Publications

Topics:
  1. A. M. Bronstein, M. M. Bronstein, R. Kimmel, Robust expression-invariant face recognition from partially missing data, Proc. European Conf. on Computer Vision (ECCV), 2006 details

    Robust expression-invariant face recognition from partially missing data

    A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Proc. European Conf. on Computer Vision (ECCV), 2006

    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.

    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), 2006 details

    Matching two-dimensional articulated shapes using generalized multidimensional scaling

    A. M. Bronstein, M. M. Bronstein, A. M. Bruckstein, R. Kimmel
    Proc. Conf. on Articulated Motion and Deformable Objects (AMDO), 2006

    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.

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, Face2Face: an isometric model for facial animation, Proc. Conf. on Articulated Motion and Deformable Objects (AMDO), 2006 details

    Face2Face: an isometric model for facial animation

    A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Proc. Conf. on Articulated Motion and Deformable Objects (AMDO), 2006

    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.

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, Efficient computation of isometry-invariant distances between surfaces, SIAM J. Scientific Computing, Vol. 28(5), 2006
    A. M. Bronstein, M. M. Bronstein, M. Zibulevsky, On separation of semitransparent dynamic images from static background, Proc. Int'l Conf. on Independent Component Analysis and Blind Signal Separation, 2006 details

    On separation of semitransparent dynamic images from static background

    A. M. Bronstein, M. M. Bronstein, M. Zibulevsky
    Proc. Int'l Conf. on Independent Component Analysis and Blind Signal Separation, 2006

    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.

    M. M. Bronstein, A. M. Bronstein, R. Kimmel, I. Yavneh, Multigrid multidimensional scaling, Numerical Linear Algebra with Applications (NLAA), Vol. 13(2), 2006 (Special issue on multigrid methods) details

    Multigrid multidimensional scaling

    M. M. Bronstein, A. M. Bronstein, R. Kimmel, I. Yavneh
    Numerical Linear Algebra with Applications (NLAA), Vol. 13(2), 2006 (Special issue on multigrid methods)

    Multidimensional scaling (MDS) is a generic name for a family of algorithms that construct a configuration of points in a target metric space from information about inter-point distances measured in some other metric space. Large-scale MDS problems often occur in data analysis, representation, and visualization. Solving such problems efficiently is of key importance in many applications. In this paper, we present a multigrid framework for MDS problems. We demonstrate the performance of our algorithm on dimensionality reduction and isometric embedding problems, two classical problems requiring efficient large-scale MDS. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms.

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching, Proc. US National Academy of Sciences (PNAS), Vol. 103(5), 2006 details

    Generalized multidimensional scaling: a framework for isometry-invariant partial surface matching

    A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Proc. US National Academy of Sciences (PNAS), Vol. 103(5), 2006

    An efficient algorithm for isometry-invariant matching of surfaces is presented. The key idea is computing the minimum-distortion mapping between two surfaces. For this purpose, we introduce the generalized multidimensional scaling, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another. The generalized multidimensional scaling algorithm allows for both full and partial surface matching. As an example, it is applied to the problem of expression- invariant three-dimensional face recognition.

    A. M. Bronstein, M. M. Bronstein, R. Kimmel, Expression invariant face recognition: faces as isometric surfaces, Chapter in Face Processing: Advanced Modeling and Methods (Rama Chellappa, Wenyi Zhao Eds.), Academic Press, 2006. details

    Expression invariant face recognition: faces as isometric surfaces

    A. M. Bronstein, M. M. Bronstein, R. Kimmel
    Chapter in Face Processing: Advanced Modeling and Methods (Rama Chellappa, Wenyi Zhao Eds.), Academic Press, 2006.

    One of the hardest problems in face recognition is dealing with facial expressions. Finding an expression-invariant representation of the face could be a remedy for this problem. We suggest treating faces as deformable surfaces in the context of Riemannian geometry, and propose to approximate facial expressions as isometries of the facial surface. This way, we can define geometric invariants of a given face under different expressions. One such invariant is constructed by isometrically embedding the facial surface structure into a low-dimensional flat space. Based on this approach, we built an accurate three-dimensional face recognition system that is able to distinguish between identical twins under various facial expressions. In this chapter we show how under the near-isometric model assumption, the difficult problem of face recognition in the presence of facial expressions can be solved in a relatively simple way.