framework. Extensive validation on both synthetic and real data, along with various ablation studies, demonstrate promising results, revealing the potential in what has been, so far, an unexplored connection between learning disentangled representations and MTL. The code will be made publicly available upon acceptance., Comment: Under review in Pattern Recognition Letters

The application of mobile biometrics as a user-friendly authentication method has increased in the last years. Recent studies have proposed novel behavioral biometric recognition systems based on Transformers, which currently outperform the state of the art in several application scenarios. On-line handwritten signature verification aims to verify the identity of subjects, based on their biometric signatures acquired using electronic devices such as tablets or smartphones. This paper investigates the suitability of architectures based on recent Transformers for on-line signature verification. In particular, four different configurations are studied, two of them rely on the Vanilla Transformer encoder, and the two others have been successfully applied to the tasks of gait and activity recognition. We evaluate the four proposed configurations according to the experimental protocol proposed in the SVC-onGoing competition. The results obtained in our experiments are promising, and promote the use of Transformers for on-line signature verification., Comment: 2 pages, 2 figures

Face recognition systems have significantly advanced in recent years, driven by the availability of large-scale datasets. However, several issues have recently came up, including privacy concerns that have led to the discontinuation of well-established public datasets. Synthetic datasets have emerged as a solution, even though current synthesis methods present other drawbacks such as limited intra-class variations, lack of realism, and unfair representation of demographic groups. This study introduces GANDiffFace, a novel framework for the generation of synthetic datasets for face recognition that combines the power of Generative Adversarial Networks (GANs) and Diffusion models to overcome the limitations of existing synthetic datasets. In GANDiffFace, we first propose the use of GANs to synthesize highly realistic identities and meet target demographic distributions. Subsequently, we fine-tune Diffusion models with the images generated with GANs, synthesizing multiple images of the same identity with a variety of accessories, poses, expressions, and contexts. We generate multiple synthetic datasets by changing GANDiffFace settings, and compare their mated and non-mated score distributions with the distributions provided by popular real-world datasets for face recognition, i.e. VGG2 and IJB-C. Our results show the feasibility of the proposed GANDiffFace, in particular the use of Diffusion models to enhance the (limited) intra-class variations provided by GANs towards the level of real-world datasets., Comment: 8 pages, 6 figures

Shape matching is a fundamental problem in computer graphics with many applications. Functional maps translate the point-wise shape-matching problem into its functional counterpart and have inspired numerous solutions over the last decade. Nearly all the solutions based on functional maps rely on the eigenfunctions of the Laplace-Beltrami Operator (LB) to describe the functional spaces defined on the surfaces and then convert the functional correspondences into point-wise correspondences. However, this final step is often error-prone and inaccurate in tiny regions and protrusions, where the energy of LB does not uniformly cover the surface. We propose a new functional basis Principal Components of a Dictionary (PCD) to address such intrinsic limitation. PCD constructs an orthonormal basis from the Principal Component Analysis (PCA) of a dictionary of functions defined over the shape. These dictionaries can target specific properties of the final basis, such as achieving an even spreading of energy. Our experimental evaluation compares seven different dictionaries on established benchmarks, showing that PCD is suited to target different shape-matching scenarios, resulting in more accurate point-wise maps than the LB basis when used in the same pipeline. This evidence provides a promising alternative for improving correspondence estimation, confirming the power and flexibility of functional maps., Comment: 22 pages, 12 figures

We introduce \emph{ReMatching}, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks even on meshes counting millions of vertices, where the original functional maps does not apply or requires a massive computational cost. The core of our procedure is a time-efficient remeshing algorithm which constructs a low-resolution geometry while acting conservatively on the original topology and metric. These properties allow translating the functional maps optimization problem on the resulting low-resolution representation, thus enabling efficient computation of correspondences with functional map approaches. Finally, we propose an efficient technique for extending the estimated correspondence to the original meshes. We show that our method is more efficient and effective through quantitative and qualitative comparisons, outperforming state-of-the-art pipelines in quality and computational cost.

In this paper, we benchmark several cancelable biometrics (CB) schemes on different biometric characteristics. We consider BioHashing, Multi-Layer Perceptron (MLP) Hashing, Bloom Filters, and two schemes based on Index-of-Maximum (IoM) Hashing (i.e., IoM-URP and IoM-GRP). In addition to the mentioned CB schemes, we introduce a CB scheme (as a baseline) based on user-specific random transformations followed by binarization. We evaluate the unlinkability, irreversibility, and recognition performance (which are the required criteria by the ISO/IEC 24745 standard) of these CB schemes on deep learning based templates extracted from different physiological and behavioral biometric characteristics including face, voice, finger vein, and iris. In addition, we provide an open-source implementation of all the experiments presented to facilitate the reproducibility of our results.

Privacy-enhancing technologies are technologies that implement fundamental data protection principles. With respect to biometric recognition, different types of privacy-enhancing technologies have been introduced for protecting stored biometric data which are generally classified as sensitive. In this regard, various taxonomies and conceptual categorizations have been proposed and standardization activities have been carried out. However, these efforts have mainly been devoted to certain sub-categories of privacy-enhancing technologies and therefore lack generalization. This work provides an overview of concepts of privacy-enhancing technologies for biometrics in a unified framework. Key aspects and differences between existing concepts are highlighted in detail at each processing step. Fundamental properties and limitations of existing approaches are discussed and related to data protection techniques and principles. Moreover, scenarios and methods for the assessment of privacy-enhancing technologies for biometrics are presented. This paper is meant as a point of entry to the field of biometric data protection and is directed towards experienced researchers as well as non-experts., Comment: 12 pages, 2 figures

Language models demonstrate both quantitative improvement and new qualitative capabilities with increasing scale. Despite their potentially transformative impact, these new capabilities are as yet poorly characterized. In order to inform future research, prepare for disruptive new model capabilities, and ameliorate socially harmful effects, it is vital that we understand the present and near-future capabilities and limitations of language models. To address this challenge, we introduce the Beyond the Imitation Game benchmark (BIG-bench). BIG-bench currently consists of 204 tasks, contributed by 450 authors across 132 institutions. Task topics are diverse, drawing problems from linguistics, childhood development, math, common-sense reasoning, biology, physics, social bias, software development, and beyond. BIG-bench focuses on tasks that are believed to be beyond the capabilities of current language models. We evaluate the behavior of OpenAI's GPT models, Google-internal dense transformer architectures, and Switch-style sparse transformers on BIG-bench, across model sizes spanning millions to hundreds of billions of parameters. In addition, a team of human expert raters performed all tasks in order to provide a strong baseline. Findings include: model performance and calibration both improve with scale, but are poor in absolute terms (and when compared with rater performance); performance is remarkably similar across model classes, though with benefits from sparsity; tasks that improve gradually and predictably commonly involve a large knowledge or memorization component, whereas tasks that exhibit "breakthrough" behavior at a critical scale often involve multiple steps or components, or brittle metrics; social bias typically increases with scale in settings with ambiguous context, but this can be improved with prompting., Comment: 27 pages, 17 figures + references and appendices, repo: https://github.com/google/BIG-bench

In graph learning, maps between graphs and their subgraphs frequently arise. For instance, when coarsening or rewiring operations are present along the pipeline, one needs to keep track of the corresponding nodes between the original and modified graphs. Classically, these maps are represented as binary node-to-node correspondence matrices and used as-is to transfer node-wise features between the graphs. In this paper, we argue that simply changing this map representation can bring notable benefits to graph learning tasks. Drawing inspiration from recent progress in geometry processing, we introduce a spectral representation for maps that is easy to integrate into existing graph learning models. This spectral representation is a compact and straightforward plug-in replacement and is robust to topological changes of the graphs. Remarkably, the representation exhibits structural properties that make it interpretable, drawing an analogy with recent results on smooth manifolds. We demonstrate the benefits of incorporating spectral maps in graph learning pipelines, addressing scenarios where a node-to-node map is not well defined, or in the absence of exact isomorphism. Our approach bears practical benefits in knowledge distillation and hierarchical learning, where we show comparable or improved performance at a fraction of the computational cost.

Electrocardiograms (ECGs) have shown unique patterns to distinguish between different subjects and present important advantages compared to other biometric traits, such as difficulty to counterfeit, liveness detection, and ubiquity. Also, with the success of Deep Learning technologies, ECG biometric recognition has received increasing interest in recent years. However, it is not easy to evaluate the improvements of novel ECG proposed methods, mainly due to the lack of public data and standard experimental protocols. In this study, we perform extensive analysis and comparison of different scenarios in ECG biometric recognition. Both verification and identification tasks are investigated, as well as single- and multi-session scenarios. Finally, we also perform single- and multi-lead ECG experiments, considering traditional scenarios using electrodes in the chest and limbs and current user-friendly wearable devices. In addition, we present ECGXtractor, a robust Deep Learning technology trained with an in-house large-scale database and able to operate successfully across various scenarios and multiple databases. We introduce our proposed feature extractor, trained with multiple sinus-rhythm heartbeats belonging to 55,967 subjects, and provide a general public benchmark evaluation with detailed experimental protocol. We evaluate the system performance over four different databases: i) our in-house database, ii) PTB, iii) ECG-ID, and iv) CYBHi. With the widely used PTB database, we achieve Equal Error Rates of 0.14% and 2.06% in verification, and accuracies of 100% and 96.46% in identification, respectively in single- and multi-session analysis. We release the source code, experimental protocol details, and pre-trained models in GitHub to advance in the field., Comment: 11 pages, 4 figures

We introduce Explanatory Learning (EL), a framework to let machines use existing knowledge buried in symbolic sequences -- e.g. explanations written in hieroglyphic -- by autonomously learning to interpret them. In EL, the burden of interpreting symbols is not left to humans or rigid human-coded compilers, as done in Program Synthesis. Rather, EL calls for a learned interpreter, built upon a limited collection of symbolic sequences paired with observations of several phenomena. This interpreter can be used to make predictions on a novel phenomenon given its explanation, and even to find that explanation using only a handful of observations, like human scientists do. We formulate the EL problem as a simple binary classification task, so that common end-to-end approaches aligned with the dominant empiricist view of machine learning could, in principle, solve it. To these models, we oppose Critical Rationalist Networks (CRNs), which instead embrace a rationalist view on the acquisition of knowledge. CRNs express several desired properties by construction, they are truly explainable, can adjust their processing at test-time for harder inferences, and can offer strong confidence guarantees on their predictions. As a final contribution, we introduce Odeen, a basic EL environment that simulates a small flatland-style universe full of phenomena to explain. Using Odeen as a testbed, we show how CRNs outperform empiricist end-to-end approaches of similar size and architecture (Transformers) in discovering explanations for novel phenomena., Comment: Main paper: 10 pages, References: 3 pages, Appendix: 7 pages

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 orientation awareness. More specifically, we demonstrate that unlike regular functional maps that link functional spaces of two manifolds, our complex functional maps establish a link between oriented tangent bundles, 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 orientationaware, thus favoring orientation and angle preserving correspondence 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.

Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the different shapes in high-dimensional space where the matching is easier to solve is a well-trodden path that has given many outstanding solutions. Recently, a new trend has shown advantages in learning such representations. This novel idea motivated us to investigate which properties differentiate these data-driven embeddings and which ones promote state-of-the-art results. In this study, we analyze, for the first time, properties that arise in data-driven learned embedding and their relation to the shape-matching task. Our discoveries highlight the close link between matching and smoothness, which naturally emerge from training. Also, we demonstrate the relation between the orthogonality of the embedding and the bijectivity of the correspondence. Our experiments show exciting results, overcoming well-established alternatives and shedding a different light on relevant contexts and properties for learned embeddings.

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.

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., Comment: Accepted at SGP2022

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.

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., Comment: Published at CVPR 2021

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., Comment: 18 pages, 20 figures

Most state-of-the-art works in trajectory forecasting for automotive target predicting the pose and orientation of the agents in the scene. This represents a particularly useful problem, for instance in autonomous driving, but it does not cover a spectrum of applications in control and simulation that require information on vehicle dynamics features other than pose and orientation. Also, multi-step dynamic simulation of complex multibody models does not seem to be a viable solution for real-time long-term prediction, due to the high computational time required. To bridge this gap, we present a deep-learning framework to model and predict the evolution of the coupled driver-vehicle system dynamics jointly on a complex road geometry. It consists of two components. The first, a neural network predictor, is based on Long Short-Term Memory autoencoders and fuses the information on the road geometry and the past driver-vehicle system dynamics to produce context-aware predictions. The second, a Bayesian optimiser, is proposed to tune some significant hyperparameters of the network. These govern the network complexity, as well as the features importance. The result is a self-tunable framework with real-time applicability, which allows the user to specify the features of interest. The approach has been validated with a case study centered on motion cueing algorithms, using a dataset collected during test sessions of a non-professional driver on a dynamic driving simulator. A 3D track with complex geometry has been employed as driving environment to render the prediction task challenging. Finally, the robustness of the neural network to changes in the driver and track was investigated to set guidelines for future works., Comment: 12 pages, 10 figures, 2 tables. This work has been submitted to Elsevier for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible