192 results found
Bronstein AM, Bronstein MM, 2015, Manifold intrinsic similarity, Handbook of Mathematical Methods in Imaging: Volume 1, Second Edition, Pages: 1859-1908, ISBN: 9781493907892
© Springer Science+Business Media New York 2011, 2015. Nonrigid shapes are ubiquitous in nature and are encountered at all levels of life, from macro to nano. The need to model such shapes and understand their behavior arises in many applications in imaging sciences, pattern recognition, computer vision, and computer graphics. Of particular importance is understanding which properties of the shape are attributed to deformations and which are invariant, i.e., remain unchanged. This chapter presents an approach to nonrigid shapes from the point of view of metric geometry. Modeling shapes as metric spaces, one can pose the problem of shape similarity as the similarity of metric spaces and harness tools from theoretical metric geometry for the computation of such a similarity.
Masci J, Boscaini D, Bronstein M, et al., 2015, Geodesic convolutional neural networks on riemannian manifolds, Pages: 37-45
Bronstein AM, Bronstein MM, Ovsjanikov M, 2014, Feature-based methods in 3D shape analysis, 3D Imaging, Analysis and Applications, Pages: 185-219, ISBN: 9781447140627
© 2012 Springer-Verlag London. All rights are reserved. The computer vision and pattern recognition communities have recently witnessed a surge in feature-based methods for numerous applications including object recognition and image retrieval. Similar concepts and analogous approaches are penetrating the world of 3D shape analysis in a variety of areas including non-rigid shape retrieval and matching. In this chapter, we present both mature concepts and the state-of-the-art of feature-based approaches in 3D shape analysis. In particular, approaches to the detection of interest points and the generation of local shape descriptors are discussed. A wide range of methods is covered including those based on curvature, those based on difference-of-Gaussian scale space, and those that employ recent advances in heat kernel methods.
Kovnatsky A, Eynard D, Bronstein MM, 2014, Gamut mapping with image Laplacian commutators, Pages: 635-639
© 2014 IEEE. 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 commu-tativity 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.
Pickup D, Sun X, Rosin PL, et al., 2014, SHREC'14 track: Shape retrieval of non-rigid 3D human models, ISSN: 1997-0463
© The Eurographics Association 2014. We have created a new benchmarking dataset for testing non-rigid 3D shape retrieval algorithms, 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, and so the ability to distinguish between body shapes is an important shape retrieval problem. In this track nine groups have submitted the results of a total of 22 different methods which have been tested on our new dataset.
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.
Eynard D, Kovnatsky A, Bronstein MM, 2014, Laplacian colormaps: A framework for structure-preserving color transformations, Computer Graphics Forum, Vol: 33, Pages: 215-224, ISSN: 0167-7055
Mappings between color spaces are ubiquitous in image processing problems such as gamut mapping, decolorization, and image optimization for color-blind people. Simple color transformations often result in information loss and ambiguities, and one wishes to find an image-specific transformation that would preserve as much as possible the structure of the original image in the target color space. In this paper, we propose Laplacian colormaps, a generic framework for structure-preserving color transformations between images. We use the image Laplacian to capture the structural information, and show that if the color transformation between two images preserves the structure, the respective Laplacians have similar eigenvectors, or in other words, are approximately jointly diagonalizable. Employing the relation between joint diagonalizability and commutativity of matrices, we use Laplacians commutativity as a criterion of color mapping quality and minimize it w.r.t. the parameters of a color transformation to achieve optimal structure preservation. We show numerous applications of our approach, including color-to-gray conversion, gamut mapping, multispectral image fusion, and image optimization for color deficient viewers. © 2014 The Author(s) Computer Graphics Forum © 2014 The Eurographics Association and John Wiley & Sons Ltd. Published by John Wiley & Sons Ltd.
Masci J, Bronstein AM, Bronstein MM, et al., 2014, Sparse similarity-preserving hashing
© 2014 International Conference on Learning Representations, ICLR. All rights reserved. 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 multimodal data shows the benefits of the proposed method.
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.
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.
© Springer Science+Business Media New York 2013. Traditional models of bendable surfaces are based on the exact or approximate invariance to deformations that do not tear or stretch the shape, leaving intact an intrinsic geometry associated with it. These geometries are typically defined using either the shortest path length (geodesic distance), or properties of heat diffusion (diffusion distance) on the surface. Both measures are implicitly derived from the metric induced by the ambient Euclidean space. In this paper, we depart from this restrictive assumption by observing that a different choice of the metric results in a richer set of geometric invariants. We apply equi-affine geometry for analyzing arbitrary shapes with positive Gaussian curvature. The potential of the proposed framework is explored in a range of applications such as shape matching and retrieval, symmetry detection, and computation of Voroni tes- sellation. We show that in some shape analysis tasks, equiaffine- invariant intrinsic geometries often outperform their Euclidean-based counterparts.We further explore the potential of this metric in facial anthropometry of newborns. We show that intrinsic properties of this homogeneous group are better captured using the equi-affine metric
Boscaini D, Girdziušas R, Bronstein MM, 2014, Coulomb shapes: Using electrostatic forces for deformation-invariant shape representation, ISSN: 1997-0463
© The Eurographics Association 2014. 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.
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.
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.
The use of Laplacian eigenbases has been shown to be fruitful in many computer graphics applications. Today, state-of-the-art approaches to shape analysis, synthesis, and correspondence rely on these natural harmonic bases that allow using classical tools from harmonic analysis on manifolds. However, many applications involving multiple shapes are obstacled by the fact that Laplacian eigenbases computed independently on different shapes are often incompatible with each other. In this paper, we propose the construction of common approximate eigenbases for multiple shapes using approximate joint diagonalization algorithms, taking as input a set of corresponding functions (e.g. indicator functions of stable regions) on the two shapes. We illustrate the benefits of the proposed approach on tasks from shape editing, pose transfer, correspondence, and similarity. © 2013 The Eurographics Association and Blackwell Publishing Ltd.
We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so the correspondence between the regions is not know, nor we know how many regions correspond in the two shapes. We show that even with such scarce information, it is possible to establish very accurate correspondence between the shapes by using methods from the field of sparse modeling, being this, the first non-trivial use of sparse models in shape correspondence. We formulate the problem of permuted sparse coding, in which we solve simultaneously for an unknown permutation ordering the regions on two shapes and for an unknown correspondence in functional representation. We also propose a robust variant capable of handling incomplete matches. Numerically, the problem is solved efficiently by alternating the solution of a linear assignment and a sparse coding problem. The proposed methods are evaluated qualitatively and quantitatively on standard benchmarks containing both synthetic and scanned objects. © 2013 The Eurographics Association and Blackwell Publishing Ltd.
Litman R, Bronstein AM, Bronstein MM, 2013, Stable semi-local features for non-rigid shapes, Mathematics and Visualization, Pages: 161-189
© Springer-Verlag Berlin Heidelberg 2013. 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
© Springer-Verlag Berlin Heidelberg 2013. 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.
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.
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.
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.
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.
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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