Publications

Topics:
  1. R. Kimmel, C. Zhang, A. M. Bronstein, M. M. Bronstein, Are MSER features really interesting?, IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), Vol. 33(11), 2011 details

    Are MSER features really interesting?

    R. Kimmel, C. Zhang, A. M. Bronstein, M. M. Bronstein
    IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), Vol. 33(11), 2011

    Detection and description of affine-invariant features is a cornerstone component in numerous computer vision applications. In this note, we analyze the notion of maximally stable extremal regions (MSER) through the prism of the curvature scale space, and conclude that in its original definition, MSER prefers regular (round) regions. Arguing that interesting features in natural images usually have irregular shapes, we propose alternative definitions of MSER which are free of this bias, yet maintain their invariance properties.

    A. M. Bronstein, Spectral descriptors for deformable shapes, arXiv:1110.5015 details

    Spectral descriptors for deformable shapes

    A. M. Bronstein
    arXiv:1110.5015

    Informative and discriminative feature descriptors play a fundamental role in deformable shape analysis. For example, they have been successfully employed in correspondence, registration, and retrieval tasks. In the recent years, significant attention has been devoted to descriptors obtained from the spectral decomposition of the Laplace-Beltrami operator associated with the shape. Notable examples in this family are the heat kernel signature (HKS) and the wave kernel signature (WKS). Laplacian-based descriptors achieve state-of-the-art performance in numerous shape analysis tasks; they are computationally efficient, isometry-invariant by construction, and can gracefully cope with a variety of transformations. In this paper, we formulate a generic family of parametric spectral descriptors. We argue that in order to be optimal for a specific task, the descriptor should take into account the statistics of the corpus of shapes to which it is applied (the “signal”) and those of the class of transformations to which it is made insensitive (the “noise”). While such statistics are hard to model axiomatically, they can be learned from examples. Following the spirit of the Wiener filter in signal processing, we show a learning scheme for the construction of optimal spectral descriptors and relate it to Mahalanobis metric learning. The superiority of the proposed approach is demonstrated on the SHREC’10 benchmark.

    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 details

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

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen
    Proc. Computer Vision and Pattern Recognition (CVPR), 2011

    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 demonstrate its power in generalizing and enriching the existing set of tools for shape analysis.

    M. M. Bronstein, A. M. Bronstein, Shape recognition with spectral distances, IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), Vol. 33(5), 2011 details

    Shape recognition with spectral distances

    M. M. Bronstein, A. M. Bronstein
    IEEE Trans. Pattern Analysis and Machine Intelligence (PAMI), Vol. 33(5), 2011

    Recent works have shown the use of diffusion geometry for various pattern recognition applications, including non-rigid shape analysis. In this paper, we introduce spectral shape distance as a general framework for distribution-based shape similarity and show that two recent methods for shape similarity due to Rustamov and Mahmoudi & Sapiro are particular cases thereof.

    J. Pokrass, A. M. Bronstein, M. M. Bronstein, A correspondence-less approach to matching of deformable shapes, Proc. Scale Space and Variational Methods (SSVM), 2011 details

    A correspondence-less approach to matching of deformable shapes

    J. Pokrass, A. M. Bronstein, M. M. Bronstein
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    A. Kovnatsky, M. M. Bronstein, A. M. Bronstein, R. Kimmel, Photometric heat kernel signatures, Proc. Scale Space and Variational Methods (SSVM), 2011 details

    Photometric heat kernel signatures

    A. Kovnatsky, M. M. Bronstein, A. M. Bronstein, R. Kimmel
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    J. Aflalo, A. M. Bronstein, M. M. Bronstein, R. Kimmel, Deformable shape retrieval by learning diffusion kernels, Proc. Scale Space and Variational Methods (SSVM), 2011 details

    Deformable shape retrieval by learning diffusion kernels

    J. Aflalo, A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    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. Scale Space and Variational Methods (SSVM), 2011 details

    Group-valued regularization framework for motion segmentation of dynamic non-rigid shapes

    G. Rosman, M. M. Bronstein, A. M. Bronstein, A. Wolf, R. Kimmel
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    C. Wang, M. M. Bronstein, A. M. Bronstein, N. Paragios, Discrete minimum distortion correspondence problems for non-rigid shape matching, Proc. Scale Space and Variational Methods (SSVM), 2011 details

    Discrete minimum distortion correspondence problems for non-rigid shape matching

    C. Wang, M. M. Bronstein, A. M. Bronstein, N. Paragios
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    A. Hooda, M. M. Bronstein, A. M. Bronstein, R. Horaud, Shape palindromes: analysis of intrinsic symmetries in 2D articulated shapes, Proc. Scale Space and Variational Methods (SSVM), 2011 details

    Shape palindromes: analysis of intrinsic symmetries in 2D articulated shapes

    A. Hooda, M. M. Bronstein, A. M. Bronstein, R. Horaud
    Proc. Scale Space and Variational Methods (SSVM), 2011

    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.

    F. Michel, M. M. Bronstein, A. M. Bronstein, N. Paragios, Boosted metric learning for 3D multi-modal deformable registration, Proc. Int'l Symposium on Biomedical Imaging (ISBI), 2011 details

    Boosted metric learning for 3D multi-modal deformable registration

    F. Michel, M. M. Bronstein, A. M. Bronstein, N. Paragios
    Proc. Int'l Symposium on Biomedical Imaging (ISBI), 2011

    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.

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen, Affine-invariant geodesic geometry of deformable 3D shapes, Computers and Graphics (CAG), Vol. 35(3), 2011 details

    Affine-invariant geodesic geometry of deformable 3D shapes

    D. Raviv, A. M. Bronstein, M. M. Bronstein, R. Kimmel, N. Sochen
    Computers and Graphics (CAG), Vol. 35(3), 2011

    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. 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.

    R. Litman, A. M. Bronstein, A. M. Bronstein, Diffusion-geometric maximally stable component detection in deformable shapes, Computers and Graphics (CAG), Vol. 35(3), 2011 details

    Diffusion-geometric maximally stable component detection in deformable shapes

    R. Litman, A. M. Bronstein, A. M. Bronstein
    Computers and Graphics (CAG), Vol. 35(3), 2011

    Maximally stable component detection is a very popular method for feature analysis in images, mainly due to its low computation cost and high repeatability. With the recent advance of feature-based methods in geometric shape analysis, there is significant interest in finding analogous approaches in the 3D world. In this paper, we formulate a diffusion-geometric framework for stable component detection in non-rigid 3D shapes, which can be used for geometric feature detection and description. A quantitative evaluation of our method on the SHREC’10 feature detection benchmark shows its potential as a source of high-quality features.

    A. M. Bronstein, M. M. Bronstein, M. Ovsjanikov, L. J. Guibas, Shape Google: geometric words and expressions for invariant shape retrieval, ACM Trans. Graphics (TOG), Vol. 30(1), 2011 details

    Shape Google: geometric words and expressions for invariant shape retrieval

    A. M. Bronstein, M. M. Bronstein, M. Ovsjanikov, L. J. Guibas
    ACM Trans. Graphics (TOG), Vol. 30(1), 2011

    The computer vision and pattern recognition communities have recently witnessed a surge of feature-based methods in object recognition and image retrieval applications. These methods allow representing images as collections of “visual words” and treat them using text search approaches following the “bag of features” paradigm. In this paper, we explore analogous approaches in the 3D world applied to the problem of non-rigid shape retrieval in large databases. Using multiscale diffusion heat kernels as “geometric words”, we construct compact and informative shape descriptors by means of the “bag of features” approach. We also show that considering pairs of geometric words (“geometric expressions”) allows creating spatially-sensitive bags of features with better discriminativity. Finally, adopting metric learning approaches, we show that shapes can be efficiently represented as binary codes. Our approach achieves state-of-the-art results on the SHREC 2010 large-scale shape retrieval benchmark.

    A. M. Bronstein, M. M. Bronstein, Metric approaches to invariant shape similarity, Chapter in Handbook of Mathematical Methods in Imaging (O. Scherzer Ed.), Springer, 2011 details

    Metric approaches to invariant shape similarity

    A. M. Bronstein, M. M. Bronstein
    Chapter in Handbook of Mathematical Methods in Imaging (O. Scherzer Ed.), Springer, 2011

    Non-rigid 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 non- rigid 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.