Publications
263 results found
Masci J, Migliore D, Bronstein MM, et al., 2014, Descriptor learning for omnidirectional image matching, Studies in Computational Intelligence, Vol: 532, Pages: 49-62, ISSN: 1860-949X
Feature matching in omnidirectional vision systems is a challenging problem, mainly because complicated optical systems make the theoretical modelling of invariance and construction of invariant feature descriptors hard or even impossible. In this paper, we propose learning invariant descriptors using a training set of similar and dissimilar descriptor pairs.We use the similarity-preserving hashing framework, in which we are trying to map the descriptor data to the Hamming space preserving the descriptor similarity on the training set. A neural network is used to solve the underlying optimization problem. Our approach outperforms not only straightforward descriptor matching, but also state-of-the-art similarity-preserving hashing methods. © 2014 Springer-Verlag Berlin Heidelberg.
Masci J, Bronstein MM, Bronstein AM, et al., 2014, Multimodal similarity-preserving hashing, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 36, Pages: 824-830, ISSN: 0162-8828
We introduce an efficient computational framework for hashing data belonging to multiple modalities into a single representation space where they become mutually comparable. The proposed approach is based on a novel coupled siamese neural network architecture and allows unified treatment of intra-and inter-modality similarity learning. Unlike existing cross-modality similarity learning approaches, our hashing functions are not limited to binarized linear projections and can assume arbitrarily complex forms. We show experimentally that our method significantly outperforms state-of-the-art hashing approaches on multimedia retrieval tasks. © 2014 IEEE.
Litman R, Bronstein A, Bronstein M, et al., 2014, Supervised learning of bag-of-features shape descriptors using sparse coding, Computer Graphics Forum, Vol: 33, Pages: 127-136, ISSN: 0167-7055
We present a method for supervised learning of shape descriptors for shape retrieval applications. Many content-based shape retrieval approaches follow the bag-of-features (BoF) paradigm commonly used in text and image retrieval by first computing local shape descriptors, and then representing them in a 'geometric dictionary' using vector quantization. A major drawback of such approaches is that the dictionary is constructed in an unsupervised manner using clustering, unaware of the last stage of the process (pooling of the local descriptors into a BoF, and comparison of the latter using some metric). In this paper, we replace the clustering with dictionary learning, where every atom acts as a feature, followed by sparse coding and pooling to get the final BoF descriptor. Both the dictionary and the sparse codes can be learned in the supervised regime via bi-level optimization using a task-specific objective that promotes invariance desired in the specific application. We show significant performance improvement on several standard shape retrieval benchmarks. © 2014 The Eurographics Association and John Wiley & Sons Ltd.
Sprechmann P, Bronstein A, Bronstein M, et al., 2013, Learnable low rank sparse models for speech denoising, Pages: 136-140, ISSN: 1520-6149
In this paper we present a framework for real time enhancement of speech signals. Our method leverages a new process-centric approach for sparse and parsimonious models, where the representation pursuit is obtained applying a deterministic function or process rather than solving an optimization problem. We first propose a rank-regularized robust version of non-negative matrix factorization (NMF) for modeling time-frequency representations of speech signals in which the spectral frames are decomposed as sparse linear combinations of atoms of a low-rank dictionary. Then, a parametric family of pursuit processes is derived from the iteration of the proximal descent method for solving this model. We present several experiments showing successful results and the potential of the proposed framework. Incorporating discriminative learning makes the proposed method significantly outperform exact NMF algorithms, with fixed latency and at a fraction of it's computational complexity. © 2013 IEEE.
Glashoff K, Bronstein MM, 2013, Matrix commutators: Their asymptotic metric properties and relation to approximate joint diagonalization, Linear Algebra and Its Applications, Vol: 439, Pages: 2503-2513, ISSN: 0024-3795
We analyze the properties of the norm of the commutator of two Hermitian matrices, showing that asymptotically it behaves like a metric, and establish its relation to joint approximate diagonalization of matrices, showing that almost-commuting matrices are almost jointly diagonalizable, and vice versa. We show an application of our results in the field of 3D shape analysis. © 2013 Elsevier Inc.
Bronstein M, Geier M, 2013, Dynamic loading of aircraft structures Optimizing the design of structural elements, Pages: 1090-1103
The design and certification procedures of modern aircraft structures are usually based on static loading. Even dynamic loading conditions are usually treated as quasi-static conditions. Following the current design practice, the loads envelope, by which each aircraft structural element is sized, is considered as being statically applied. The primary objective of the DAEDALOS project is to investigate the dynamic effects on the actual loads acting on the airframe in order to improve the definition of the sizing loads for structural components of civil aircraft. The current work is focused on the different ways that dynamic loads can be applied to aircraft models and the effect on the resultant stress levels at different points on the structure. The results obtained using the dynamic loading procedures are compared to the results obtained using traditional static loading methods. The reduction in the stress levels at specific aircraft elements show the potential for new methods and procedures of loads calculations, which could lead to a more realistic sizing of critical elements of the aircraft structure.
Pokrass J, Bronstein AM, Bronstein MM, et al., 2013, Sparse Modeling of Intrinsic Correspondences, COMPUTER GRAPHICS FORUM, Vol: 32, Pages: 459-468, ISSN: 0167-7055
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- Citations: 68
Kovnatsky A, Bronstein MM, Bronstein AM, et al., 2013, Coupled quasi-harmonic bases, COMPUTER GRAPHICS FORUM, Vol: 32, Pages: 439-448, ISSN: 0167-7055
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- Citations: 110
Litman R, Bronstein AM, Bronstein MM, 2013, Stable semi-local features for non-rigid shapes, Mathematics and Visualization, Pages: 161-189, ISBN: 9783642543005
Feature-based analysis is becoming a very popular approach for geometric shape analysis. Following the success of this approach in image analysis, there is a growing interest in finding analogous methods in the 3D world. Maximally stable component detection is a low computation cost and high repeatability method for feature detection in images.In this study, a diffusion-geometry based framework for stable component detection is presented, which can be used for geometric feature detection in deformable shapes. The vast majority of studies of deformable 3D shapes models them as the two-dimensional boundary of the volume of the shape. Recent works have shown that a volumetric shape model is advantageous in numerous ways as it better captures the natural behavior of non-rigid deformations. We show that our framework easily adapts to this volumetric approach, and even demonstrates superior performance. A quantitative evaluation of our methods on the SHREC’10 and SHREC’11 feature detection benchmarks as well as qualitative tests on the SCAPE dataset show its potential as a source of high-quality features. Examples demonstrating the drawbacks of surface stable components and the advantage of their volumetric counterparts are also presented.
Rosman G, Bronstein MM, Bronstein AM, et al., 2013, Group-valued regularization for motion segmentation of articulated shapes, Mathematics and Visualization, Pages: 263-281, ISBN: 9783642543005
Motion-based segmentation is an important tool for the analysis of articulated shapes. As such, it plays an important role in mechanical engineering, computer graphics, and computer vision. In this chapter, we study motion-based segmentation of 3D articulated shapes. We formulate motion-based surface segmentation as a piecewise-smooth regularization problem for the transformations between several poses. Using Lie-group representation for the transformation at each surface point, we obtain a simple regularized fitting problem. An Ambrosio-Tortorelli scheme of a generalized Mumford-Shah model gives us the segmentation functional without assuming prior knowledge on the number of parts or even the articulated nature of the object. Experiments on several standard datasets compare the results of the proposed method to state-of-the-art algorithms.
Pokrass J, Bronstein AM, Bronstein MM, 2013, Partial shape matching without point-wise correspondence, Numerical Mathematics, Vol: 6, Pages: 223-244, ISSN: 1004-8979
Partial similarity of shapes is a challenging problem arising in many important applications in computer vision, shape analysis, and graphics, e.g. when one has to deal with partial information and acquisition artifacts. The problem is especially hard when the underlying shapes are non-rigid and are given up to a deformation. Partial matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two, taking into account possibly different parts. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes, and present experiments demonstrating the success of the proposed method. © 2013 Global-Science Press.
Kovnatsky A, Raviv D, Bronstein MM, et al., 2013, Geometric and photometric data fusion in non-rigid shape analysis, Numerical Mathematics, Vol: 6, Pages: 199-222, ISSN: 1004-8979
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local and global shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail. © 2013 Global-Science Press.
Rosman G, Bronstein AM, Bronstein MM, et al., 2012, Articulated motion segmentation of point clouds by group-valued regularization, Pages: 77-84, ISSN: 1997-0463
Motion segmentation for articulated objects is an important topic of research. Yet such a segmentation should be as free as possible from underlying assumptions so as to fit general scenes and objects. In this paper we demonstrate an algorithm for articulated motion segmentation of 3D point clouds, free of any assumptions on the underlying model and yet firmly set in a well-defined variational framework. Results on scanned images show the generality of the proposed technique and its robustness to scanning artifacts and noise. © The Eurographics Association 2012.
Kovnatsky A, Bronstein MM, Bronstein AM, et al., 2012, Affine-invariant photometric heat kernel signatures, Pages: 39-46, ISSN: 1997-0463
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local shape descriptors. Our construction is based on the definition of a modified metric, which combines geometric and photometric information, and then the diffusion process on the shape manifold is simulated. Experimental results show that such data fusion is useful in coping with shape retrieval experiments, where pure geometric and pure photometric methods fail. Apart from retrieval task the proposed diffusion process may be employed in other applications. © The Eurographics Association 2012.
Glashoff K, Bronstein MM, 2012, Structure from motion using augmented Lagrangian robust factorization, Pages: 379-386
The classical Tomasi-Kanade method for Structure from Motion (SfM) based on measurement matrix factorization using SVD is known to perform poorly in the presence of occlusions and outliers. In this paper, we present an efficient approach by which we are able to deal with both problems at the same time. We use the Augmented Lagrangian alternative minimization method to solve iteratively a robust version of the matrix factorization approach. Experiments on synthetic and real data show the computational efficiency and good convergence of the method, which make it favorably compare to other approaches used in the SfM problem. © 2012 IEEE.
Raviv D, Bronstein AM, Bronstein MM, et al., 2012, Equi-affine invariant geometries of articulated objects, Pages: 177-190, ISSN: 0302-9743
We introduce an (equi-)affine invariant geometric structure by which surfaces that go through squeeze and shear transformations can still be properly analyzed. The definition of an affine invariant metric enables us to evaluate a new form of geodesic distances and to construct an invariant Laplacian from which local and global diffusion geometry is constructed. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis. © 2012 Springer-Verlag.
Bronstein M, 2012, Flight test loads validation on a modern super mid-size business jet, Pages: 285-307
This paper presents the process of the Loads Validation Flight Tests performed at IAI for the G280 super mid-size business jet. The G280 is the latest business jet developed in IAI and although it is based on the fuselage of its predecessor, the G200, it features a totally new wing, empennage, more powerful engines and state of the art fly-by-wire systems integrated into the aircraft flight control system. The Loads Validation Flight Test program is used to verify the data and methods used for Loads Analysis and is part of the Loads Substantiation program of any newly developed aircraft. Although large efforts are made to maximize the accuracy of the different type of loads analyses, current airworthiness regulations require that loads for new aircraft models be validated by means of flight tests. The Loads Validation Test Program performed for the G280 was unprecedented in IAI due to the scope of the measurements and the complexity of the dedicated calibration test performed on prototype s/n 2002. During the G280 Flight test campaign, 401 exercises were dedicated to Loads Validation. These exercises were completed in 33 flight tests, mostly of prototype 2002 during the period of October 2010 to January 2011. This paper will present the different phases of the Loads Validation program, including definition of measured loads, instrumentation, calibration of the instrumentation, flight conditions, examples of results for the various load types measured and conclusions regarding the validity of the methods and data used in the Loads Analyses.
Kokkinos I, Bronstein MM, Litman R, et al., 2012, Intrinsic shape context descriptors for deformable shapes, Pages: 159-166, ISSN: 1063-6919
In this work, we present intrinsic shape context (ISC) descriptors for 3D shapes. We generalize to surfaces the polar sampling of the image domain used in shape contexts: for this purpose, we chart the surface by shooting geodesic outwards from the point being analyzed; angle is treated as tantamount to geodesic shooting direction, and radius as geodesic distance. To deal with orientation ambiguity, we exploit properties of the Fourier transform. Our charting method is intrinsic, i.e., invariant to isometric shape transformations. The resulting descriptor is a meta-descriptor that can be applied to any photometric or geometric property field defined on the shape, in particular, we can leverage recent developments in intrinsic shape analysis and construct ISC based on state-of-the-art dense shape descriptors such as heat kernel signatures. Our experiments demonstrate a notable improvement in shape matching on standard benchmarks. © 2012 IEEE.
Litman R, Bronstein AM, Bronstein MM, 2012, Stable volumetric features in deformable shapes, Publisher: PERGAMON-ELSEVIER SCIENCE LTD, Pages: 569-576, ISSN: 0097-8493
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- Citations: 12
Marras S, Bronstein MM, Hormann K, et al., 2012, Motion-based mesh segmentation using augmented silhouettes, Pages: 164-172, ISSN: 1524-0703
Motion-based segmentation, the problem of detecting rigid parts of an articulated three-dimensional shape, is an open challenge that has several applications in mesh animation, compression, and interpolation. We present a novel approach that uses the visual perception of the shape and its motion to distinguish the rigid from the deformable parts of the object. Using two-dimensional projections of the different shape poses with respect to a number of different view points, we derive a set of one-dimensional curves, which form a superset of the mesh silhouettes. Analysing these augmented silhouettes, we identify the vertices of the mesh that correspond to the deformable parts, and a subsequent clustering approach, which is based on the diffusion distance, yields a motion-based segmentation of the shape. © 2012 Elsevier Inc. All rights reserved.
Pokrass J, Bronstein AM, Bronstein MM, 2012, A correspondence-less approach to matching of deformable shapes, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol: 6667 LNCS, Pages: 592-603, ISSN: 0302-9743
Finding a match between partially available deformable shapes is a challenging problem with numerous applications. The problem is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise correspondence between the two. In this paper, we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid deformation. We use diffusion geometric descriptors and optimize over the integration domains on which the integral descriptors of the two parts match. The problem is regularized using the Mumford-Shah functional. We show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular meshes. Experiments demonstrating the success of the proposed method are presented. © 2012 Springer-Verlag.
Wang C, Bronstein MM, Bronstein AM, et al., 2012, Discrete minimum distortion correspondence problems for non-rigid shape matching, Pages: 580-591, ISSN: 0302-9743
Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in computer vision and pattern recognition. Many methods for shape similarity and correspondence boil down to the minimum-distortion correspondence problem, in which two shapes are endowed with certain structure, and one attempts to find the matching with smallest structure distortion between them. Defining structures invariant to some class of shape transformations results in an invariant minimum-distortion correspondence or similarity. In this paper, we model shapes using local and global structures, formulate the invariant correspondence problem as binary graph labeling, and show how different choice of structure results in invariance under various classes of deformations. © 2012 Springer-Verlag.
Rosman G, Bronstein MM, Bronstein AM, et al., 2012, Group-valued regularization framework for motion segmentation of dynamic non-rigid shapes, Pages: 725-736, ISSN: 0302-9743
Understanding of articulated shape motion plays an important role in many applications in the mechanical engineering, movie industry, graphics, and vision communities. In this paper, we study motion-based segmentation of articulated 3D shapes into rigid parts. We pose the problem as finding a group-valued map between the shapes describing the motion, forcing it to favor piecewise rigid motions. Our computation follows the spirit of the Ambrosio-Tortorelli scheme for Mumford-Shah segmentation, with a diffusion component suited for the group nature of the motion model. Experimental results demonstrate the effectiveness of the proposed method in non-rigid motion segmentation. © 2012 Springer-Verlag.
Kovnatsky A, Bronstein MM, Bronstein AM, et al., 2012, Photometric heat kernel signatures, Pages: 616-627, ISSN: 0302-9743
In this paper, we explore the use of the diffusion geometry framework for the fusion of geometric and photometric information in local heat kernel signature shape descriptors. Our construction is based on the definition of a diffusion process on the shape manifold embedded into a high-dimensional space where the embedding coordinates represent the photometric information. Experimental results show that such data fusion is useful in coping with different challenges of shape analysis where pure geometric and pure photometric methods fail. © 2012 Springer-Verlag.
Bruckstein AM, Romeny BTH, Bronstein AM, et al., 2012, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics): Preface, ISBN: 9783642247842
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- Citations: 1
Aflalo Y, Bronstein AM, Bronstein MM, et al., 2012, Deformable shape retrieval by learning diffusion kernels, Pages: 689-700, ISSN: 0302-9743
In classical signal processing, it is common to analyze and process signals in the frequency domain, by representing the signal in the Fourier basis, and filtering it by applying a transfer function on the Fourier coefficients. In some applications, it is possible to design an optimal filter. A classical example is the Wiener filter that achieves a minimum mean squared error estimate for signal denoising. Here, we adopt similar concepts to construct optimal diffusion geometric shape descriptors. The analogy of Fourier basis are the eigenfunctions of the Laplace-Beltrami operator, in which many geometric constructions such as diffusion metrics, can be represented. By designing a filter of the Laplace-Beltrami eigenvalues, it is theoretically possible to achieve invariance to different shape transformations, like scaling. Given a set of shape classes with different transformations, we learn the optimal filter by minimizing the ratio between knowingly similar and knowingly dissimilar diffusion distances it induces. The output of the proposed framework is a filter that is optimally tuned to handle transformations that characterize the training set. © 2012 Springer-Verlag.
Hooda A, Bronstein MM, Bronstein AM, et al., 2012, Shape palindromes: Analysis of intrinsic symmetries in 2D articulated shapes, Pages: 665-676, ISSN: 0302-9743
Analysis of intrinsic symmetries of non-rigid and articulated shapes is an important problem in pattern recognition with numerous applications ranging from medicine to computational aesthetics. Considering articulated planar shapes as closed curves, we show how to represent their extrinsic and intrinsic symmetries as self-similarities of local descriptor sequences, which in turn have simple interpretation in the frequency domain. The problem of symmetry detection and analysis thus boils down to analysis of descriptor sequence patterns. For that purpose, we show two efficient computational methods: one based on Fourier analysis, and another on dynamic programming. © 2012 Springer-Verlag.
Strecha C, Bronstein AM, Bronstein MM, et al., 2012, LDAHash: Improved matching with smaller descriptors, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol: 34, Pages: 66-78, ISSN: 0162-8828
SIFT-like local feature descriptors are ubiquitously employed in computer vision applications such as content-based retrieval, video analysis, copy detection, object recognition, photo tourism, and 3D reconstruction. Feature descriptors can be designed to be invariant to certain classes of photometric and geometric transformations, in particular, affine and intensity scale transformations. However, real transformations that an image can undergo can only be approximately modeled in this way, and thus most descriptors are only approximately invariant in practice. Second, descriptors are usually high dimensional (e.g., SIFT is represented as a 128-dimensional vector). In large-scale retrieval and matching problems, this can pose challenges in storing and retrieving descriptor data. We map the descriptor vectors into the Hamming space in which the Hamming metric is used to compare the resulting representations. This way, we reduce the size of the descriptors by representing them as short binary strings and learn descriptor invariance from examples. We show extensive experimental validation, demonstrating the advantage of the proposed approach. © 2012 IEEE.
Litany O, Bronstein AM, Bronstein MM, 2012, Putting the pieces together: Regularized multi-part shape matching, Pages: 1-11, ISSN: 0302-9743
Multi-part shape matching is an important class of problems, arising in many fields such as computational archaeology, biology, geometry processing, computer graphics and vision. In this paper, we address the problem of simultaneous matching and segmentation of multiple shapes. We assume to be given a reference shape and multiple parts partially matching the reference. Each of these parts can have additional clutter, have overlap with other parts, or there might be missing parts. We show experimental results of efficient and accurate assembly of fractured synthetic and real objects. © 2012 Springer-Verlag.
Rosman G, Bronstein AM, Bronstein MM, et al., 2012, Group-valued regularization for analysis of articulated motion, Pages: 52-62, ISSN: 0302-9743
We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector- and matrix- valued functions on parametric surfaces. We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners. © 2012 Springer-Verlag.
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