207 results found
Bronstein AM, Bronstein MM, Zibulevsky M, et al., 2003, Optimal nonlinear line-of-flight estimation in positron emission tomography, IEEE TRANSACTIONS ON NUCLEAR SCIENCE, Vol: 50, Pages: 421-426, ISSN: 0018-9499
Bronstein AM, Bronstein MM, Zibulevsky M, et al., 2003, Separation of reflections via sparse ICA, Wavelets - Applications in Signal and Image Processing X Conference, Publisher: SPIE-INT SOC OPTICAL ENGINEERING, Pages: 292-296, ISSN: 0277-786X
Bronstein AM, Bronstein MM, Kimmel R, 2003, Expression-invariant 3D face recognition, 4th International Conference on Audio- and Video-Based Biometric Person Authentication, Publisher: SPRINGER-VERLAG BERLIN, Pages: 62-69, ISSN: 0302-9743
Bronstein MM, Bronstein AM, Zibulevsky M, et al., 2003, Separation of reflections via sparse ICA, IEEE International Conference on Image Processing, Publisher: IEEE, Pages: 313-316, ISSN: 1522-4880
Bronstein AM, Bronstein MM, Zibulevsky M, et al., 2003, Separation of semireflective layers using Sparse ICA, IEEE International Conference on Acoustics, Speech, and Signal Processing, Publisher: IEEE, Pages: 733-736
Bronstein MM, Bronstein AM, 2002, Biometrics was no match for hair-raising tricks, NATURE, Vol: 420, Pages: 739-739, ISSN: 0028-0836
Bronstein MM, Bronstein AM, Zibulevsky M, et al., 2002, Reconstruction in diffraction ultrasound tomography using nonuniform FFT, IEEE TRANSACTIONS ON MEDICAL IMAGING, Vol: 21, Pages: 1395-1401, ISSN: 0278-0062
Bronstein MM, Bronstein AM, Zibulevsky M, et al., 2002, Application of the NUFFT for reconstruction problems in diffraction tomography, 22nd Convention of Electrical and Electronics Engineers in Israel, Publisher: IEEE, Pages: 345-347
Bronstein M, Bronstein A, Zibulevsky M, 2002, Iterative reconstruction in diffraction tomography using non-uniform fast fourier transform, IEEE International Symposium on Biomedical Imaging, Publisher: IEEE, Pages: 633-636
Bronstein AM, Bronstein MM, Zibulevsky M, et al., 2002, Optimal non-linear line-of-flight estimation in positron emission tomography, 22nd Convention of Electrical and Electronics Engineers in Israel, Publisher: IEEE, Pages: 341-344
Bronstein A, Bronstein M, Zibulevsky M, et al., 2002, Optimal nonlinear estimation of photon coordinates in PET, IEEE International Symposium on Biomedical Imaging, Publisher: IEEE, Pages: 541-544
Glashoff K, Bronstein MM, Optimization on the biorthogonal manifold
In this paper, we consider optimization problems w.r.t. to pairs oforthogonal matrices $XY = I$. Problems of this form arise in severalapplications such as finding shape correspondence in computer graphics. We showthat the space of such matrices is a Riemannian manifold, which we call thebiorthogonal manifold. To our knowledge, this manifold has not been studiedbefore. We give expressions of tangent space projection, exponential map, andretraction operators of the biorthogonal manifold, and discuss their numericalimplementation.
Monti F, Shchur O, Bojchevski A, et al., Dual-Primal Graph Convolutional Networks
In recent years, there has been a surge of interest in developing deeplearning methods for non-Euclidean structured data such as graphs. In thispaper, we propose Dual-Primal Graph CNN, a graph convolutional architecturethat alternates convolution-like operations on the graph and its dual. Ourapproach allows to learn both vertex- and edge features and generalizes theprevious graph attention (GAT) model. We provide extensive experimentalvalidation showing state-of-the-art results on a variety of tasks tested onestablished graph benchmarks, including CORA and Citeseer citation networks aswell as MovieLens, Flixter, Douban and Yahoo Music graph-guided recommendersystems.
Eynard D, Kovnatsky A, Bronstein MM, Structure-preserving color transformations using Laplacian commutativity
Mappings between color spaces are ubiquitous in image processing problemssuch as gamut mapping, decolorization, and image optimization for color-blindpeople. Simple color transformations often result in information loss andambiguities (for example, when mapping from RGB to grayscale), and one wishesto find an image-specific transformation that would preserve as much aspossible the structure of the original image in the target color space. In thispaper, we propose Laplacian colormaps, a generic framework forstructure-preserving color transformations between images. We use the imageLaplacian to capture the structural information, and show that if the colortransformation between two images preserves the structure, the respectiveLaplacians have similar eigenvectors, or in other words, are approximatelyjointly diagonalizable. Employing the relation between joint diagonalizabilityand commutativity of matrices, we use Laplacians commutativity as a criterionof color mapping quality and minimize it w.r.t. the parameters of a colortransformation to achieve optimal structure preservation. We show numerousapplications of our approach, including color-to-gray conversion, gamutmapping, multispectral image fusion, and image optimization for color deficientviewers.
Bronstein MM, Glashoff K, Loring TA, Making Laplacians commute
In this paper, we construct multimodal spectral geometry by finding a pair ofclosest commuting operators (CCO) to a given pair of Laplacians. The CCOs arejointly diagonalizable and hence have the same eigenbasis. Our constructionnaturally extends classical data analysis tools based on spectral geometry,such as diffusion maps and spectral clustering. We provide several syntheticand real examples of applications in dimensionality reduction, shape analysis,and clustering, demonstrating that our method better captures the inherentstructure of multi-modal data.
Glashoff K, Bronstein MM, Asymptotic metrics on the space of matrices under the commutation relation
We show that the norm of the commutator defines "almost a metric" on thequotient space of commuting matrices, in the sense that it is a semi-metricsatisfying the triangle inequality asymptotically for large matrices drawn froma "good" distribution.
Glashoff K, Bronstein MM, Almost-commuting matrices are almost jointly diagonalizable
We study the relation between approximate joint diagonalization ofself-adjoint matrices and the norm of their commutator, and show that almostcommuting self-adjoint matrices are almost jointly diagonalizable by a unitarymatrix.
Sprechmann P, Bronstein AM, Sapiro G, Learning Robust Low-Rank Representations
In this paper we present a comprehensive framework for learning robustlow-rank representations by combining and extending recent ideas for learningfast sparse coding regressors with structured non-convex optimizationtechniques. This approach connects robust principal component analysis (RPCA)with dictionary learning techniques and allows its approximation via trainableencoders. We propose an efficient feed-forward architecture derived from anoptimization algorithm designed to exactly solve robust low dimensionalprojections. This architecture, in combination with different trainingobjective functions, allows the regressors to be used as online approximants ofthe exact offline RPCA problem or as RPCA-based neural networks. Simplemodifications of these encoders can handle challenging extensions, such as theinclusion of geometric data transformations. We present several examples withreal data from image, audio, and video processing. When used to approximateRPCA, our basic implementation shows several orders of magnitude speedupcompared to the exact solvers with almost no performance degradation. We showthe strength of the inclusion of learning to the RPCA approach on a musicsource separation application, where the encoders outperform the exact RPCAalgorithms, which are already reported to produce state-of-the-art results on abenchmark database. Our preliminary implementation on an iPad showsfaster-than-real-time performance with minimal latency.
Eynard D, Glashoff K, Bronstein MM, et al., Multimodal diffusion geometry by joint diagonalization of Laplacians
We construct an extension of diffusion geometry to multiple modalitiesthrough joint approximate diagonalization of Laplacian matrices. This naturallyextends classical data analysis tools based on spectral geometry, such asdiffusion maps and spectral clustering. We provide several synthetic and realexamples of manifold learning, retrieval, and clustering demonstrating that thejoint diffusion geometry frequently better captures the inherent structure ofmulti-modal data. We also show that many previous attempts to constructmultimodal spectral clustering can be seen as particular cases of jointapproximate diagonalization of the Laplacians.
Bronstein MM, Multimodal diff-hash
Many applications require comparing multimodal data with different structureand dimensionality that cannot be compared directly. Recently, there has beenincreasing interest in methods for learning and efficiently representing suchmultimodal similarity. In this paper, we present a simple algorithm formultimodal similarity-preserving hashing, trying to map multimodal data intothe Hamming space while preserving the intra- and inter-modal similarities. Weshow that our method significantly outperforms the state-of-the-art method inthe field.
Bronstein MM, Kernel diff-hash
This paper presents a kernel formulation of the recently introduced diff-hashalgorithm for the construction of similarity-sensitive hash functions. Ourkernel diff-hash algorithm that shows superior performance on the problem ofimage feature descriptor matching.
Bronstein AM, Spectral descriptors for deformable shapes
Informative and discriminative feature descriptors play a fundamental role indeformable shape analysis. For example, they have been successfully employed incorrespondence, registration, and retrieval tasks. In the recent years,significant attention has been devoted to descriptors obtained from thespectral decomposition of the Laplace-Beltrami operator associated with theshape. Notable examples in this family are the heat kernel signature (HKS) andthe wave kernel signature (WKS). Laplacian-based descriptors achievestate-of-the-art performance in numerous shape analysis tasks; they arecomputationally efficient, isometry-invariant by construction, and cangracefully cope with a variety of transformations. In this paper, we formulatea generic family of parametric spectral descriptors. We argue that in order tobe optimal for a specific task, the descriptor should take into account thestatistics of the corpus of shapes to which it is applied (the "signal") andthose of the class of transformations to which it is made insensitive (the"noise"). While such statistics are hard to model axiomatically, they can belearned from examples. Following the spirit of the Wiener filter in signalprocessing, we show a learning scheme for the construction of optimal spectraldescriptors and relate it to Mahalanobis metric learning. The superiority ofthe proposed approach is demonstrated on the SHREC'10 benchmark.
Kovnatsky A, Bronstein MM, Bronstein AM, et al., Diffusion framework for geometric and photometric data fusion in non-rigid shape analysis
In this paper, we explore the use of the diffusion geometry framework for thefusion of geometric and photometric information in local and global shapedescriptors. Our construction is based on the definition of a diffusion processon the shape manifold embedded into a high-dimensional space where theembedding coordinates represent the photometric information. Experimentalresults show that such data fusion is useful in coping with differentchallenges of shape analysis where pure geometric and pure photometric methodsfail.
Bronstein AM, Bronstein MM, Kimmel R, The Video Genome
Fast evolution of Internet technologies has led to an explosive growth ofvideo data available in the public domain and created unprecedented challengesin the analysis, organization, management, and control of such content. Theproblems encountered in video analysis such as identifying a video in a largedatabase (e.g. detecting pirated content in YouTube), putting together videofragments, finding similarities and common ancestry between different versionsof a video, have analogous counterpart problems in genetic research andanalysis of DNA and protein sequences. In this paper, we exploit the analogybetween genetic sequences and videos and propose an approach to video analysismotivated by genomic research. Representing video information as video DNAsequences and applying bioinformatic algorithms allows to search, match, andcompare videos in large-scale databases. We show an application forcontent-based metadata mapping between versions of annotated video.
Gong S, Bahri M, Bronstein MM, et al., Geometrically Principled Connections in Graph Neural Networks
Graph convolution operators bring the advantages of deep learning to avariety of graph and mesh processing tasks previously deemed out of reach. Withtheir continued success comes the desire to design more powerful architectures,often by adapting existing deep learning techniques to non-Euclidean data. Inthis paper, we argue geometry should remain the primary driving force behindinnovation in the emerging field of geometric deep learning. We relate graphneural networks to widely successful computer graphics and data approximationmodels: radial basis functions (RBFs). We conjecture that, like RBFs, graphconvolution layers would benefit from the addition of simple functions to thepowerful convolution kernels. We introduce affine skip connections, a novelbuilding block formed by combining a fully connected layer with any graphconvolution operator. We experimentally demonstrate the effectiveness of ourtechnique and show the improved performance is the consequence of more than theincreased number of parameters. Operators equipped with the affine skipconnection markedly outperform their base performance on every task weevaluated, i.e., shape reconstruction, dense shape correspondence, and graphclassification. We hope our simple and effective approach will serve as a solidbaseline and help ease future research in graph neural networks.
Kulon D, Güler RA, Kokkinos I, et al., Weakly-Supervised Mesh-Convolutional Hand Reconstruction in the Wild
We introduce a simple and effective network architecture for monocular 3Dhand pose estimation consisting of an image encoder followed by a meshconvolutional decoder that is trained through a direct 3D hand meshreconstruction loss. We train our network by gathering a large-scale dataset ofhand action in YouTube videos and use it as a source of weak supervision. Ourweakly-supervised mesh convolutions-based system largely outperformsstate-of-the-art methods, even halving the errors on the in the wild benchmark.The dataset and additional resources are available athttps://arielai.com/mesh_hands.
Bronstein MM, Glashoff K, Heat kernel coupling for multiple graph analysis
In this paper, we introduce heat kernel coupling (HKC) as a method ofconstructing multimodal spectral geometry on weighted graphs of different sizewithout vertex-wise bijective correspondence. We show that Laplacian averagingcan be derived as a limit case of HKC, and demonstrate its applications onseveral problems from the manifold learning and pattern recognition domain.
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