Imperial College London

ProfessorMichaelBronstein

Faculty of EngineeringDepartment of Computing

Chair in Machine Learning and Pattern Recognition
 
 
 
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Contact

 

m.bronstein Website

 
 
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569Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Publication Type
Year
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201 results found

Gainza P, Sverrisson F, Monti F, Rodola E, Boscaini D, Bronstein MM, Correia BEet al., 2020, Deciphering interaction fingerprints from protein molecular surfaces using geometric deep learning, NATURE METHODS, Vol: 17, Pages: 184-+, ISSN: 1548-7091

Journal article

Gonzalez G, Gong S, Laponogov I, Veselkov K, Bronstein Met al., 2020, Graph attentional autoencoder for anticancer hyperfood prediction, Publisher: arXiv

Recent research efforts have shown the possibility to discover anticancerdrug-like molecules in food from their effect on protein-protein interactionnetworks, opening a potential pathway to disease-beating diet design. Weformulate this task as a graph classification problem on which graph neuralnetworks (GNNs) have achieved state-of-the-art results. However, GNNs aredifficult to train on sparse low-dimensional features according to ourempirical evidence. Here, we present graph augmented features, integratinggraph structural information and raw node attributes with varying ratios, toease the training of networks. We further introduce a novel neural networkarchitecture on graphs, the Graph Attentional Autoencoder (GAA) to predict foodcompounds with anticancer properties based on perturbed protein networks. Wedemonstrate that the method outperforms the baseline approach andstate-of-the-art graph classification models in this task.

Working paper

Kulon D, Wang H, Güler RA, Bronstein M, Zafeiriou Set al., 2020, Single image 3D hand reconstruction with mesh convolutions

© 2019. The copyright of this document resides with its authors. Monocular 3D reconstruction of deformable objects, such as human body parts, has been typically approached by predicting parameters of heavyweight linear models. In this paper, we demonstrate an alternative solution that is based on the idea of encoding images into a latent non-linear representation of meshes. The prior on 3D hand shapes is learned by training an autoencoder with intrinsic graph convolutions performed in the spectral domain. The pre-trained decoder acts as a non-linear statistical deformable model. The latent parameters that reconstruct the shape and articulated pose of hands in the image are predicted using an image encoder. We show that our system reconstructs plausible meshes and operates in real-time. We evaluate the quality of the mesh reconstructions produced by the decoder on a new dataset and show latent space interpolation results. Our code, data, and models will be made publicly available.

Conference paper

Bermant PC, Bronstein MM, Wood RJ, Gero S, Gruber DFet al., 2019, Publisher Correction: Deep Machine Learning Techniques for the Detection and Classification of Sperm Whale Bioacoustics., Sci Rep, Vol: 9

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Journal article

Wang Y, Sun Y, Liu Z, Sarma SE, Bronstein MM, Solomon JMet al., 2019, Dynamic Graph CNN for Learning on Point Clouds, ACM TRANSACTIONS ON GRAPHICS, Vol: 38, ISSN: 0730-0301

Journal article

Frasca F, Galeano D, Gonzalez G, Laponogov I, Veselkov K, Paccanaro A, Bronstein MMet al., 2019, Learning interpretable disease self-representations for drug repositioning, Publisher: arxiv

Drug repositioning is an attractive cost-efficient strategy for thedevelopment of treatments for human diseases. Here, we propose an interpretablemodel that learns disease self-representations for drug repositioning. Ourself-representation model represents each disease as a linear combination of afew other diseases. We enforce proximity in the learnt representations in a wayto preserve the geometric structure of the human phenome network - adomain-specific knowledge that naturally adds relational inductive bias to thedisease self-representations. We prove that our method is globally optimal andshow results outperforming state-of-the-art drug repositioning approaches. Wefurther show that the disease self-representations are biologicallyinterpretable.

Working paper

Bermant PC, Bronstein MM, Wood RJ, Gero S, Gruber DFet al., 2019, Deep Machine Learning Techniques for the Detection and Classification of Sperm Whale Bioacoustics., Sci Rep, Vol: 9

We implemented Machine Learning (ML) techniques to advance the study of sperm whale (Physeter macrocephalus) bioacoustics. This entailed employing Convolutional Neural Networks (CNNs) to construct an echolocation click detector designed to classify spectrograms generated from sperm whale acoustic data according to the presence or absence of a click. The click detector achieved 99.5% accuracy in classifying 650 spectrograms. The successful application of CNNs to clicks reveals the potential of future studies to train CNN-based architectures to extract finer-scale details from cetacean spectrograms. Long short-term memory and gated recurrent unit recurrent neural networks were trained to perform classification tasks, including (1) "coda type classification" where we obtained 97.5% accuracy in categorizing 23 coda types from a Dominica dataset containing 8,719 codas and 93.6% accuracy in categorizing 43 coda types from an Eastern Tropical Pacific (ETP) dataset with 16,995 codas; (2) "vocal clan classification" where we obtained 95.3% accuracy for two clan classes from Dominica and 93.1% for four ETP clan types; and (3) "individual whale identification" where we obtained 99.4% accuracy using two Dominica sperm whales. These results demonstrate the feasibility of applying ML to sperm whale bioacoustics and establish the validity of constructing neural networks to learn meaningful representations of whale vocalizations.

Journal article

Veselkov K, Gonzalez Pigorini G, Aljifri S, Galea D, Mirnezami R, Youssef J, Bronstein M, Laponogov Iet al., 2019, HyperFoods: Machine intelligent mapping of cancer-beating molecules in foods, Scientific Reports, Vol: 9, ISSN: 2045-2322

Recent data indicate that up-to 30–40% of cancers can be prevented by dietary and lifestyle measures alone. Herein, we introduce a unique network-based machine learning platform to identify putative food-based cancer-beating molecules. These have been identified through their molecular biological network commonality with clinically approved anti-cancer therapies. A machine-learning algorithm of random walks on graphs (operating within the supercomputing DreamLab platform) was used to simulate drug actions on human interactome networks to obtain genome-wide activity profiles of 1962 approved drugs (199 of which were classified as “anti-cancer” with their primary indications). A supervised approach was employed to predict cancer-beating molecules using these ‘learned’ interactome activity profiles. The validated model performance predicted anti-cancer therapeutics with classification accuracy of 84–90%. A comprehensive database of 7962 bioactive molecules within foods was fed into the model, which predicted 110 cancer-beating molecules (defined by anti-cancer drug likeness threshold of >70%) with expected capacity comparable to clinically approved anti-cancer drugs from a variety of chemical classes including flavonoids, terpenoids, and polyphenols. This in turn was used to construct a ‘food map’ with anti-cancer potential of each ingredient defined by the number of cancer-beating molecules found therein. Our analysis underpins the design of next-generation cancer preventative and therapeutic nutrition strategies.

Journal article

Cosmo L, Panine M, Rampini A, Ovsjanikov M, Bronstein MM, Rodola Ret al., 2019, Isospectralization, or how to hear shape, style, and correspondence, Pages: 7521-7530, ISSN: 1063-6919

© 2019 IEEE. 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.

Conference paper

Melzi S, Spezialetti R, Tombari F, Bronstein MM, Stefano LD, Rodola Eet al., 2019, Gframes: Gradient-based local reference frame for 3D shape matching, Pages: 4624-4633, ISSN: 1063-6919

© 2019 IEEE. We introduce GFrames, a novel local reference frame (LRF) construction for 3D meshes and point clouds. GFrames are based on the computation of the intrinsic gradient of a scalar field defined on top of the input shape. The resulting tangent vector field defines a repeatable tangent direction of the local frame at each point; importantly, it directly inherits the properties and invariance classes of the underlying scalar function, making it remarkably robust under strong sampling artifacts, vertex noise, as well as non-rigid deformations. Existing local descriptors can directly benefit from our repeatable frames, as we showcase in a selection of 3D vision and shape analysis applications where we demonstrate state-of-the-art performance in a variety of challenging settings.

Conference paper

Bronstein MV, Everaert J, Castro A, Joormann J, Cannon TDet al., 2019, Pathways to paranoia: Analytic thinking and belief flexibility., Behav Res Ther, Vol: 113, Pages: 18-24

Delusions have been repeatedly linked to reduced engagement in analytic (i.e., conscious and effortful) reasoning. However, the mechanisms underlying this relationship remain unclear. One hypothesis is that less analytic reasoning might maintain persecutory delusions by reducing belief flexibility. An important aspect of belief flexibility is the ability to revise beliefs in response to disconfirmatory evidence. The present study recruited 231 participants from the general population that represented a wide range of paranoid ideation. Participants completed tasks in which they encountered a series of ambiguous scenarios with initially-appealing explanations that were later disconfirmed by statements supporting alternative interpretations. Three types of scenarios were employed: two presented participants with emotionally valenced explanations (i.e., negative or positive) and one presented participants with emotionally neutral explanations. In each type of reasoning scenario, impaired belief revision ability was found to partially mediate the relationship between reduced engagement in analytic reasoning and persecutory ideation. These results are consistent with the notion that reduced engagement in analytic reasoning may help maintain paranoid delusions by interfering with the ability to revise beliefs in the presence of disconfirmatory information.

Journal article

Rodolà E, Lähner Z, Bronstein AM, Bronstein MM, Solomon Jet al., 2019, Functional Maps Representation On Product Manifolds, Computer Graphics Forum, ISSN: 0167-7055

© 2019 The Authors Computer Graphics Forum © 2019 The Eurographics Association and John Wiley & Sons Ltd. We consider the tasks of representing, analysing 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.

Journal article

Choma N, Monti F, Gerhardt L, Palczewski T, Ronaghi Z, Prabhat P, Bhimji W, Bronstein M, Klein S, Bruna Jet al., 2019, Graph Neural Networks for IceCube Signal Classification, Pages: 386-391

© 2018 IEEE. Tasks involving the analysis of geometric (graph-and manifold-structured) data have recently gained prominence in the machine learning community, giving birth to a rapidly developing field of geometric deep learning. In this work, we leverage graph neural networks to improve signal detection in the IceCube neutrino observatory. The IceCube detector array is modeled as a graph, where vertices are sensors and edges are a learned function of the sensors spatial coordinates. As only a subset of IceCubes sensors is active during a given observation, we note the adaptive nature of our GNN, wherein computation is restricted to the input signal support. We demonstrate the effectiveness of our GNN architecture on a task classifying IceCube events, where it outperforms both a traditional physics-based method as well as classical 3D convolution neural networks.

Conference paper

Bouritsas G, Bokhnyak S, Ploumpis S, Bronstein M, Zafeiriou Set al., 2019, Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation, 2019 IEEE/CVF INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV 2019), Pages: 7212-7221, ISSN: 1550-5499

Journal article

Dyke RM, Stride C, Lai YK, Rosin PL, Aubry M, Boyarski A, Bronstein AM, Bronstein MM, Cremers D, Fisher M, Groueix T, Guo D, Kim VG, Kimmel R, Lähner Z, Li K, Litany O, Remez T, Rodolà E, Russell BC, Sahillioglu Y, Slossberg R, Tam GKL, Vestner M, Wu Z, Yang Jet al., 2019, SHREC'19: Shape correspondence with isometric and non-isometric deformations, Pages: 111-119, ISSN: 1997-0463

© 2019 The Author(s) The registration of surfaces with non-rigid deformation, especially non-isometric deformations, is a challenging problem. When applying such techniques to real scans, the problem is compounded by topological and geometric inconsistencies between shapes. In this paper, we capture a benchmark dataset of scanned 3D shapes undergoing various controlled deformations (articulating, bending, stretching and topologically changing), along with ground truth correspondences. With the aid of this tiered benchmark of increasingly challenging real scans, we explore this problem and investigate how robust current state-of-the-art methods perform in different challenging registration and correspondence scenarios. We discover that changes in topology is a challenging problem for some methods and that machine learning-based approaches prove to be more capable of handling non-isometric deformations on shapes that are moderately similar to the training set.

Conference paper

Svoboda J, Masci J, Monti F, Bronstein MM, Guibas Let al., 2019, Peernets: Exploiting peer wisdom against adversarial attacks

© 7th International Conference on Learning Representations, ICLR 2019. All Rights Reserved. Deep learning systems have become ubiquitous in many aspects of our lives. Unfortunately, it has been shown that such systems are vulnerable to adversarial attacks, making them prone to potential unlawful uses. Designing deep neural networks that are robust to adversarial attacks is a fundamental step in making such systems safer and deployable in a broader variety of applications (e.g. autonomous driving), but more importantly is a necessary step to design novel and more advanced architectures built on new computational paradigms rather than marginally building on the existing ones. In this paper we introduce PeerNets, a novel family of convolutional networks alternating classical Euclidean convolutions with graph convolutions to harness information from a graph of peer samples. This results in a form of non-local forward propagation in the model, where latent features are conditioned on the global structure induced by the graph, that is up to 3× more robust to a variety of white- and black-box adversarial attacks compared to conventional architectures with almost no drop in accuracy.

Conference paper

Gong S, Chen L, Bronstein M, Zafeiriou Set al., 2019, SpiralNet plus plus : A Fast and Highly Efficient Mesh Convolution Operator, IEEE/CVF International Conference on Computer Vision (ICCV), Publisher: IEEE COMPUTER SOC, Pages: 4141-4148, ISSN: 2473-9936

Conference paper

Svoboda J, Masci J, Monti F, Bronstein MM, Guibas Let al., 2019, Peernets: Exploiting peer wisdom against adversarial attacks

© 7th International Conference on Learning Representations, ICLR 2019. All Rights Reserved. Deep learning systems have become ubiquitous in many aspects of our lives. Unfortunately, it has been shown that such systems are vulnerable to adversarial attacks, making them prone to potential unlawful uses. Designing deep neural networks that are robust to adversarial attacks is a fundamental step in making such systems safer and deployable in a broader variety of applications (e.g. autonomous driving), but more importantly is a necessary step to design novel and more advanced architectures built on new computational paradigms rather than marginally building on the existing ones. In this paper we introduce PeerNets, a novel family of convolutional networks alternating classical Euclidean convolutions with graph convolutions to harness information from a graph of peer samples. This results in a form of non-local forward propagation in the model, where latent features are conditioned on the global structure induced by the graph, that is up to 3× more robust to a variety of white- and black-box adversarial attacks compared to conventional architectures with almost no drop in accuracy.

Conference paper

Litany O, Bronstein A, Bronstein M, Makadia Aet al., 2018, Deformable Shape Completion with Graph Convolutional Autoencoders, Pages: 1886-1895, ISSN: 1063-6919

© 2018 IEEE. The availability of affordable and portable depth sensors has made scanning objects and people simpler than ever. However, dealing with occlusions and missing parts is still a significant challenge. The problem of reconstructing a (possibly non-rigidly moving) 3D object from a single or multiple partial scans has received increasing attention in recent years. In this work, we propose a novel learning-based method for the completion of partial shapes. Unlike the majority of existing approaches, our method focuses on objects that can undergo non-rigid deformations. The core of our method is a variational autoencoder with graph convolutional operations that learns a latent space for complete realistic shapes. At inference, we optimize to find the representation in this latent space that best fits the generated shape to the known partial input. The completed shape exhibits a realistic appearance on the unknown part. We show promising results towards the completion of synthetic and real scans of human body and face meshes exhibiting different styles of articulation and partiality.

Conference paper

Levie R, Monti F, Bresson X, Bronstein MMet al., 2018, CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters, IEEE Transactions on Signal Processing, Vol: 67, Pages: 97-109, ISSN: 1053-587X

© 1991-2012 IEEE. The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain convolutional architecture for deep learning on graphs. The core ingredient of our model is a new class of parametric rational complex functions (Cayley polynomials) allowing to efficiently compute spectral filters on graphs that specialize on frequency bands of interest. Our model generates rich spectral filters that are localized in space, scales linearly with the size of the input data for sparsely connected graphs, and can handle different constructions of Laplacian operators. Extensive experimental results show the superior performance of our approach, in comparison to other spectral domain convolutional architectures, on spectral image classification, community detection, vertex classification, and matrix completion tasks.

Journal article

Litany O, Rodolà E, Bronstein A, Bronstein M, Cremers Det al., 2018, Partial Single- and Multishape Dense Correspondence Using Functional Maps, Handbook of Numerical Analysis, Vol: 19, Pages: 55-90, ISSN: 1570-8659

© 2018 Elsevier B.V. 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 nonrigid deformations and only partial views are available, the problem becomes very challenging. In this chapter we describe recent techniques designed to tackle such problems. Specifically, we explain how the renown functional maps framework can be extended to tackle the partial setting. We then present a further extension to the multipart case in which one tries to establish correspondence between a collection of shapes. Finally, we focus on improving the technique efficiency, by disposing of its spatial ingredient and thus keeping the computation in the spectral domain. Extensive experimental results are provided along with the theoretical explanations, to demonstrate the effectiveness of the described methods in these challenging scenarios.

Journal article

Monti F, Bronstein MM, Bresson X, 2018, Deep geometric matrix completion: A new way for recommender systems, Pages: 6852-6856, ISSN: 1520-6149

© 2018 IEEE. In the last years, Graph Convolutional Neural Networks gained popularity in the Machine Learning community for their capability of extracting local compositional features on signals defined on non-Euclidean domains. Shape correspondence, document classification, molecular properties predictions are just few of the many different problems where these techniques have been successfully applied. In this paper we will present Deep Geometric Matrix Completion, a recent application of Graph Convolutional Neural Networks to the matrix completion problem. We will illustrate MGCNN (a multi-graph CNN able to deal with signals defined over multiple domains) and we will show how coupling such technique with a RNN, a learnable diffusion process can be realized for reconstructing the desired information. Extensive experimental evaluation shows how Geometric Deep Learning techniques allow to outperform previous state of the art solutions on the matrix completion problem.

Conference paper

Monti F, Otness K, Bronstein MM, 2018, MOTIFNET: A MOTIF-BASED GRAPH CONVOLUTIONAL NETWORK for DIRECTED GRAPHS, Pages: 225-228

© 2018 IEEE. Deep learning on graphs and in particular, graph convolutional neural networks, have recently attracted significant attention in the machine learning community. Many of such techniques explore the analogy between the graph Laplacian eigenvectors and the classical Fourier basis, allowing to formulate the convolution as a multiplication in the spectral domain. One of the key drawback of spectral CNNs is their explicit assumption of an undirected graph, leading to a symmetric Laplacian matrix with orthogonal eigendecomposition. In this work we propose MotifNet, a graph CNN capable of dealing with directed graphs by exploiting local graph motifs. We present experimental evidence showing the advantage of our approach on real data.

Conference paper

Wang L, Gehre A, Bronstein MM, Solomon Jet al., 2018, Kernel functional maps, Symposium on Geometry Processing, Publisher: Wiley, Pages: 27-36, ISSN: 0167-7055

Functional maps provide a means of extracting correspondences between surfaces using linear‐algebraic machinery. While the functional framework suggests efficient algorithms for map computation, the basic technique does not incorporate the intuition that pointwise modifications of a descriptor function (e.g. composition of a descriptor and a nonlinearity) should be preserved under the mapping; the end result is that the basic functional maps problem can be underdetermined without regularization or additional assumptions on the map. In this paper, we show how this problem can be addressed through kernelization , in which descriptors are lifted to higher‐dimensional vectors or even infinite‐length sequences of values. The key observation is that optimization problems for functional maps only depend on inner products between descriptors rather than descriptor values themselves. These inner products can be evaluated efficiently through use of kernel functions. In addition to deriving a kernelized version of functional maps including a recent extension in terms of pointwise multiplication operators, we provide an efficient conjugate gradient algorithm for optimizing our generalized problem as well as a strategy for low‐rank estimation of kernel matrices through the Nyström approximation.

Conference paper

Gehre A, Bronstein M, Kobbelt L, Solomon Jet al., 2018, Interactive curve constrained functional maps, Symposium on Geometry Processing, Publisher: Wiley, Pages: 1-12, ISSN: 0167-7055

Functional maps have gained popularity as a versatile framework for representing intrinsic correspondence between 3D shapes using algebraic machinery. A key ingredient for this framework is the ability to find pairs of corresponding functions (typically, feature descriptors) across the shapes. This is a challenging problem on its own, and when the shapes are strongly non‐isometric, nearly impossible to solve automatically. In this paper, we use feature curve correspondences to provide flexible abstractions of semantically similar parts of non‐isometric shapes. We design a user interface implementing an interactive process for constructing shape correspondence, allowing the user to update the functional map at interactive rates by introducing feature curve correspondences. We add feature curve preservation constraints to the functional map framework and propose an efficient numerical method to optimize the map with immediate feedback. Experimental results show that our approach establishes correspondences between geometrically diverse shapes with just a few clicks.

Conference paper

Melzi S, Rodolà E, Castellani U, Bronstein MMet al., 2018, Localized Manifold Harmonics for Spectral Shape Analysis, Computer Graphics Forum, Vol: 37, Pages: 20-34, ISSN: 0167-7055

© 2017 The Authors Computer Graphics Forum © 2017 The Eurographics Association and John Wiley & Sons Ltd. 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.

Journal article

Vestner M, Lahner Z, Boyarski A, Litany O, Slossberg R, Remez T, Rodola E, Bronstein A, Bronstein M, Kimmel R, Cremers Det al., 2018, Efficient deformable shape correspondence via kernel matching, Pages: 517-526

© 2017 IEEE. 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.

Conference paper

Gasparetto A, Cosmo L, Rodola E, Bronstein M, Torsello Aet al., 2018, Spatial Maps: From low rank spectral to sparse spatial functional representations, Pages: 477-485

© 2017 IEEE. Functional representation is a well-established approach to represent dense correspondences between deformable shapes. The approach provides an efficient low rank representation of a continuous mapping between two shapes, however under that framework the correspondences are only intrinsically captured, which implies that the induced map is not guaranteed to map the whole surface, much less to form a continuous mapping. In this work, we define a novel approach to the computation of a continuous bijective map between two surfaces moving from the low rank spectral representation to a sparse spatial representation. Key to this is the observation that continuity and smoothness of the optimal map induces structure both on the spectral and the spatial domain, the former providing effective low rank approximations, while the latter exhibiting strong sparsity and locality that can be used in the solution of large-scale problems. We cast our approach in terms of the functional transfer through a fuzzy map between shapes satisfying infinitesimal mass transportation at each point. The result is that, not only the spatial map induces a sub-vertex correspondence between the surfaces, but also the transportation of the whole surface, and thus the bijectivity of the induced map is assured. The performance of the proposed method is assessed on several popular benchmarks.

Conference paper

Nogneng D, Melzi S, Rodolá E, Castellani U, Bronstein M, Ovsjanikov Met al., 2018, Improved functional mappings via product preservation, Computer Graphics Forum: the international journal of the Eurographics Association, Vol: 37, Pages: 179-190, ISSN: 0167-7055

In this paper, we consider the problem of information transfer across shapes and propose an extension to the widely used functional map representation. Our main observation is that in addition to the vector space structure of the functional spaces, which has been heavily exploited in the functional map framework, the functional algebra (i.e., the ability to take pointwise products of functions) can significantly extend the power of this framework. Equipped with this observation, we show how to improve one of the key applications of functional maps, namely transferring real-valued functions without conversion to point-to-point correspondences. We demonstrate through extensive experiments that by decomposing a given function into a linear combination consisting not only of basis functions but also of their pointwise products, both the representation power and the quality of the function transfer can be improved significantly. Our modification, while computationally simple, allows us to achieve higher transfer accuracy while keeping the size of the basis and the functional map fixed. We also analyze the computational complexity of optimally representing functions through linear combinations of products in a given basis and prove NP-completeness in some general cases. Finally, we argue that the use of function products can have a wide-reaching effect in extending the power of functional maps in a variety of applications, in particular by enabling the transfer of highfrequency functions without changing the representation size or complexity.

Journal article

Svoboda J, Monti F, Bronstein MM, 2018, Generative convolutional networks for latent fingerprint reconstruction, Pages: 429-436

© 2017 IEEE. Performance of fingerprint recognition depends heavily on the extraction of minutiae points. Enhancement of the fingerprint ridge pattern is thus an essential pre-processing step that noticeably reduces false positive and negative detection rates. A particularly challenging setting is when the fingerprint images are corrupted or partially missing. In this work, we apply generative convolutional networks to denoise visible minutiae and predict the missing parts of the ridge pattern. The proposed enhancement approach is tested as a pre-processing step in combination with several standard feature extraction methods such as MINDTCT, followed by biometric comparison using MCC and BO-ZORTH3. We evaluate our method on several publicly available latent fingerprint datasets captured using different sensors.

Conference paper

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