Publications

Topics:
  1. D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen,, Affine-invariant geodesic geometry of deformable 3D shapes, arXiv:1012.5936 details

    Affine-invariant geodesic geometry of deformable 3D shapes

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen,
    arXiv:1012.5936

    Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R3 in order to extend the set of existing non-rigid shape analysis tools. In fact, we show that by re-defining the surface metric as its equi-affine version, the surface with its modified metric tensor can be treated as a canonical Euclidean object on which most classical Euclidean processing and analysis tools can be applied. The new definition of a metric is used to extend the fast marching method technique for computing geodesic distances on surfaces, where now, the distances are defined with respect to an affine invariant arclength. Applications of the proposed framework demonstrate its invariance, efficiency, and accuracy in shape analysis.

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen, Affine-invariant diffusion geometry for the analysis of deformable 3D shapes, arXiv:1012.5933 details

    Affine-invariant diffusion geometry for the analysis of deformable 3D shapes

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen
    arXiv:1012.5933

    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 local and global geometric structures are extracted. Applications of the proposed framework demon- strate its power in generalizing and enriching the existing set of tools for shape analysis.

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, Full and partial symmetries of non-rigid shapes, Int'l Journal of Computer Vision (IJCV), Vol. 89(1), 2010 details

    Full and partial symmetries of non-rigid shapes

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Int'l Journal of Computer Vision (IJCV), Vol. 89(1), 2010

    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 present a generalization of symmetries for non-rigid shapes and a numerical framework for their analysis, addressing the problems of full and partial exact and approximate symmetry detection and classification.

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, M. Mahmoudi, G. Sapiro, A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching, Int'l Journal of Computer Vision (IJCV), Vol. 89(2), 2010 details

    A Gromov-Hausdorff framework with diffusion geometry for topologically-robust non-rigid shape matching

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, M. Mahmoudi, G. Sapiro
    Int'l Journal of Computer Vision (IJCV), Vol. 89(2), 2010

    In this paper, the problem of non-rigid shape recognition is viewed from the perspective of metric geometry, and the applicability of diffusion distances within the Gromov-Hausdorff framework is explored. While the commonly used geodesic distance exploits the shortest path between points on the surface, the diffusion distance averages all paths connecting between the points. The diffusion distance provides an intrinsic distance measure which is robust, in particular to topological changes. Such changes may be a result of natural non-rigid deformations, as well as acquisition noise, in the form of holes or missing data, and representation noise due to inaccurate mesh construction. The presentation of the proposed framework is complemented with numerous examples demonstrating that in addition to the relatively low complexity involved in the computation of the diffusion distances between surface points, its recognition and matching performances favorably compare to the classical geodesic distances in the presence of topological changes between the non-rigid shapes.

    N. Mitra, A. M. Bronstein, M. M. Bronstein, Intrinsic regularity detection in 3D geometry, Proc. European Conf. Computer Vision (ECCV), 2010 details

    Intrinsic regularity detection in 3D geometry

    N. Mitra, A. M. Bronstein, M. M. Bronstein
    Proc. European Conf. Computer Vision (ECCV), 2010

    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.

    A. M. Bronstein, M. M. Bronstein, Spatially-sensitive affine-invariant image descriptors, Proc. European Conf. Computer Vision (ECCV), 2010 details

    Spatially-sensitive affine-invariant image descriptors

    A. M. Bronstein, M. M. Bronstein
    Proc. European Conf. Computer Vision (ECCV), 2010

    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.

    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 details

    Data fusion through cross-modality metric learning using similarity-sensitive hashing

    M. M. Bronstein, A. M. Bronstein, F. Michel, N. Paragios
    Proc. Computer Vision and Pattern Recognition (CVPR), 2010

    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.

    D. Raviv, M. M. Bronstein, A. M. Bronstein, R. Kimmel, Volumetric heat kernel signatures, Proc. Int'l Workshop on 3D Object Retrieval (3DOR), ACM Multimedia, 2010 details

    Volumetric heat kernel signatures

    D. Raviv, M. M. Bronstein, A. M. Bronstein, R. Kimmel
    Proc. Int'l Workshop on 3D Object Retrieval (3DOR), ACM Multimedia, 2010

    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.

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, G. Sapiro, Diffusion symmetries of non-rigid shapes, Proc. Int'l Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), 2010 details

    Diffusion symmetries of non-rigid shapes

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, G. Sapiro
    Proc. Int'l Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), 2010

    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

    G. Rosman, M. M. Bronstein, A. M. Bronstein, R. Kimmel, Nonlinear dimensionality reduction by topologically constrained isometric embedding, Intl. Journal of Computer Vision (IJCV), Vol. 89(1), 2010 details

    Nonlinear dimensionality reduction by topologically constrained isometric embedding

    G. Rosman, M. M. Bronstein, A. M. Bronstein, R. Kimmel
    Intl. Journal of Computer Vision (IJCV), Vol. 89(1), 2010

    Many manifold learning procedures try to embed a given feature data into a flat space of low dimensionality while preserving as much as possible the metric in the natural feature space. The embedding process usually relies on distances between neighboring features, mainly since distances between features that are far apart from each other often provide an unreliable estimation of the true distance on the feature manifold due to its non-convexity. Distortions resulting from using long geodesics indiscriminately lead to a known limitation of the Isomap algorithm when used to map nonconvex manifolds. Presented is a framework for nonlinear dimensionality reduction that uses both local and global distances in order to learn the intrinsic geometry of flat manifolds with boundaries. The resulting algorithm filters out potentially problematic distances between distant feature points based on the properties of the geodesics connecting those points and their relative distance to the boundary of the feature manifold, thus avoiding an inherent limitation of the Isomap algorithm. Since the proposed algorithm matches non-local structures, it is robust to strong noise. We show experimental results demonstrating the advantages of the proposed approach over conventional dimensionality reduction techniques, both global and local in nature.

    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 details

    SHREC 2010: robust large-scale shape retrieval benchmark

    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
    Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010

    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.

    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 details

    SHREC 2010: robust feature detection and description benchmark

    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
    Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010

    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.

    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 details

    SHREC 2010: robust correspondence benchmark

    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
    Proc. EUROGRAPHICS Workshop on 3D Object Retrieval (3DOR), 2010

    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.