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O. Litany, A. M. Bronstein, M. M. Bronstein, A. Makadia,
"Deformable shape completion with graph convolutional autoencoders",
Proc. Computer Vision and Pattern Recognition (CVPR), 2018. Abstract: 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. |
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F. Monti, M. M. Bronstein, X. Bresson,
"Geometric matrix completion with recurrent multi-graph neural networks",
Proc. Neural Information Processing Systems (NIPS), 2017. Abstract: Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local stationarity structures of user/item graphs, and the number of parameters to learn is linear w.r.t. the number of users and items. We propose a novel approach to overcome these limitations by using geometric deep learning on graphs. Our matrix completion architecture combines graph convolutional neural networks and recurrent neural networks to learn meaningful statistical graph-structured patterns and the non-linear diffusion process that generates the known ratings. This neural network system requires a constant number of parameters independent of the matrix size. We apply our method on both synthetic and real datasets, showing that it outperforms state-of-the-art techniques. |
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O. Litany, T. Remez, E. Rodolà, A. M. Bronstein, M. M. Bronstein,
"Deep functional maps: Structured prediction for dense shape correspondence",
Proc. Int. Conf. Computer Vision (ICCV), 2017. Abstract: We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality. Code |
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Z. Lähner, M. Vestner, A. Boyarski, O. Litany, R. Slossberg, T. Remez, E. Rodolà, A. M. Bronstein, M. M. Bronstein, R. Kimmel, D. Cremers,
"Efficient deformable shape correspondence via kernel matching",
Proc. Int. Conf. 3D Vision (3DV), 2017. Abstract: 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. Code |
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A. Gasparetto, L. Cosmo, E. Rodolà, A. Torsello, M. M. Bronstein,
"Spatial Maps: From low rank spectral to sparse spatial functional representations",
Proc. Int. Conf. 3D Vision (3DV), 2017. Abstract: 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. |
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J. Svoboda, F. Monti, M. M. Bronstein,
"Generative convolutional networks for latent fingerprint reconstruction",
Proc. Int. Joint Conf. Biometrics (IJCB), 2017. Abstract: 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 BOZORTH3. We evaluate our method on several publicly available latent fingerprint datasets captured using different sensors. |
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F. Monti, D. Boscaini, J. Masci, E. Rodolà, J. Svoboda, M. M. Bronstein,
"Geometric deep learning on graphs and manifolds using mixture model CNNs",
Proc. Computer Vision and Pattern Recognition (CVPR), 2017. Oral Abstract: Deep learning has achieved a remarkable performance breakthrough in several fields, most notably in speech recognition, natural language processing, and computer vision. In particular, convolutional neural network (CNN) architectures currently produce state-of-the-art performance on a variety of image analysis tasks such as object detection and recognition. Most of deep learning research has so far focused on dealing with 1D, 2D, or 3D Euclidean-structured data such as acoustic signals, images, or videos. Recently, there has been an increasing interest in geometric deep learning, attempting to generalize deep learning methods to non-Euclidean structured data such as graphs and manifolds, with a variety of applications from the domains of network analysis, computational social science, or computer graphics. In this paper, we propose a unified framework allowing to generalize CNN architectures to non-Euclidean domains (graphs and manifolds) and learn local, stationary, and compositional task-specific features. We show that various non-Euclidean CNN methods previously proposed in the literature can be considered as particular instances of our framework. We test the proposed method on standard tasks from the realms of image-, graph- and 3D shape analysis and show that it consistently outperforms previous approaches. |
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A. Boyarski, A. M. Bronstein, M. M. Bronstein,
"Subspace least squares multidimensional scaling",
Proc. Scale Space and Variational Methods (SSVM), 2017. Abstract: Multidimensional Scaling (MDS) is one of the most popular methods for dimensionality reduction and visualization of high dimensional data. Apart from these tasks, it also found applications in the field of geometry processing for the analysis and reconstruction of non-rigid shapes. In this regard, MDS can be thought of as a shape from metric algorithm, consisting of finding a configuration of points in the Euclidean space that realize, as isometrically as possible, some given distance structure. In the present work we cast the least squares variant of MDS (LS-MDS) in the spectral domain. This uncovers a multiresolution property of distance scaling which speeds up the optimization by a significant amount, while producing comparable, and sometimes even better, embeddings. |
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E. Rodolà, L. Cosmo, O. Litany, M. M. Bronstein, A. M. Bronstein,
N. Audebert, A. Ben Hamza, A. Boulch, U. Castellani, M. N. Do, A.-D. Duong, T. Furuya, A. Gasparetto, Y. Hong, J. Kim,
B. Le Saux, R. Litman, M. Masoumi, G. Minello, H-D. Nguyen, V.-T. Nguyen, R. Ohbuchi, V.-K. Pham, T. V. Phan,
M. Rezaei, A. Torsello, M-T. Tran, Q-T. Tran, B. Truong, L. Wan, C. Zou
"SHREC'17: Deformable shape retrieval with missing parts",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2017. Abstract: Partial similarity problems arise in numerous applications that involve real data acquisition by 3D sensors, inevitably leading to missing parts due to occlusions and partial views. In this setting, the shapes to be retrieved may undergo a variety of transformations simultaneously, such as non-rigid deformations (changes in pose), topological noise, and missing parts - a combination of nuisance factors that renders the retrieval process extremely challenging. With this benchmark, we aim to evaluate the state of the art in deformable shape retrieval under such kind of transformations. The benchmark is organized in two sub-challenges exemplifying different data modalities (3D vs. 2.5D). A total of 15 retrieval algorithms were evaluated in the contest; this paper presents the details of the dataset, and shows thorough comparisons among all competing methods. |
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D. Boscaini, J. Masci, E. Rodolà, M. M. Bronstein,
"Learning shape correspondence with
anisotropic convolutional neural networks",
Proc. Neural Information Processing Systems (NIPS), 2016. Abstract: Convolutional neural networks have achieved extraordinary results in many computer vision and pattern recognition applications; however, their adoption in the computer graphics and geometry processing communities is limited due to the non-Euclidean structure of their data. In this paper, we propose Anisotropic Convolutional Neural Network (ACNN), a generalization of classical CNNs to non-Euclidean domains, where classical convolutions are replaced by projections over a set of oriented anisotropic diffusion kernels. We use ACNNs to effectively learn intrinsic dense correspondences between deformable shapes, a fundamental problem in geometry processing, arising in a wide variety of applications. We tested ACNNs performance in challenging settings, achieving state-of-the-art results on recent correspondence benchmarks. |
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A. Kovnatsky, K. Glashoff, M. M. Bronstein,
"MADMM: a generic algorithm for non-smooth optimization on manifolds",
Proc. European Conf. Computer Vision (ECCV), 2016. Abstract: Numerous problems in computer vision, pattern recognition, and machine learning are formulated as optimization with manifold constraints. In this paper, we propose the Manifold alternating directions method of multipliers (MADMM), an extension of the classical ADMM scheme for manifold-constrained non-smooth optimization problems. To our knowledge, MADMM is the first generic non-smooth manifold optimization method. We showcase our method on several challenging problems in dimensionality reduction, non-rigid correspondence, multi-modal clustering, and multidimensional scaling. |
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S. Melzi, E. Rodolà, U. Castellani, M. M. Bronstein,
"Shape analysis with anisotropic windowed Fourier transform",
Proc. Int. Conf. 3D Vision (3DV), 2016. Abstract: We propose Anisotropic Windowed Fourier Transform (AWFT), a framework for localized space-frequency analysis of deformable 3D shapes. With AWFT, we are able to extract meaningful intrinsic localized orientation-sensitive structures on surfaces, and use them in applications such as shape segmentation, salient point detection, feature point description, and shape correspondence. Our method outperforms previous approaches in the considered applications. |
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D. Eynard, K. Glashoff, E. Rodolà, M. M. Bronstein,
"Coupled functional maps",
Proc. Int. Conf. 3D Vision (3DV), 2016. Abstract: Classical formulations of the shape matching problem involve the definition of a matching cost that directly depends on the action of the desired map when applied to some input data. Such formulations are typically one-sided - they seek for a mapping from one shape to the other, but not vice versa. In this paper we consider an unbiased formulation of this problem, in which we solve simultaneously for a low-distortion map relating the two given shapes and its inverse. We phrase the problem in the spectral domain using the language of functional maps, resulting in an especially compact and efficient optimization problem. The benefits of our proposed regularization are especially evident in the scarce data setting, where we demonstrate highly competitive results with respect to the state of the art. |
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L. Cosmo, E. Rodolà, J. Masci, A. Torsello, M. M. Bronstein,
"Matching deformable objects in clutter",
Proc. Int. Conf. 3D Vision (3DV), 2016. Abstract: We consider the problem of deformable object detection and dense correspondence in cluttered 3D scenes. Key ingredient to our method is the choice of representation: we formulate the problem in the spectral domain using the functional maps framework, where we seek for the most regular nearly-isometric parts in the model and the scene that minimize correspondence error. The problem is initialized by solving a sparse relaxation of a quadratic assignment problem on features obtained via data-driven metric learning. The resulting matching pipeline is solved efficiently, and yields accurate results in challenging settings that were previously left unexplored in the literature. |
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J. Svoboda, J. Masci, M. M. Bronstein,
"Palmprint recognition via discriminative index learning",
Proc. Int. Conf. Pattern Recognition (ICPR), 2016. Abstract: In the past years, deep convolutional neural networks (CNNs) have become extremely popular in the computer vision and pattern recognition community. The computational power of modern processors, efficient stochastic optimization algorithms, and large amounts of training data allowed training complex tasks-specific features directly from the data in an end-to-end fashion, as opposed to the traditional way of using hand-crafted feature descriptors. CNNs are currently state-of- the-art methods in many computer vision problems, and have been successfully used in biometric applications such as face, fingerprint, and voice recognition. In palmprint recognition applications, CNNs have not yet been explored, and the majority of methods still rely on hand-crafted representations which do not scale well to large datasets and that usually require a complex manual parameter tuning. In this work, we show that CNNs can be successfully used for palmprint recognition. The training of our network uses a novel loss function related to the d-prime index, which allows to achieve a better genuine/impostor score distribution separation than previous approaches. Our approach does not require cumbersome parameter tuning and achieves state-of-the-art results on the standard IIT Delhi and CASIA palmprint datasets. |
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Z. Lähner, E. Rodolà, F. Schmidt, M. M. Bronstein, D. Cremers,
"Efficient globally optimal 2D-to-3D deformable shape matching",
Proc. Computer Vision and Pattern Recognition (CVPR), 2016. Abstract: We propose the first algorithm for non-rigid 2D-to-3D shape matching, where the input is a 2D shape represented as a planar curve and a 3D shape represented as a surface; the output is a continuous curve on the surface. We cast the problem as finding the shortest circular path on the product 3-manifold of the surface and the curve. We prove that the optimal matching can be computed in polynomial time with a (worst-case) complexity of O(mn^2 log(n)), where m and n denote the number of vertices on the template curve and the 3D shape respectively. We also demonstrate that in practice the runtime is essentially linear in mn making it an efficient method for shape analysis and shape retrieval. Quantitative evaluation confirms that the methods provides excellent results for sketch-based deformable 3D shape retrieval. |
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Z. Lähner, E. Rodolà, M. M. Bronstein, D. Cremers, O. Burghard, L. Cosmo, A. Dieckmann, R. Klein, Y. Sahillioğlu,
"SHREC'16: Matching of deformable shapes with topological noise",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2016. Abstract: A particularly challenging setting of the shape matching problem arises when the shapes being matched have topological artifacts due to the coalescence of spatially close surface regions - a scenario that frequently occurs when dealing with real data under suboptimal acquisition conditions. This track of the SHREC'16 contest evaluates shape matching algorithms that operate on 3D shapes under synthetically produced topological changes. The task is to produce a pointwise matching (either sparse or dense) between 90 pairs of shapes, representing the same individual in different poses but with different topology. A separate set of 15 shapes with ground-truth correspondence was provided as training data for learning-based techniques and for parameter tuning. Three research groups participated in the contest; this paper presents the track dataset, and describes the different methods and the contest results. |
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L. Cosmo, E. Rodolà, M. M. Bronstein, A. Torsello, D. Cremers, Y. Sahillioğlu,
"SHREC'16: Partial matching of deformable shapes",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2016. Abstract: Matching deformable 3D shapes under partiality transformations is a challenging problem that has received limited focus in the computer vision and graphics communities. With this benchmark, we explore and thoroughly investigate the robustness of existing matching methods in this challenging task. Participants are asked to provide a point-to-point correspondence (either sparse or dense) between deformable shapes undergoing different kinds of partiality transformations, resulting in a total of 400 matching problems to be solved for each method - making this benchmark the biggest and most challenging of its kind. Five matching algorithms were evaluated in the contest; this paper presents the details of the dataset, the adopted evaluation measures, and shows thorough comparisons among all competing methods. |
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J. Masci, D. Boscaini, M. M. Bronstein, P. Vandergheynst,
"Geodesic convolutional neural networks on Riemannian manifolds",
Proc. Workshop on 3D Representation and Recognition (3dRR), 2015. Abstract: Feature descriptors play a crucial role in a wide range of geometry analysis and processing applications, including shape correspondence, retrieval, and segmentation. In this paper, we introduce Geodesic Convolutional Neural Networks (GCNN), a generalization of the convolutional networks (CNN) paradigm to non-Euclidean manifolds. Our construction is based on a local geodesic system of polar coordinates to extract "patches", which are then passed through a cascade of filters and linear and non-linear operators. The coefficients of the filters and linear combination weights are optimization variables that are learned to minimize a task-specific cost function. We use GCNN to learn invariant shape features, allowing to achieve state-of-the-art performance in problems such as shape description, retrieval, and correspondence. |
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N. Shahid, V. Kalofolias, X. Bresson, M. M. Bronstein, P. Vandergheynst,
"Robust principal component analysis on graphs",
Proc. International Conference on Computer Vision (ICCV), 2015. Abstract: Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called 'Robust PCA on Graphs' which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks. |
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N. Shahid, V. Kalofolias, X. Bresson, M. M. Bronstein, P. Vandergheynst,
"Robust principal component analysis on graphs",
Proc. SPARS, 2015. Abstract: Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. The classical PCA formulation is susceptible to outliers and errors in the data. Thus, even minute errors in the data can result in erratic principal directions. Robust PCA overcomes this problem by modeling the data matrix as the sum of a low rank and a sparse matrix, where the low rank matrix is a product of principal components and principal directions and the sparse matrix corresponds to the outliers or errors. The clustering property of PCA can be enhanced in the low dimensional space by benefiting from manifold information in the form of a graph. However, most of the works target on explicitly learning a parts based representation for low rank matrix approximation, with a smoothness assumption on the low dimensional embedding, i.e. one of the two factors of the low rank matrix. The underlying assumption is that the principal components of the data in the low dimensional subspace lie on a smooth manifold. A parts based PCA formulation results in non-convex optimization problem and the dimensionality of the subspace has to be specified up-front. Moreover, most of these works do not simultaneously leverage the robustness and the manifold regularization. |
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A. Kovnatsky, M. M. Bronstein, X. Bresson, P. Vandergheynst,
"Functional correspondence by matrix completion",
Proc. Computer Vision and Pattern Recognition (CVPR), 2015. Abstract: In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold geometric structure and inducing functional localization with the L1 norm. We discuss efficient numerical procedures for the solution of our problem. Our method compares favorably to the accuracy of state-of-the art correspondence algorithms on non-rigid shape matching benchmarks, and is especially advantageous in settings when only scares data is available. |
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J. Svoboda, M. M. Bronstein, M. Drahansky,
"Contactless biometric hand recognition using a low-cost 3D camera",
Proc. Intl. Conf. Biometrics (ICB), 2015. Abstract: In the past decade, the interest in using 3D data for biometric person authentication has increased dramatically, propelled by the availability of affordable 3D sensors. The adoption of 3D features has been especially successful in face recognition applications, leading to several commercial 3D face recognition products. In other biometric modalities such as hand recognition, several studies have shown the potential advantage of using 3D geometric information, however, no commercial-grade systems are currently available. In this paper, we present a contactless 3D hand recognition system based on the novel Intel RealSense camera, the first mass-produced embeddable 3D sensor. The small form factor and low cost make this sensor especially appealing for commercial biometric applications, however, they come at the price of lower resolution compared to more expensive 3D scanners used in previous research. We analyze the robustness of several 2D and 3D features that can be extracted from the images captured by the sensor and study the use of metric learning for their fusion. Our evaluation shows that the performance of our system is comparable with the state-of-the-art results reported in the literature. |
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I. Sipiran, B. Bustos, T. Schreck, A. M. Bronstein, M. M. Bronstein, U. Castellani, S. Choi,
L. Lai, H. Li, R. Litman, L. Sun,
"SHREC'15 Track: Scalability of non-rigid 3D shape
retrieval",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2015. Abstract: Due to recent advances in 3D acquisition and modeling, increasingly large amounts of 3D shape data become available in many application domains. This rises not only the need for effective methods for 3D shape retrieval, but also efficient retrieval and robust implementations. Previous 3D retrieval challenges have mainly considered data sets in the range of a few thousands of queries. In the 2015 SHREC track on Scalability of 3D Shape Retrieval we provide a benchmark with more than 96 thousand shapes. The data set is based on a non-rigid retrieval benchmark enhanced by other existing shape benchmarks. From the baseline models, a large set of partial objects were automatically created by simulating a range-image acquisition process. Four teams have participated in the track, with most methods providing very good to near-perfect retrieval results, and one less complex baseline method providing fair performance. Timing results indicate that three of the methods including the latter baseline one provide near- interactive time query execution. Generally, the cost of data pre-processing varies depending on the method. |
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V. Kalofolias, X. Bresson, M. M. Bronstein, P. Vandergheynst,
"Matrix completion on graphs",
Proc. NIPS Workshop Out of the Box: Robustness in High Dimension, 2014. Abstract: The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard, Candes and Recht showed that it can be exactly relaxed if the number of observed entries is sufficiently large. In this work, we introduce a novel matrix completion model that makes use of proximity information about rows and columns by assuming they form communities. This assumption makes sense in several real-world problems like in recommender systems, where there are communities of people sharing preferences, while products form clusters that receive similar ratings. Our main goal is thus to find a low-rank solution that is structured by the proximities of rows and columns encoded by graphs. We borrow ideas from manifold learning to constrain our solution to be smooth on these graphs, in order to implicitly force row and column proximities. Our matrix recovery model is formulated as a convex non-smooth optimization problem, for which a well-posed iterative scheme is provided. We study and evaluate the proposed matrix completion on synthetic and real data, showing that the proposed structured low-rank recovery model outperforms the standard matrix completion model in many situations. |
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A. Kovnatsky, D. Eynard, M. M. Bronstein,
"Gamut mapping with image Laplacian commutators",
Proc. Int. Conf. Image Processing (ICIP), 2014. Abstract: In this paper, we present a gamut mapping algorithm that is based on spectral properties of image Laplacians as image structure descriptors. Using the fact that structurally similar images have similar Laplacian eigenvectors and employing the relation between joint diagonalizability and commutativity of matrices, we minimize the Laplacians commutator w.r.t. the parameters of a color transformation to achieve optimal structure preservation while complying with the target gamut. Our method is computationally efficient, favorably compares to state-of-the-art approaches in terms of quality, allows mapping to devices with any number of primaries, and supports gamma correction, accounting for brightness response of computer displays. |
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D. Boscaini, R. Girdziusas, M. M. Bronstein,
"Coulomb shapes: using electrostatic forces for deformation-invariant shape representation"
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2014. Abstract: Canonical shape analysis is a popular method in deformable shape matching, trying to bring the shape into a canonical form that undoes its non-rigid deformations, thus reducing the problem of non-rigid matching into a rigid one. The canonization can be performed by measuring geodesic distances between all pairs of points on the shape and embedding them into a Euclidean space by means of multidimensional scaling (MDS), which reduces the intrinsic isometries of the shape into the extrinsic (Euclidean) isometries of the embedding space. A notable drawback of MDS-based canonical forms is their sensitivity to topological noise: different shape connectivity can affect dramatically the geodesic distances, resulting in a global distortion of the canonical form. In this paper, we propose a different shape canonization approach based on a physical model of electrostatic repulsion. We minimize the Coulomb energy subject to the local distance constraints between adjacent shape vertices. Our model naturally handles topological noise, allowing to 'tear' the shape at points of strong repulsion. Furthermore, the problem is computationally efficient, as it lends itself to fast multipole methods. We show experimental results in which our method compares favorably to MDS-based canonical forms. |
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D. Pickup, X. Sun, P. L. Rosin, R. R. Martin, Z. Cheng, Z. Lian, M. Aono, A. Ben Hamza, A. M. Bronstein, M. M. Bronstein, S. Bu, U. Castellani, S. Cheng, V. Garro, A. Giachetti, A. Godil, J. Han, H. Johan, L. Lai, B. Li, C. Li, H. Li, R. Litman, X. Liu, Z. Liu, Y. Lu, A. Tatsuma, J. Ye,
"Shape Retrieval of Non-Rigid 3D Human Models",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2014. Abstract: We have created a new dataset for non-rigid 3D shape retrieval, one that is much more challenging than existing datasets. Our dataset features exclusively human models, in a variety of body shapes and poses. 3D models of humans are commonly used within computer graphics and vision, therefore the ability to distinguish between body shapes is an important feature for shape retrieval methods. In this track nine groups have submitted the results of a total of 22 different methods which have been tested on our new dataset. |
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S. Biasotti, A. Cerri, A. M. Bronstein, M. M. Bronstein,
"Quantifying 3D shape similarity using maps:
Recent trends, applications and perspectives", Proc. EUROGRAPHICS STARS, 2014. Abstract: Shape similarity is an acute issue in Computer Vision and Computer Graphics that involves many aspects of human perception of the real world, including judged and perceived similarity concepts, deterministic and probabilistic decisions and their formalization. 3D models carry multiple information with them (e.g., geometry, topology, texture, time evolution, appearance), which can be thought as the filter that drives the recognition process. Assessing and quantifying the similarity between 3D shapes is necessary to explore large dataset of shapes, and tune the analysis framework to the userŐs needs. Many efforts have been done in this sense, including several attempts to formalize suitable notions of similarity and distance among 3D objects and their shapes. In the last years, 3D shape analysis knew a rapidly growing interest in a number of challenging issues, ranging from deformable shape similarity to partial matching and view-point selection. In this panorama, we focus on methods which quantify shape similarity (between two objects and sets of models) and compare these shapes in terms of their properties (i.e., global and local, geometric, differential and topological) conveyed by (sets of) maps. After presenting in detail the theoretical foundations underlying these methods, we review their usage in a number of 3D shape application domains, ranging from matching and retrieval to annotation and segmentation. Particular emphasis will be given to analyze the suitability of the different methods for specific classes of shapes (e.g. rigid or isometric shapes), as well as the flexibility of the various methods at the different stages of the shape comparison process. Finally, the most promising directions for future research developments are discussed. |
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J. Masci, A. M. Bronstein, M. M. Bronstein, P. Sprechmann, G. Sapiro, "Sparse similarity-preserving hashing"
Proc. International Conference on Learning Representations (ICLR), 2014. Abstract: In recent years, a lot of attention has been devoted to efficient nearest neighbor search by means of similarity-preserving hashing. One of the plights of existing hashing techniques is the intrinsic trade-off between performance and computational complexity: while longer hash codes allow for lower false positive rates, it is very difficult to increase the embedding dimensionality without incurring in very high false negatives rates or prohibiting computational costs. In this paper, we propose a way to overcome this limitation by enforcing the hash codes to be sparse. Sparse high-dimensional codes enjoy from the low false positive rates typical of long hashes, while keeping the false negative rates similar to those of a shorter dense hashing scheme with equal number of degrees of freedom. We use a tailored feed-forward neural network for the hashing function. Extensive experimental evaluation involving visual and multi-modal data shows the benefits of the proposed method. |
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P. Sprechmann, A. M. Bronstein, M. M. Bronstein, G. Sapiro
"Learnable low rank sparse models for speech denoising"
Proc. International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2013. Abstract: 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 its computational complexity. |
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K. Glashoff, M. M. Bronstein,
"Structure from motion using augmented Lagrangian robust factorization"
Proc. Conf. on 3D Imaging, Modeling, Processing, Visualization, and Transmission (3DimPVT), 2012. Abstract: 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. |
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O. Litany, A. M. Bronstein, M. M. Bronstein,
"Putting the pieces together: regularized multi-shape partial matching"
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2012. Abstract: Multi-part shape matching in 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. |
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A. Kovnatsky, A. M. Bronstein, M. M. Bronstein,
"Stable spectral mesh filtering"
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2012. Abstract: The rapid development of 3D acquisition technology has brought with itself the need to perform standard signal processing operations such as filters on 3D data. It has been shown that the eigenfunctions of the Laplace-Beltrami operator (manifold harmonics) of a surface play the role of the Fourier basis in the Euclidean space; it is thus possible to formulate signal analysis and synthesis in the manifold harmonics basis. In particular, geometry filtering can be carried out in the manifold harmonics domain by decomposing the embedding coordinates of the shape in this basis. However, since the basis functions depend on the shape itself, such filtering is valid only for weak (near all-pass) filters, and produces severe artifacts otherwise. In this paper, we analyze this problem and propose the fractional filtering approach, wherein we apply iteratively weak fractional powers of the filter, followed by the update of the basis functions. Experimental results show that such a process produces more plausible and meaningful results. |
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G. Rosman, A. M. Bronstein, M. M. Bronstein, X.-C. Tai, R. Kimmel,
"Group-valued regularization for analysis of
articulated motion"
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2012. Abstract: 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. |
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I. Kokkinos, M. M. Bronstein, R. Litman, A. M. Bronstein,
"Intrinsic shape context descriptors for deformable shapes",
Proc. Computer Vision and Pattern Recognition (CVPR), 2012. Abstract: 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. ISC Code |
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A. Kovnatsky, D. Raviv, M. M. Bronstein, A. M. Bronstein, R. Kimmel
"Affine-invariant photometric heat kernel signatures",
Proc. Workshop on 3D Object Retrieval (3DOR), 2012. Abstract: 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 of retrieval task the proposed diffusion process may be employed in other applications. |
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G. Rosman, A. M. Bronstein, M. M. Bronstein, R. Kimmel
"Articulated motion segmentation of point clouds by group-valued regularization",
Proc. Workshop on 3D Object Retrieval (3DOR), 2012. Abstract: 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 variational, well-defined, framework. Results on scanned images show the generality of the proposed technique and its robustness to scanning artifacts and noise. |
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D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen,
"Affine-invariant diffusion geometry for the analysis of deformable 3D shapes",
Proc. Computer Vision and Pattern Recognition (CVPR), 2011. Abstract: We introduce an (equi-)affine invariant diffusion geometry 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 construct an invariant Laplacian from which the structure of the geometry is extracted. Applications of the proposed framework demonstrate its power in generalizing and enriching the existing set of tools for shape analysis. |
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A. Kovnatsky, M. M. Bronstein, A. M. Bronstein, R. Kimmel,
"Photometric heat kernel signatures",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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. |
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A. Hooda, M. M. Bronstein, A. M. Bronstein, R. Horaud,
"Shape palindromes: analysis of intrinsic symmetries in 2D articulated shapes",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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. Metaphorically, the later can be compared to finding palindromes in text sequences. |
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J. Aflalo, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Deformable shape retrieval by learning diffusion kernels",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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. |
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J. Pokrass, A. M. Bronstein, M. M. Bronstein,
"A correspondence-less approach to matching of deformable shapes",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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. |
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G. Rosman, M. M. Bronstein, A. M. Bronstein, A. Wolf, R. Kimmel,
"Group-valued regularization framework for motion segmentation of dynamic non-rigid shapes",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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, and force it to be piece- wise rigid. 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. |
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C. Wang, M. M. Bronstein, N. Paragios, A. M. Bronstein,
"Discrete minimum distortion correspondence problems for non-rigid shape matching",
Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), 2011. Abstract: 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 and formulate the invariant correspondence problem as binary graph labeling. We show how different choice of structure results in invariance under various classes of deformations. |
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E. Boyer, A. M. Bronstein, M. M. Bronstein, B. Bustos, T. Darom, R. Horaud, I. Hotz, Y. Keller, J. Keustermans, A. Kovnatsky, R. Litman, J. Reininghaus, I. Sipiran, D. Smeets, P. Suetens, D. Vandermeulen, A. Zaharescu, V. Zobel,
"SHREC 2011: robust feature detection and description benchmark",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2011. Abstract: Feature-based approaches have recently become very popular in computer vision and image analysis application, and are becoming a promising direction in shape retrieval applications. SHREC'10 robust feature detection and description benchmark simulates feature detection and description stage of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of different transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the SHREC'11 robust feature detection and description benchmark results. SHREC'11 feature detection benchmark |
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F. Michel, M. M. Bronstein, A. M. Bronstein, N. Paragios,
"Boosted metric learning for 3D multi-modal deformable registration",
Proc. Intl. Symposium on Biomedical Imaging (ISBI), 2011. Abstract: Defining a suitable metric is one of the biggest challenges in deformable image fusion from different modalities. In this paper, we propose a novel approach for multi-modal metric learning in the deformable registration framework that consists of embedding data from both modalities into a common metric space whose metric is used to parametrize the similarity. Specifically, we use image representation in the Fourier/Gabor space which introduces invariance to the local pose parameters, and the Hamming metric as the target embedding space, which allows constructing the embedding using boosted learning algorithms. The resulting metric is incorporated into a discrete optimization framework. Very promising results demonstrate the potential of the proposed method. |
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D. Raviv, M. M. Bronstein, A. M. Bronstein, R. Kimmel,
"Volumetric heat kernel signatures",
Proc. Intl. Workshop on 3D Object Retrieval, ACM Multimedia, 2010. Abstract: Invariant shape descriptors are instrumental in numerous shape analysis tasks including deformable shape comparison, registration, classification, and retrieval. Most existing constructions model a 3D shape as a two-dimensional surface describing the shape boundary, typically represented as a triangular mesh or a point cloud. Using intrinsic properties of the surface, invariant descriptors can be designed. One such example is the recently introduced heat kernel signature, based on the Laplace-Beltrami operator of the surface. In many applications, however, a volumetric shape model is more natural and convenient. Moreover, modeling shape deformations as approximate isometries of the volume of an object, rather than its boundary, better captures natural behavior of non-rigid deformations in many cases. Here, we extend the idea of heat kernel signature to robust isometry-invariant volumetric descriptors, and show their utility in shape retrieval. The proposed approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark. |
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N. Mitra, A. M. Bronstein, M. M. Bronstein,
"Intrinsic regularity detection in 3D geometry",
Proc. European Conf. Computer Vision (ECCV), 2010. Abstract: Automatic detection of symmetries, regularity, and repetitive structures in 3D geometry is a fundamental problem in shape analysis and pattern recognition with applications in computer vision and graphics. Especially challenging is to detect intrinsic regularity, where the repetitions are on an intrinsic grid, without any apparent Euclidean pattern to describe the shape, but rising out of (near) isometric deformation of the underlying surface. In this paper, we employ multidimensional scaling to reduce the problem of intrinsic structure detection to a simpler problem of 2D grid detection. Potential 2D grids are then identified using an autocorrelation analysis, refined using local fitting, validated, and finally projected back to the spatial domain. We test the detection algorithm on a variety of scanned plaster models in presence of imperfections like missing data, noise and outliers. We also present a range of applications including scan completion, shape editing, super-resolution, and structural correspondence. |
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A. M. Bronstein, M. M. Bronstein,
"Spatially-sensitive affine-invariant image descriptors",
Proc. European Conf. Computer Vision (ECCV), 2010. Abstract: Invariant image descriptors play an important role in many computer vision and pattern recognition problems such as image search and retrieval. A dominant paradigm today is that of "bags of features", a representation of images as distributions of primitive visual elements. The main disadvantage of this approach is the loss of spatial relations between features, which often carry important information about the image. In this paper, we show how to construct spatially-sensitive image descriptors in which both the features and their relation are affine-invariant. Our construction is based on a vocabulary of pairs of features coupled with a vocabulary of invariant spatial relations between the features. Experimental results show the advantage of our approach in image retrieval applications. |
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M. M. Bronstein, I. Kokkinos,
"Scale-invariant heat kernel signatures for non-rigid shape recognition",
Proc. Computer Vision and Pattern Recognition (CVPR), 2010. Abstract: One of the biggest challenges in non-rigid shape retrieval and comparison is the design of a shape descriptor that would maintain invariance under a wide class of transformations the shape can undergo. Recently, heat kernel signature was introduced as an intrinsic local shape descriptor based on diffusion scale-space analysis. In this paper, we develop a scale-invariant version of the heat kernel descriptor. Our construction is based on a logarithmically sampled scale-space in which shape scaling corresponds, up to a multiplicative constant, to a translation. This translation is undone using the magnitude of the Fourier transform. The proposed scale-invariant local descriptors can be used in the bag-of-features framework for shape retrieval in the presence of transformations such as isometric deformations, missing data, topological noise, and global and local scaling. We get significant performance improvement over state-of-the-art algorithms on recently established non-rigid shape retrieval benchmarks. CVPR trailer video | SI-HKS Code |
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M. M. Bronstein, A. M. Bronstein, F. Michel, N. Paragios,
"Data fusion through cross-modality metric learning using similarity-sensitive hashing",
Proc. Computer Vision and Pattern Recognition (CVPR), 2010. Abstract: Visual understanding is often based on measuring similarity between observations. Learning similarities specific to a certain perception task from a set of examples has been shown advantageous in various computer vision and pattern recognition problems. In many important applications, the data that one needs to compare come from different representations or modalities, and the similarity between such data operates on objects that may have different and often incommensurable structure and dimensionality. In this paper, we propose a framework for supervised similarity learning based on embedding the input data from two arbitrary spaces into the Hamming space. The mapping is expressed as a binary classification problem with positive and negative examples, and can be efficiently learned using boosting algorithms. The utility and efficiency of such a generic approach is demonstrated on several challenging applications including cross-representation shape retrieval and alignment of multi-modal medical images. CVPR trailer video | CM-SSH Code |
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A. M. Bronstein, M. M. Bronstein, U. Castellani, B. Falcidieno, A. Fusiello, A. Godil,
L. J. Guibas, I. Kokkinos, Z. Lian, M. Ovsjanikov, G. Patané, M. Spagnuolo, R. Toldo,
"SHREC 2010: robust large-scale shape retrieval benchmark",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010. Abstract: SHREC'10 robust large-scale shape retrieval benchmark simulates a retrieval scenario, in which the queries include multiple modifications and transformations of the same shape. The benchmark allows evaluating how algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the SHREC'10 robust large-scale shape retrieval benchmark results. SHREC'10 shape retrieval benchmark |
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A. M. Bronstein, M. M. Bronstein, B. Bustos, U. Castellani, M. Crisani, B. Falcidieno,
L. J. Guibas, I. Kokkinos, V. Murino, M. Ovsjanikov, G. Patané, I. Sipiran, M. Spagnuolo, J. Sun,
"SHREC 2010: robust feature detection and description benchmark",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010. Abstract: Feature-based approaches have recently become very popular in computer vision and image analysis application, and are becoming a promising direction in shape retrieval applications. SHREC'10 robust feature detection and description benchmark simulates feature detection and description stage of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of different transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the SHREC'10 robust feature detection and description benchmark results. SHREC'10 feature detection benchmark |
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A. M. Bronstein, M. M. Bronstein, U. Castellani, A. Dubrovina, L. J. Guibas, R. P. Horaud, R. Kimmel,
D. Knossow, E. von Lavante, D. Mateus, M. Ovsjanikov, A. Sharma,
"SHREC 2010: robust correspondence benchmark",
Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010. Abstract: SHREC'10 robust correspondence benchmark simulates a one-to-one shape matching scenario, in which one of the shapes undergoes multiple modifications and transformations. The benchmark allows evaluating how correspondence algorithms cope with certain classes of transformations and what is the strength of the transformations that can be dealt with. The present paper is a report of the SHREC'10 robust correspondence benchmark results. SHREC'10 correspondence benchmark |
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D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, G. Sapiro,
"Diffusion symmetries of non-rigid shapes",
Proc. Intl. Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), 2010. Abstract: Detection and modeling of self-similarity and symmetry is important in shape recognition, matching, synthesis, and reconstruction. While the detection of rigid shape symmetries is well-established, the study of symmetries in non- rigid shapes is a much less researched problem. A particularly challenging setting is the detection of symmetries in non-rigid shapes affected by topological noise and asymmetric connectivity. In this paper, we treat shapes as metric spaces, with the metric induced by heat diffusion properties, and define non-rigid symmetries as self-isometries with respect to the diffusion metric. Experimental results show the advantage of the diffusion metric over the previously proposed geodesic metric for exploring intrinsic symmetries of bendable shapes with possible topological irregularities. |
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M. Ovsjanikov, A. M. Bronstein, M. M. Bronstein, L. J. Guibas,
"ShapeGoogle: a computer vision approach for invariant shape retrieval",
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2009. Abstract: Feature-based methods have recently gained popularity in computer vision and pattern recognition communities, in applications such as object recognition and image retrieval. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape search and retrieval in large databases. |
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Y. Devir, G. Rosman, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"On reconstruction of non-rigid shapes with intrinsic regularization",
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2009. Abstract: Shape-from-X is a generic type of inverse problems in computer vision, in which a shape is reconstructed from some measurements. A specially challenging setting of this problem is the case in which the reconstructed shapes are non-rigid. In this paper, we propose a framework for intrinsic regularization of such problems. The assumption is that we have the geometric structure of a shape which is intrinsically (up to bending) similar to the one we would like to reconstruct. For that goal, we formulate a variation with respect to vertex coordinates of a triangulated mesh approximating the continuous shape. The numerical core of the proposed method is based on differentiating the fast marching update step for geodesic distance computation. |
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O. Rubinstein, Y. Honen, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"3D color video camera",
Proc. Workshop on 3D Digital Imaging and Modeling (3DIM), 2009. Abstract: We introduce a design of a coded light-based 3D color video camera optimized for build up cost as well as accuracy in depth reconstruction and acquisition speed. The components of the system include a monochromatic camera and an off-the-shelf LED projector synchronized by a miniature circuit. The projected patterns are captured and processed at a rate of 200 fps and allow for real-time reconstruction of both depth and color at video rates. The reconstruction and display are performed at around 30 depth profiles and color texture per second using a graphics processing unit (GPU). |
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A. M. Bronstein, M. M. Bronstein,
"Regularized partial matching of rigid shapes",
Proc. European Conf. Computer Vision (ECCV), pp. 143-154, 2008. Abstract: Matching of rigid shapes is an important problem in numerous applications across the boundary of computer vision, pattern recognition and computer graphics communities. A particularly challenging setting of this problem is partial matching, where the two shapes are dissimilar in general, but have significant similar parts. In this paper, we show a rigorous approach allowing to find matching parts of rigid shapes with controllable size and regularity. The regularity term we use is similar to the spirit of the Mumford-Shah functional, extended to non-Euclidean spaces. Numerical experiments show that the regularized partial matching produces better results compared to the non-regularized one. |
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A. M. Bronstein, M. M. Bronstein,
"Not only size matters: regularized partial matching of nonrigid shapes",
Proc. Workshop on Nonrigid Shape Analysis and Deformable Image Alignment (NORDIA), 2008. Abstract: Partial matching is probably one of the most challenging problems in nonrigid shape analysis. The problem consists of matching similar parts of shapes that are dissimilar on the whole and can assume different forms by undergoing nonrigid deformations. Conceptually, two shapes can be considered partially matching if they have significant similar parts, with the simplest definition of significance being the size of the parts. Thus, partial matching can be defined as a multcriterion optimization problem trying to simultaneously maximize the similarity and the size of these parts. In this paper, we propose a different definition of significance, taking into account the regularity of parts besides their size. The regularity term proposed here is similar to the spirit of the Mumford-Shah functional. Numerical experiments show that the regularized partial matching produces semantically better results compared to the non-regularized one. |
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R. Giryes, A. M. Bronstein, Y. Moshe, M. M. Bronstein,
"Embedded System for 3D Shape Reconstruction",
In Proc. European DSP Education and Research Symposium (EDERS), 2008. Abstract: Many applications that use three-dimensional scanning require a low cost, accurate and fast solution. This paper presents a fixed-point implementation of a real time active stereo threedimensional acquisition system on a Texas Instruments DM6446 EVM board which meets these requirements. A time-multiplexed structured light reconstruction technique is described and a fixed point algorithm for its implementation is proposed. This technique uses a standard camera and a standard projector. The fixed point reconstruction algorithm runs on the DSP core while the ARM controls the DSP and is responsible for communication with the camera and projector. The ARM uses the projector to project coded light and the camera to capture a series of images. The captured data is sent to the DSP. The DSP, in turn, performs the 3D reconstruction and returns the results to the ARM for storing. The inter-core communication is performed using the xDM interface and VISA API. Performance evaluation of a fully working prototype proves the feasibility of a fixed-point embedded implementation of a real time three-dimensional scanner, and the suitability of the DM6446 chip for such a system. |
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G. Rosman, A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Topologically constrained isometric embedding",
In Human Motion Understanding, Modelling, Capture, and Animation, Computational Imaging and Vision, Vol. 36, Springer, pp. 243-262, 2008. Abstract: We present a new algorithm for nonlinear dimensionality reduction that consistently uses global information, which enables understanding the intrinsic geometry of non-convex manifolds. Compared to methods that consider only local information, our method appears to be more robust to noise. We demonstrate the performance of our algorithm and compare it to state-of-the-art methods on synthetic as well as real data. |
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D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, "Symmetries of non-rigid shapes", Proc. Workshop on Non-rigid Registration and Tracking through Learning (NRTL), 2007. Abstract: Symmetry and self-similarity is the cornerstone of Nature, exhibiting itself through the shapes of natural creations and ubiquitous laws of physics. Since many natural objects are symmetric, the absence of symmetry can often be an indication of some anomaly or abnormal behavior. Therefore, detection of asymmetries is important in numerous practical applications, including crystallography, medical imaging, and face recognition, to mention a few. Conversely, the assumption of underlying shape symmetry can facilitate solutions to many problems in shape reconstruction and analysis. Traditionally, symmetries are described as extrinsic geometric properties of the shape. While being adequate for rigid shapes, such a description is inappropriate for non-rigid ones. Extrinsic symmetry can be broken as a result of shape deformations, while its intrinsic symmetry is preserved. In this paper, we pose the problem of finding intrinsic symmetries of non-rigid shapes and propose an efficient method for their computation. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel, "Rock, Paper, and Scissors: extrinsic vs. intrinsic similarity of non-rigid shapes", Proc. Intl. Conf. Computer Vision (ICCV), 2007. Abstract: This paper explores similarity criteria between non-rigid shapes. Broadly speaking, such criteria are divided into intrinsic and extrinsic, the first referring to the metric structure of the objects and the latter to the geometry of the shapes in the Euclidean space. Both criteria have their advantages and disadvantages; extrinsic similarity is sensitive to non-rigid deformations of the shapes, while intrinsic similarity is sensitive to topological noise. Here, we present an approach unifying both criteria in a single distance. Numerical results demonstrate the robustness of our approach in cases where using only extrinsic or intrinsic criteria fail. |
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A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel, "Paretian similarity for partial comparison of non-rigid objects", Proc. Conf. on Scale Space and Variational Methods in Computer Vision (SSVM), pp. 264-275, 2007. Abstract: In this paper, we address the problem of partial comparison of non-rigid objects. We introduce a new class of set-valued distances, related to the concept of Pareto optimality in economics. Such distances allow to capture intrinsic geometric similarity between parts of non-rigid objects, obtaining semantically meaningful comparison results. The numerical implementation of our method is computationally efficient and is similar to GMDS, a multidimensional scaling-like continuous optimization problem. |
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A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel, "Partial similarity of objects and text sequences", Proc. Information Theory and Applications Workshop, San Diego, 2007. Abstract: Similarity is one of the most important abstract concepts in the human perception of the world. In computer vision, numerous applications deal with comparing objects observed in a scene with some a priori known patterns. Often, it happens that while two objects are not similar, they have large similar parts, that is, they are partially similar. Here, we present a novel approach to quantify this semantic definition of partial similarity using the notion of Pareto optimality. We exemplify our approach on the problems of recognizing non-rigid objects and analyzing text sequences. |
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A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel,
"Matching two-dimensional articulated shapes using generalized multidimensional scaling",
Proc. Conf. on Articulated Motion and Deformable Objects (AMDO), pp. 48-57, 2006. Abstract: We present a theoretical and computational framework for matching of two-dimensional articulated shapes. Assuming that articulations can be modeled as near-isometries, we show an axiomatic construction of an articulation-invariant distance between shapes, formulated as a generalized multidimensional scaling (GMDS) problem and solved efficiently. Some numerical results demonstrating the accuracy of our method are presented. 2D tools dataset |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Face2Face: an isometric model for facial animation",
Proc. Conf. on Articulated Motion and Deformable Objects (AMDO), pp. 38-47, 2006. Abstract: A geometric framework for finding intrinsic correspondence between animated 3D faces is presented. We model facial expressions as isometries of the facial surface and find the correspondence between two faces as the minimum-distortion mapping. Generalized multidimensional scaling is used for this goal. We apply our approach to texture mapping onto 3D video, expression exaggeration and morphing between faces. 3D face video |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Robust expression-invariant face recognition from partially missing data",
Proc. European Conf. on Computer Vision (ECCV), pp. 396-408, 2006. Abstract: Recent studies on three-dimensional face recognition proposed to model facial expressions as isometries of the facial surface. Based on this model, expression-invariant signatures of the face were constructed by means of approximate isometric embedding into flat spaces. Here, we apply a new method for measuring isometry-invariant similarity between faces by embedding one facial surface into another. We demonstrate that our approach has several significant advantages, one of which is the ability to handle partially missing data. Promising face recognition results are obtained in numerical experiments even when the facial surfaces are severely occluded. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"On separation of semitransparent dynamic images from static background",
Proc. Intl. Conf. on Independent Component Analysis and Blind Signal Separation, pp. 934-940, 2006. Abstract: Presented here is the problem of recovering a dynamic image superimposed on a static background. Such a problem is ill-posed and may arise e.g. in imaging through semireflective media, in separation of an illumination image from a reflectance image, in imaging with diffraction phenomena, etc. In this work we study regularization of this problem in spirit of Total Variation and general sparsifying transformations. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Expression-invariant face recognition via spherical embedding",
Proc. Intl. Conf. on Image Processing (ICIP), Vol. 3, pp. 756-759, 2005. Abstract: Recently, it was proven empirically that facial expressions can be modelled as isometries, that is, geodesic distances on the facial surface were shown to be significantly less sensitive to facial expressions compared to Euclidean ones. Based on this assumption, the 3DFACE face recognition system was built. The system efficiently computes expression invariant signatures based on isometry-invariant representation of the facial surface. One of the crucial steps in the recognition system was embedding of the face geometric structure into a Euclidean (flat) space. Here, we propose to replace the flat embedding by a spherical one to construct isometric invariant representations of the facial image. We refer to these new invariants as spherical canonical images. Compared to its Euclidean counterpart, spherical embedding leads to notably smaller metric distortion. We demonstrate experimentally that representations with lower embedding error lead to better recognition. In order to efficiently compute the invariants we introduce a dissimilarity measure between the spherical canonical images based on the spherical harmonic transform. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Unmixing tissues: sparse component analysis in multi-contrast MRI",
Proc. Intl. Conf. on Image Processing (ICIP), Vol. 2, pp. 1282-1285, 2005. Abstract: We pose the problem of tissue classification in MRI as a blind source separation (BSS) problem and solve it by means of sparse component analysis (SCA). Assuming that most MR images can be sparsely represented, we consider their optimal sparse representation. Sparse components define a physically-meaningful feature space for classification. We demonstrate our approach on simulated and real multi-contrast MRI data. The proposed framework is general in that it is applicable to other modalities of medical imaging as well, whenever the linear mixing model is applicable. |
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M. M. Bronstein, A. M. Bronstein, R. Kimmel, I. Yavneh,
"A multigrid approach for multi-dimensional scaling",
Proc. Copper Mountain Conf. Multigrid Methods, 2005. Best Paper Award Abstract: A multigrid approach for the efficient solution of large-scale multidimensional scaling (MDS) problems is presented. The main motivation is a recent application of MDS to isometry-invariant representation of surfaces, in particular, for expression-invariant recognition of human faces. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms. Multigrid MDS code | Tutorial |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Isometric embedding of facial surfaces into $S^3$",
Proc. Intl. Conf. on Scale Space and PDE Methods in Computer Vision, pp. 622-631, 2005. Abstract: The problem of isometry-invariant representation and comparison of surfaces is of cardinal importance in pattern recognition applications dealing with deformable objects. Particularly, in three-dimensional face recognition treating facial expressions as isometries of the facial surface allows to perform robust recognition insensitive to expressions. Isometry-invariant representation of surfaces can be constructed by isometrically embedding them into some convenient space, and carrying out the comparison in that space. Presented here is a discussion on isometric embedding into $S^3$, which appears to be superior over the previously used Euclidean space in sense of the representation accuracy. |
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A. M. Bronstein, M. M. Bronstein, E. Gordon, R. Kimmel,
"Fusion of 2D and 3D data in three-dimensional face recognition",
Proc. Intl. Conf. on Image Processing (ICIP), pp. 87-90, 2004. Abstract: We discuss the synthesis between the 3D and the 2D data in three-dimensional face recognition. We show how to compensate for the illumination and facial expressions using the 3D facial geometry and present the approach of canonical images, which allows to incorporate geometric information into standard face recognition approaches. |
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M. M. Bronstein, A. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Optimal sparse representations for blind source separation and blind deconvolution: a learning approach", Proc. Intl. Conf. on Image Processing (ICIP), pp. 1815-1818, 2004. Abstract: We present a generic approach, which allows to adapt sparse blind deconvolution and blind source separation algorithms to arbitrary sources. The key idea is to bring the problem to the case in which the underlying sources are sparse by applying a sparsifying transformation on the mixtures. We present simulation results and show that such transformation can be found by training. Properties of the optimal sparsifying transformation are highlighted by an example with aerial images. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Fast relative Newton algorithm for blind deconvolution of images", Proc. Intl. Conf. on Image Processing (ICIP), pp. 1233-1236, 2004. Abstract: We present an efficient Newton-like algorithm for quasimaximum likelihood (QML) blind deconvolution of images. This algorithm exploits the sparse structure of the Hessian. An optimal distribution-shaping approach by means of sparsification allows one to use simple and convenient sparsity prior for processing of a wide range of natural images. Simulation results demonstrate the efficiency of the proposed method. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky,
"Blind source separation using the block-coordinate relative Newton method",
Proc. Intl. Conf. on Independent Component Analysis and Blind Signal Separation, Lecture Notes in Comp. Science No. 3195, Springer, pp. 406-413, 2004. Abstract: Presented here is a generalization of the modified relative Newton method, recently proposed by Zibulevsky for quasi-maximum likelihood blind source separation. Special structure of the Hessian matrix allows to perform block-coordinate Newton descent, which significantly reduces the algorithm computational complexity and boosts its performance. Simulations based on artificial and real data show that the separation quality using the proposed algorithm outperforms other accepted blind source separation methods. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"QML blind deconvolution: asymptotic analysis",
Proc. Intl. Conf. on Independent Component Analysis and Blind Signal Separation, Lecture Notes in Comp. Science No. 3195, Springer, pp. 677-684, 2004. Abstract: Blind deconvolution is considered as a problem of quasi maximum likelihood (QML) estimation of the restoration kernel. Simple closed-form expressions for the asymptotic estimation error are derived. The asymptotic performance bounds coincide with the Cramér-Rao bounds, when the true ML estimator is used. Conditions for asymptotic stability of the QML estimator are derived. Special cases when the estimator is super-efficient are discussed. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Optimal sparse representations for blind deconvolution of images",
Proc. Intl. Conf. on Independent Component Analysis and Blind Signal Separation, Lecture Notes in Comp. Science No. 3195, Springer, pp. 500-507, 2004. Abstract: The relative Newton algorithm, previously proposed for quasi maximum likelihood blind source separation and blind deconvolution of one-dimensional signals is generalized for blind deconvolution of images. Smooth approximation of the absolute value is used in modelling the log probability density function, which is suitable for sparse sources.We propose a method of sparsification, which allows blind deconvolution of sources with arbitrary distribution, and show how to find optimal sparsifying transformations by training. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel, A. Spira,
"Face recognition from facial surface metric",
Proc. European Conf. on Computer Vision (ECCV), pp. 225-237, 2004. Abstract: Recently, a 3D face recognition approach based on geometric invariant signatures, has been proposed. The key idea is a representation of the facial surface, invariant to isometric deformations, such as those resulting from facial expressions. One important stage in the construction of the geometric invariants involves in measuring geodesic distances on triangulated surfaces, which is carried out by the fast marching on triangulated domains algorithm. Proposed here is a method that uses only the metric tensor of the surface for geodesic distance computation. That is, the explicit integration of the surface in 3D from its gradients is not needed for the recognition task. It enables the use of simple and cost-efficient 3D acquisition techniques such as photometric stereo. Avoiding the explicit surface reconstruction stage saves computational time and reduces numerical errors. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Quasi maximum likelihood blind deconvolution of images acquired through scattering media",
Proc. Intl. Symposium on Biomedical Imaging (ISBI), pp. 352-355, 2004. Abstract: We address the problem of restoration of images obtained through a scattering medium. We present an efficient quasi-maximum likelihood blind deconvolution approach based on the fast relative Newton algorithm and optimal distributionshaping approach (sparsification), which allows to use simple and convenient sparsity prior for a wide class of images. Simulation results prove the efficiency of the proposed method. |
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A. M. Bronstein, M. M. Bronstein, R. Kimmel,
"Expression-invariant 3D face recognition",
Proc. Audio- and Video-based Biometric Person Authentication (AVBPA), Lecture Notes in Comp. Science No. 2688, Springer, pp. 62-69, 2003. Abstract: We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the face. The obtained geometric invariants allow mapping 2D facial texture images into special images that incorporate the 3D geometry of the face. These signature images are then decomposed into their principal components. The result is an efficient and accurate face recognition algorithm that is robust to facial expressions. We demonstrate the results of our method and compare it to existing 2D and 3D face recognition algorithms. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi,
"Separation of semireflective layers using Sparse ICA",
Proc. Intl. Conf. on Acoustics Speech and Signal Processing (ICASSP), Vol. 3, pp. 733-736, 2003. Abstract: We address the problem of Blind Source Separation (BSS) of superimposed images and, in particular, consider the recovery of a scene recorded through a semirefective medium (e.g. glass windshield) from its mixture with a virtual reflected image. We extend the Sparse ICA (SPICA) approach to BSS and apply it to the separation of the desired image from the superimposed images, without having any a priory knowledge about its structure and/or statistics. Advances in the SPICA approach are discussed. Simulations and experimental results illustrate the efficiency of the proposed approach, and of its specific implementation in a simple algorithm of a low computational cost. The approach and the algorithm are generic in that they can be adapted and applied to a wide range of BSS problems involving one-dimensional signals or images. |
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M. M. Bronstein, A. M. Bronstein, M. Zibulevsky,
"Iterative reconstruction in diffraction tomography using non-uniform fast Fourier transform",
Proc. Intl. Symposium on Biomedical Imaging (ISBI), pp. 633-636, 2002. Abstract: We show an iterative reconstruction framework for diffraction ultrasound tomography. The use of broadband illumination allows the number of projections to be reduced significantly compared to straight ray tomography. The proposed algorithm makes use of fast forward non-uniform Fourier transform (NUFFT) for iterative Fourier inversion. Incorporation of total variation regularization allows noise and Gibbs phenomena to be reduced whilst preserving the edges. |
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A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, Y. Y. Zeevi, "Optimal nonlinear estimation of photon coordinates in PET",
Proc. Intl. Symposium on Biomedical Imaging (ISBI), pp. 541-544, 2002. Abstract: We consider detection of high-energy photons in PET using thick scintillation crystals. Parallax effect and multiple Compton interactions in this type of crystals significantly reduce the accuracy of conventional detection methods. In order to estimate the scintillation point coordinates based on photomultiplier responses, we use asymptotically optimal nonlinear techniques, implemented by feed-forward neural networks, radial basis functions (RBF) networks, and neuro-fuzzy systems. Incorporation of information about angles of incidence of photons, significantly improves accuracy of estimation. The proposed estimators are fast enough to perform detection, using conventional computers. |
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