Ron Kimmel - Research
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RESEARCH | ISOMETRY & BIOMETRY

  • We apply metric geometry tools to various applications like computer aided diagnostics in medical imaging.
  • GIP Lab in a brief (2014 clips):
  • Deformable and non-rigid objects, both natural and artificial, surround us at all scales from nano to macro, and play an important role in many applications ranging from medical image analysis to robotics and gaming. Such applications require the ability to acquire, reconstruct, analyze, and synthesize non-rigid three-dimensional shapes. These procedures pose challenging problems both theoretically and practically due to the vast number of degrees of freedom involved in non-rigid deformations. While modelling and analysis of non-rigid shapes has greatly advanced in the past decade, existing solutions are largely based on parametric models restricting the objects of interest to a narrow class of similar shapes. Broadly speaking, reconstruction, analysis, and synthesis of arbitrary deformable shapes remain unsolved problems, a practical solution of which would be a major milestone in computer vision and related fields. My research aims at answering these fundamental questions by adopting tools from modern metric geometry, a field of theoretical mathematics which in the past few decades has undergone a series of revolutions that remained largely unnoticed and unused in applied sciences. We believe that metric geometry tools could systematically answer these questions, and, coupled with modern numerical optimization techniques and novel hardware architectures, pave the computational way to the next generation in deformable shape analysis. Our goal is to develop such numerical tools while demonstrating their efficiency on several challenging real-life applications such as surgery prediction and planning, biometry, and computer-aided diagnosis. So far, while exploring metric and differential geometry we developed computational tools like
  • Fast computation of distances on surfaces. See SIGGRAPH'08 trailer
  • Integral geometric measures, and variational techniques for processing and analysis of imagees.
  • The Beltrami framework and the geodesic active contours models.
  • Modeling non-rigid surfaces as near isometries.
  • Treating images as geometric structures, and geometric structures as images.
  • Shape reconstruction from various cues and priors.
  • Implicit formulations of propagating interfaces, accurate segmentation, and optical flow computation.

  • Some of these models and tools were used in our 3DFACE project that deals with face recognition. Three-dimensional (3D) face recognition is the process of using the geometric structure of the face for accurate identification of the subject. While traditional two-dimensional (2D) face recognition methods are sensitive to variations in illumination, pose, makeup and cosmetics, 3D methods are more robust to these factors. Yet, facial expressions introduce a major challenge to 3D face recognition, as the geometry of the face changes significantly.

    Together with my students (at the time) Alex and Michael Bronstein, we developed an expression-invariant 3D face recognition approach based on the isometric model of facial expressions. According to this model, a person's identity is associated with the intrinsic geometry of his or her facial surface, while the facial expressions are associated with the extrinsic geometry. Our first attempt was to represent the intrinsic geometry of the surface by isometrically embedding it into a low-dimensional Euclidean space. The embedding is performed using Multidimensional Scaling (MDS). The result is an expression-invariant representation of the face called canonical form. Canonical forms, enabled accurate face recognition.

    3D face recognition system
    Prototype of our 3D face recognition system developed at the Technion.

    (Photo: November 2004)
    Next, we generalized the canonical forms approach by embedding into non-Euclidean spaces. Particularly, two- and three-dimensional spaces with spherical geometry were found to be appealing for the representation of faces, as the resulting metric distortion is usually smaller compared to a Euclidean space.

    Later on, we introduced the concept of Generalized Multidimensional Scaling (GMDS), which allows embedding into manifolds with an arbitrary geometric structure. Instead of embedding the facial surfaces into a common embedding space, we embed one surface into the other and use the metric distortion as a measure of their dissimilarity. The GMDS approach is more accurate compared to canonical forms and allows face recognition even when parts of the surfaces are missing.


    COVER STORIES:
    Reuters article on CNN news: Twins crack face recognition puzzle
    R. Kimmel and G. Sapiro, The mathematics of face recognition, SIAM News, 36(3), 2003
    D. Voth, Face recognition technology, IEEE Magazine on Intelligent Systems, 18(3):4-7, 2003
    G. Sapiro, Abel Prize lecture: Revolutionary work in geometry and shape analysis, SIAM News, 42(6), 2009
    R. Kimmel, Metric geometry in action, SIAM News, 44(8), 2011


    Behind the scene:
  • 3DFace recognition started as an undergraduate project in the course Numerical Geometry of Images
  • American Technion Society 2003 fund raising was based on the 3DFace project.
  • Asi Elad presented the first mathematical engine of our system during CVPR'2001 (Hawaii).
  • More than 400 companies showed (written) interest in the project.
  • About 100 expressed willingness to invest money.
  • About 30 companies were interested to integrate a prototype into their products.
  • About 15 expressed interest to jointly develop a product.
  • The startup Invision licensed the technology in 2009. It was subsequently acquired by Intel in 2011.
  • The first journalist to professionally cover the project was Haim Rivlin from Israeli Channel 2.
  • As identical twins, Alex and Michael have the same DNA, and almost identical fingerprints.
  • Both were invited to the International Achievement Summit in Washington DC. where Michael met Clinton.
  • Our first 3D scanner was built out of LEGO parts and a laser pointer by Gil Zigelman and Eyal Gordon.
  • The second generation scanner was built in two days before a Science Fair in Jerusalem.
  • At the Science Fair, Matan Vilnai, minister of science at the time, was scanned.
  • Our 3D video scanner features auto-calibration, rapid scan at 50 msec/frame and 0.5mm depth resolution.
  • The project received the Hershel Rich Innovation prize.

    Sampling the world press:
    3D Face Scan Distinguishes Twins
    Panorama:Firma facciale contro il terrorismo
    Face recognition
    Gemelos israelíes revolucionan identificación de rostros
    Gêmeos criam novo sistema de identificação facial
    BIOMETRÍA Dos gemelos israelíes revolucionan la técnica de identificación de rostros
    Revolucionan la biometría por unas buenas notas
    Desarrollan tecnolog?a en identificaci?n de rostros
    Oblicejový podpis je vytesán z nul a jednicek
    Gemelli identici creano tecnologia di video-riconoscimento volti


    On TV:
  • W-NBC (asf 3.6M) .
  • Russian TV (asf 2.8M) .
  • Israel Channel 2 (avi 1.6M) .

    Our research has been supported by:
    Advanced ERC (EU), General Motors, BSF, ISF, Intel, and US-ONR
  • © Ron Kimmel   (c) Ron Kimmel   Technion - Israel Institute of Technology